|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(arctan(c(x))); > end; exact_soln_y := proc(x) return arctan(c(x)) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 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0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre div CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_1D0[1] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre div CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := neg(ats(2,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp1[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre div CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := neg(ats(3,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre div CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := neg(ats(4,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre div CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := neg(ats(5,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit div CONST FULL $eq_no = 1 i = 1 > array_tmp3[kkk] := neg(ats(kkk,array_tmp2,array_tmp3,2)) / array_tmp2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_x[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := array_const_1D0[1]/array_tmp2[1]; array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := neg(ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_x[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := neg(ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := neg(ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := neg(ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := neg(ats(kkk, array_tmp2, array_tmp3, 2))/array_tmp2[1]; array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 20; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=16; > max_terms:=20; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(20),[]); > array_norms:= Array(0..(20),[]); > array_fact_1:= Array(0..(20),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(20),[]); > array_x:= Array(0..(20),[]); > array_tmp0:= Array(0..(20),[]); > array_tmp1:= Array(0..(20),[]); > array_tmp2:= Array(0..(20),[]); > array_tmp3:= Array(0..(20),[]); > array_tmp4:= Array(0..(20),[]); > array_m1:= Array(0..(20),[]); > array_y_higher := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(20) ,(0..20+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 20) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=20) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1D0); > array_const_1D0[1] := c(1.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 20; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing2postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=16;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -2.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_h := c(0.001);"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 2;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(arctan(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -2.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_h := c(0.001); > glob_min_h := c(0.001); > glob_type_given_pole := 2; > array_given_rad_poles[1,1] := c(0.0); > array_given_rad_poles[1,2] := c(1.0); > array_given_ord_poles[1,1] := c(1.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:22:53-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"sing2 diffeq.mxt") > ; > logitem_str(html_log_file,"sing2 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_1D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 20; Digits := 16; max_terms := 20; glob_html_log := true; array_y_init := Array(0 .. 20, []); array_norms := Array(0 .. 20, []); array_fact_1 := Array(0 .. 20, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 20, []); array_x := Array(0 .. 20, []); array_tmp0 := Array(0 .. 20, []); array_tmp1 := Array(0 .. 20, []); array_tmp2 := Array(0 .. 20, []); array_tmp3 := Array(0 .. 20, []); array_tmp4 := Array(0 .. 20, []); array_m1 := Array(0 .. 20, []); array_y_higher := Array(0 .. 2, 0 .. 21, []); array_y_higher_work := Array(0 .. 2, 0 .. 21, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []); array_y_set_initial := Array(0 .. 2, 0 .. 21, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 20, 0 .. 21, []); term := 1; while term <= 20 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 20 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 20 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 20 do term := 1; while term <= 20 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1D0); array_const_1D0[1] := c(1.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing2postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=16;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -2.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_h := c(0.001);"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 2;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(arctan(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, 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omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := -2.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 2; array_given_rad_poles[1, 1] := c(0.); array_given_rad_poles[1, 2] := c(1.0); array_given_ord_poles[1, 1] := c(1.0); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = 1.0 / ( x * \ x + 1.0 ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:22:53-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 1.\ 0 / ( x * x + 1.0 ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "sing2 diffeq.mxt"); logitem_str(html_log_file, "sing2 maple results") ; logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sing2postcpx.cpx################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=16; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 2; array_given_rad_poles[1,1] := c(0.0); array_given_rad_poles[1,2] := c(1.0); array_given_ord_poles[1,1] := c(1.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(arctan(c(x))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 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0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -2.1 0.1 h = 0.0001 0.005 y[1] (numeric) = -1.12709378614 0.0184585655028 y[1] (closed_form) = -1.12709378614 0.0184585655028 absolute error = 0 relative error = 0 % Correct digits = 14 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0999 0.105 h = 0.0001 0.003 y[1] (numeric) = -1.12714839348 0.0193802636328 y[1] (closed_form) = -1.1271487504 0.0193802311016 absolute error = 3.584e-07 relative error = 3.179e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.283 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0998 0.108 h = 0.001 0.001 y[1] (numeric) = -1.12717615814 0.0199337215076 y[1] (closed_form) = -1.1271760863 0.0199337244718 absolute error = 7.190e-08 relative error = 6.378e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0988 0.109 h = 0.001 0.003 y[1] (numeric) = -1.12700787787 0.0201333491884 y[1] (closed_form) = -1.1270075903 0.0201332982571 absolute error = 2.920e-07 relative error = 2.591e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0978 0.112 h = 0.0001 0.004 y[1] (numeric) = -1.12687081187 0.0207015291265 y[1] (closed_form) = -1.12687096902 0.0207015696951 absolute error = 1.623e-07 relative error = 1.440e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0977 0.116 h = 0.003 0.006 y[1] (numeric) = -1.12691753159 0.0214400948446 y[1] (closed_form) = -1.12691794945 0.0214398497944 absolute error = 4.844e-07 relative error = 4.298e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.276 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0947 0.122 h = 0.0001 0.005 y[1] (numeric) = -1.12646674544 0.0225954813746 y[1] (closed_form) = -1.12646761424 0.022596874147 absolute error = 1.642e-06 relative error = 0.0001457 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.271 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0946 0.127 h = 0.0001 0.003 y[1] (numeric) = -1.12653830402 0.0235203186318 y[1] (closed_form) = -1.12653869412 0.0235207141924 absolute error = 5.556e-07 relative error = 4.930e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0945 0.13 h = 0.001 0.001 y[1] (numeric) = -1.12657573052 0.0240751582866 y[1] (closed_form) = -1.12657569065 0.0240755997942 absolute error = 4.433e-07 relative error = 3.934e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.268 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0935 0.131 h = 0.001 0.003 y[1] (numeric) = -1.12641033766 0.024278365152 y[1] (closed_form) = -1.12641007973 0.024278757679 absolute error = 4.697e-07 relative error = 4.169e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.267 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0925 0.134 h = 0.0001 0.004 y[1] (numeric) = -1.12628264047 0.0248508223397 y[1] (closed_form) = -1.1262828316 0.0248512961364 absolute error = 5.109e-07 relative error = 4.535e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0924 0.138 h = 0.003 0.006 y[1] (numeric) = -1.12634229876 0.0255910425433 y[1] (closed_form) = -1.12634274498 0.0255912230995 absolute error = 4.814e-07 relative error = 4.273e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.263 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0894 0.144 h = 0.0001 0.005 y[1] (numeric) = -1.1259100197 0.0267580577271 y[1] (closed_form) = -1.12591095834 0.0267598730626 absolute error = 2.044e-06 relative error = 0.0001815 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.258 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0893 0.149 h = 0.0001 0.003 y[1] (numeric) = -1.1259978494 0.027684686269 y[1] (closed_form) = -1.1259982831 0.0276855111889 absolute error = 9.320e-07 relative error = 8.274e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0892 0.152 h = 0.001 0.001 y[1] (numeric) = -1.12604501687 0.0282406823268 y[1] (closed_form) = -1.12604501969 0.0282415637444 absolute error = 8.814e-07 relative error = 7.825e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.255 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0882 0.153 h = 0.001 0.003 y[1] (numeric) = -1.12588261106 0.0284474160367 y[1] (closed_form) = -1.12588239362 0.0284482534862 absolute error = 8.652e-07 relative error = 7.682e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.253 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=35.4MB, alloc=40.3MB, time=0.46 x[1] = -2.0872 0.156 h = 0.0001 0.004 y[1] (numeric) = -1.1257644299 0.0290239457638 y[1] (closed_form) = -1.12576466557 0.0290248540646 absolute error = 9.384e-07 relative error = 8.333e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0871 0.16 h = 0.003 0.006 y[1] (numeric) = -1.12583712768 0.0297655173794 y[1] (closed_form) = -1.12583761257 0.029766124934 absolute error = 7.773e-07 relative error = 6.902e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0841 0.166 h = 0.0001 0.005 y[1] (numeric) = -1.12542372222 0.0309437711302 y[1] (closed_form) = -1.12542474117 0.0309460092006 absolute error = 2.459e-06 relative error = 0.0002184 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.245 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.084 0.171 h = 0.0001 0.003 y[1] (numeric) = -1.12552794216 0.0318718077378 y[1] (closed_form) = -1.12552842999 0.0318730629906 absolute error = 1.347e-06 relative error = 0.0001196 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.243 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0839 0.174 h = 0.001 0.001 y[1] (numeric) = -1.12558492369 0.0324287311502 y[1] (closed_form) = -1.12558498002 0.0324300535425 absolute error = 1.324e-06 relative error = 0.0001175 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0829 0.175 h = 0.001 0.003 y[1] (numeric) = -1.12542560366 0.0326389361573 y[1] (closed_form) = -1.12542543766 0.0326402196883 absolute error = 1.294e-06 relative error = 0.000115 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0819 0.178 h = 0.0001 0.004 y[1] (numeric) = -1.1253170807 0.0332193281953 y[1] (closed_form) = -1.1253173716 0.0332206719779 absolute error = 1.375e-06 relative error = 0.0001221 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0818 0.182 h = 0.003 0.006 y[1] (numeric) = -1.12540291073 0.0339619433733 y[1] (closed_form) = -1.12540344473 0.0339629790285 absolute error = 1.165e-06 relative error = 0.0001035 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.237 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0788 0.188 h = 0.0001 0.005 y[1] (numeric) = -1.12500873631 0.0351510325985 y[1] (closed_form) = -1.12500984613 0.0351536932711 absolute error = 2.883e-06 relative error = 0.0002561 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.232 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0787 0.193 h = 0.0001 0.003 y[1] (numeric) = -1.12512945522 0.0360800882639 y[1] (closed_form) = -1.12513000778 0.0360817745243 absolute error = 1.774e-06 relative error = 0.0001576 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0786 0.196 h = 0.001 0.001 y[1] (numeric) = -1.12519631767 0.0366377064714 y[1] (closed_form) = -1.12519643843 0.0366394705951 absolute error = 1.768e-06 relative error = 0.0001571 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.229 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0776 0.197 h = 0.0001 0.004 y[1] (numeric) = -1.12504018114 0.0368513240242 y[1] (closed_form) = -1.12504007763 0.0368530544844 absolute error = 1.734e-06 relative error = 0.000154 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0775 0.201 h = 0.003 0.006 y[1] (numeric) = -1.12513681481 0.0375945401607 y[1] (closed_form) = -1.12513752424 0.0375958458464 absolute error = 1.486e-06 relative error = 0.000132 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.226 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0745 0.207 h = 0.0001 0.005 y[1] (numeric) = -1.12475959507 0.0387923889239 y[1] (closed_form) = -1.12476091625 0.0387953133958 absolute error = 3.209e-06 relative error = 0.0002851 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0744 0.212 h = 0.0001 0.003 y[1] (numeric) = -1.12489460039 0.0397218079406 y[1] (closed_form) = -1.12489534201 0.0397237661951 absolute error = 2.094e-06 relative error = 0.000186 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.219 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0743 0.215 h = 0.001 0.001 y[1] (numeric) = -1.12497002116 0.0402797167518 y[1] (closed_form) = -1.12497033108 0.0402817621581 absolute error = 2.069e-06 relative error = 0.0001838 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0733 0.216 h = 0.001 0.003 y[1] (numeric) = -1.12481674191 0.0404961827376 y[1] (closed_form) = -1.12481682608 0.0404981990453 absolute error = 2.018e-06 relative error = 0.0001793 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0723 0.219 h = 0.0001 0.004 y[1] (numeric) = -1.12472659077 0.041083064885 y[1] (closed_form) = -1.12472713797 0.0410851212268 absolute error = 2.128e-06 relative error = 0.0001891 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.215 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0722 0.223 h = 0.003 0.006 y[1] (numeric) = -1.1248370784 0.0418266284429 y[1] (closed_form) = -1.12483785657 0.0418283633645 absolute error = 1.901e-06 relative error = 0.0001689 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.213 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0692 0.229 h = 0.0001 0.005 y[1] (numeric) = -1.12447972382 0.0430345246551 y[1] (closed_form) = -1.12448115564 0.04303787053 absolute error = 3.639e-06 relative error = 0.0003234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.208 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0691 0.234 h = 0.0001 0.003 y[1] (numeric) = -1.12463139706 0.0439642234418 y[1] (closed_form) = -1.12463222338 0.0439666130167 absolute error = 2.528e-06 relative error = 0.0002246 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.069 0.237 h = 0.001 0.001 y[1] (numeric) = -1.12471680328 0.0445223849216 y[1] (closed_form) = -1.12471719817 0.0445248724974 absolute error = 2.519e-06 relative error = 0.0002238 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.068 0.238 h = 0.001 0.003 y[1] (numeric) = -1.12456688549 0.0447421444966 y[1] (closed_form) = -1.12456705296 0.0447446083297 absolute error = 2.470e-06 relative error = 0.0002194 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.204 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.067 0.241 h = 0.0001 0.004 y[1] (numeric) = -1.1244867669 0.0453322566408 y[1] (closed_form) = -1.12448740035 0.0453347494346 absolute error = 2.572e-06 relative error = 0.0002285 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0669 0.245 h = 0.003 0.006 y[1] (numeric) = -1.12461060127 0.0460759579173 y[1] (closed_form) = -1.12461145887 0.0460781223183 absolute error = 2.328e-06 relative error = 0.0002068 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0639 0.251 h = 0.0001 0.005 y[1] (numeric) = -1.12427344054 0.0472934624592 y[1] (closed_form) = -1.12427499368 0.0472972287091 absolute error = 4.074e-06 relative error = 0.000362 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.196 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0638 0.256 h = 0.0001 0.003 y[1] (numeric) = -1.12444185917 0.0482230371573 y[1] (closed_form) = -1.12444278101 0.0482258578427 absolute error = 2.967e-06 relative error = 0.0002637 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0637 0.259 h = 0.001 0.001 y[1] (numeric) = -1.12453729905 0.0487812097195 y[1] (closed_form) = -1.12453779005 0.0487841393109 absolute error = 2.970e-06 relative error = 0.0002639 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.193 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=81.5MB, alloc=44.3MB, time=1.05 x[1] = -2.0627 0.26 h = 0.001 0.003 y[1] (numeric) = -1.12439083689 0.0490041950283 y[1] (closed_form) = -1.12439109896 0.0490071063133 absolute error = 2.923e-06 relative error = 0.0002597 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0617 0.263 h = 0.0001 0.004 y[1] (numeric) = -1.12432087158 0.049597306839 y[1] (closed_form) = -1.12432160226 0.0496002358598 absolute error = 3.019e-06 relative error = 0.0002682 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.189 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0616 0.267 h = 0.003 0.006 y[1] (numeric) = -1.12445811189 0.0503408217656 y[1] (closed_form) = -1.12445905964 0.0503434155803 absolute error = 2.762e-06 relative error = 0.0002453 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.188 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0586 0.273 h = 0.0001 0.005 y[1] (numeric) = -1.12414146275 0.051567483303 y[1] (closed_form) = -1.12414314794 0.0515716685792 absolute error = 4.512e-06 relative error = 0.0004009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0585 0.278 h = 0.0001 0.003 y[1] (numeric) = -1.12432669286 0.052496525403 y[1] (closed_form) = -1.12432772111 0.0524997766708 absolute error = 3.410e-06 relative error = 0.000303 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.181 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0584 0.281 h = 0.001 0.001 y[1] (numeric) = -1.12443220781 0.0530544646285 y[1] (closed_form) = -1.12443280614 0.0530578357538 absolute error = 3.424e-06 relative error = 0.0003042 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0574 0.282 h = 0.001 0.003 y[1] (numeric) = -1.12428929403 0.0532806046549 y[1] (closed_form) = -1.12428966205 0.0532839629865 absolute error = 3.378e-06 relative error = 0.0003002 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.179 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0564 0.285 h = 0.0001 0.004 y[1] (numeric) = -1.12422959665 0.053876480907 y[1] (closed_form) = -1.12423043561 0.0538798456063 absolute error = 3.468e-06 relative error = 0.0003081 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.177 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0563 0.289 h = 0.003 0.006 y[1] (numeric) = -1.12438029294 0.0546194817774 y[1] (closed_form) = -1.12438134165 0.0546225046255 absolute error = 3.200e-06 relative error = 0.0002842 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.176 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0533 0.295 h = 0.0001 0.005 y[1] (numeric) = -1.12408446175 0.0558548370035 y[1] (closed_form) = -1.12408628971 0.055859439633 absolute error = 4.952e-06 relative error = 0.00044 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.171 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0532 0.3 h = 0.0001 0.003 y[1] (numeric) = -1.1242865578 0.0567829336661 y[1] (closed_form) = -1.12428770339 0.0567866146654 absolute error = 3.855e-06 relative error = 0.0003425 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0531 0.303 h = 0.001 0.001 y[1] (numeric) = -1.12440218229 0.057340392494 y[1] (closed_form) = -1.12440289919 0.057344204339 absolute error = 3.879e-06 relative error = 0.0003445 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0521 0.304 h = 0.0001 0.004 y[1] (numeric) = -1.12426290807 0.0575696130794 y[1] (closed_form) = -1.12426339345 0.0575734177158 absolute error = 3.835e-06 relative error = 0.0003407 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.167 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.052 0.308 h = 0.003 0.006 y[1] (numeric) = -1.12442463788 0.0583119267396 y[1] (closed_form) = -1.12442589681 0.0583152028372 absolute error = 3.510e-06 relative error = 0.0003117 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.166 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.049 0.314 h = 0.0001 0.005 y[1] (numeric) = -1.12414705818 0.0595541325235 y[1] (closed_form) = -1.12414913212 0.0595589768098 absolute error = 5.270e-06 relative error = 0.0004681 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.161 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0489 0.319 h = 0.0001 0.003 y[1] (numeric) = -1.12436368841 0.0604808801652 y[1] (closed_form) = -1.1243650584 0.0604848144349 absolute error = 4.166e-06 relative error = 0.00037 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0488 0.322 h = 0.001 0.001 y[1] (numeric) = -1.12448802726 0.0610376049222 y[1] (closed_form) = -1.12448897004 0.0610416794969 absolute error = 4.182e-06 relative error = 0.0003714 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.158 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0478 0.323 h = 0.001 0.003 y[1] (numeric) = -1.12435199304 0.0612693705822 y[1] (closed_form) = -1.12435270345 0.0612734428223 absolute error = 4.134e-06 relative error = 0.0003671 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0468 0.326 h = 0.0001 0.004 y[1] (numeric) = -1.12431171159 0.061869623382 y[1] (closed_form) = -1.12431289626 0.0618736804675 absolute error = 4.227e-06 relative error = 0.0003754 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0467 0.33 h = 0.003 0.006 y[1] (numeric) = -1.12448753179 0.0626106228848 y[1] (closed_form) = -1.12448891188 0.062614326327 absolute error = 3.952e-06 relative error = 0.0003509 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0437 0.336 h = 0.0001 0.005 y[1] (numeric) = -1.12423130227 0.0638606259837 y[1] (closed_form) = -1.12423353896 0.063865883507 absolute error = 5.714e-06 relative error = 0.0005074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.149 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0436 0.341 h = 0.0001 0.003 y[1] (numeric) = -1.12446486301 0.0647856493018 y[1] (closed_form) = -1.12446637075 0.0647900107159 absolute error = 4.615e-06 relative error = 0.0004097 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0435 0.344 h = 0.001 0.001 y[1] (numeric) = -1.12459935352 0.0653414273851 y[1] (closed_form) = -1.12460043592 0.065345940129 absolute error = 4.641e-06 relative error = 0.000412 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.146 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0425 0.345 h = 0.001 0.003 y[1] (numeric) = -1.12446712306 0.0655761262915 y[1] (closed_form) = -1.12446797216 0.0655806424069 absolute error = 4.595e-06 relative error = 0.000408 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.145 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0415 0.348 h = 0.0001 0.004 y[1] (numeric) = -1.12443739934 0.0661784438518 y[1] (closed_form) = -1.12443872409 0.0661829330888 absolute error = 4.681e-06 relative error = 0.0004155 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.143 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0414 0.352 h = 0.003 0.006 y[1] (numeric) = -1.12462676229 0.066917973867 y[1] (closed_form) = -1.12462827447 0.0669221033502 absolute error = 4.398e-06 relative error = 0.0003903 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.142 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0384 0.358 h = 0.0001 0.005 y[1] (numeric) = -1.12439215393 0.0681752783756 y[1] (closed_form) = -1.12439456411 0.0681809465165 absolute error = 6.159e-06 relative error = 0.0005468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.137 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=127.6MB, alloc=44.3MB, time=1.63 x[1] = -2.0383 0.363 h = 0.0001 0.003 y[1] (numeric) = -1.12464266506 0.0690981541679 y[1] (closed_form) = -1.12464432156 0.0691029409298 absolute error = 5.065e-06 relative error = 0.0004495 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0382 0.366 h = 0.001 0.001 y[1] (numeric) = -1.12478732101 0.0696527321693 y[1] (closed_form) = -1.12478855436 0.0696576812924 absolute error = 5.100e-06 relative error = 0.0004526 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.135 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0372 0.367 h = 0.001 0.003 y[1] (numeric) = -1.12465898038 0.069890281334 y[1] (closed_form) = -1.12465997969 0.0698952395943 absolute error = 5.058e-06 relative error = 0.0004489 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.133 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0362 0.37 h = 0.0001 0.004 y[1] (numeric) = -1.12463990374 0.0704944110992 y[1] (closed_form) = -1.12464137973 0.07049933065 absolute error = 5.136e-06 relative error = 0.0004558 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.131 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0361 0.374 h = 0.003 0.006 y[1] (numeric) = -1.12484282228 0.0712321325158 y[1] (closed_form) = -1.1248444775 0.071236686406 absolute error = 4.845e-06 relative error = 0.0004299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0331 0.38 h = 0.0001 0.005 y[1] (numeric) = -1.12463009283 0.0724962316656 y[1] (closed_form) = -1.12463268721 0.0725023074688 absolute error = 6.607e-06 relative error = 0.0005862 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.033 0.385 h = 0.0001 0.003 y[1] (numeric) = -1.12489756171 0.073416533753 y[1] (closed_form) = -1.12489937799 0.0734217437284 absolute error = 5.517e-06 relative error = 0.0004894 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0329 0.388 h = 0.001 0.001 y[1] (numeric) = -1.1250523894 0.0739696564313 y[1] (closed_form) = -1.12505378507 0.0739750397952 absolute error = 5.561e-06 relative error = 0.0004933 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0319 0.389 h = 0.001 0.003 y[1] (numeric) = -1.1249280227 0.0742099698328 y[1] (closed_form) = -1.12492918374 0.0742153681541 absolute error = 5.522e-06 relative error = 0.0004898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.122 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0309 0.392 h = 0.0001 0.004 y[1] (numeric) = -1.12491967543 0.074815655164 y[1] (closed_form) = -1.12492131385 0.0748210028477 absolute error = 5.593e-06 relative error = 0.0004961 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0308 0.396 h = 0.003 0.006 y[1] (numeric) = -1.12513615235 0.0755512265883 y[1] (closed_form) = -1.12513796157 0.0755562029174 absolute error = 5.295e-06 relative error = 0.0004696 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0278 0.402 h = 0.0001 0.005 y[1] (numeric) = -1.12494554586 0.0768216030805 y[1] (closed_form) = -1.12494833513 0.0768280832518 absolute error = 7.055e-06 relative error = 0.0006257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.114 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0277 0.407 h = 0.0001 0.003 y[1] (numeric) = -1.12522996715 0.0777389026869 y[1] (closed_form) = -1.12523195422 0.0777445334006 absolute error = 5.971e-06 relative error = 0.0005294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0276 0.41 h = 0.001 0.001 y[1] (numeric) = -1.12539496526 0.0782903131954 y[1] (closed_form) = -1.12539653462 0.0782961283093 absolute error = 6.023e-06 relative error = 0.0005339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0266 0.411 h = 0.0001 0.004 y[1] (numeric) = -1.12527465447 0.0785333018162 y[1] (closed_form) = -1.12527598879 0.0785391377574 absolute error = 5.987e-06 relative error = 0.0005307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0265 0.415 h = 0.003 0.006 y[1] (numeric) = -1.1255022104 0.079266838904 y[1] (closed_form) = -1.12550426286 0.0792720463091 absolute error = 5.597e-06 relative error = 0.0004961 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0235 0.421 h = 0.0001 0.005 y[1] (numeric) = -1.12533089743 0.0805419294849 y[1] (closed_form) = -1.12533396466 0.0805486236313 absolute error = 7.363e-06 relative error = 0.0006527 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0234 0.426 h = 0.0001 0.003 y[1] (numeric) = -1.12562985389 0.081456098002 y[1] (closed_form) = -1.12563209867 0.0814619577159 absolute error = 6.275e-06 relative error = 0.000556 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0233 0.429 h = 0.001 0.001 y[1] (numeric) = -1.12580357483 0.0820057070193 y[1] (closed_form) = -1.12580540479 0.0820117605506 absolute error = 6.324e-06 relative error = 0.0005603 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0223 0.43 h = 0.001 0.003 y[1] (numeric) = -1.12568684955 0.0822508752393 y[1] (closed_form) = -1.12568844432 0.0822569546885 absolute error = 6.285e-06 relative error = 0.0005569 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0213 0.433 h = 0.0001 0.004 y[1] (numeric) = -1.12569867242 0.0828586291052 y[1] (closed_form) = -1.12570074476 0.082864635501 absolute error = 6.354e-06 relative error = 0.0005629 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0212 0.437 h = 0.003 0.006 y[1] (numeric) = -1.12594031533 0.083589123628 y[1] (closed_form) = -1.12594254213 0.0835947487788 absolute error = 6.050e-06 relative error = 0.0005358 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0182 0.443 h = 0.0001 0.005 y[1] (numeric) = -1.12579153491 0.0848694996753 y[1] (closed_form) = -1.12579481673 0.0848765910265 absolute error = 7.814e-06 relative error = 0.0006921 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0181 0.448 h = 0.0001 0.003 y[1] (numeric) = -1.12610739415 0.0857798627357 y[1] (closed_form) = -1.12610983013 0.0857861375337 absolute error = 6.731e-06 relative error = 0.000596 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.092 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.018 0.451 h = 0.001 0.001 y[1] (numeric) = -1.1262912593 0.0863272784252 y[1] (closed_form) = -1.12629328401 0.0863337579884 absolute error = 6.789e-06 relative error = 0.000601 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.017 0.452 h = 0.001 0.003 y[1] (numeric) = -1.12617873532 0.0865749474855 y[1] (closed_form) = -1.12618052475 0.0865814589128 absolute error = 6.753e-06 relative error = 0.0005979 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.016 0.455 h = 0.0001 0.004 y[1] (numeric) = -1.12620147921 0.0871835012673 y[1] (closed_form) = -1.12620374587 0.0871899274989 absolute error = 6.814e-06 relative error = 0.0006033 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.088 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0159 0.459 h = 0.003 0.006 y[1] (numeric) = -1.12645662737 0.087910859725 y[1] (closed_form) = -1.12645903945 0.0879168996802 absolute error = 6.504e-06 relative error = 0.0005756 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=173.8MB, alloc=44.3MB, time=2.21 x[1] = -2.0129 0.465 h = 0.0001 0.005 y[1] (numeric) = -1.12633058165 0.0891959760175 y[1] (closed_form) = -1.12633408859 0.0892034603015 absolute error = 8.265e-06 relative error = 0.0007315 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0128 0.47 h = 0.0001 0.003 y[1] (numeric) = -1.12666330085 0.090102099794 y[1] (closed_form) = -1.12666593897 0.09010878621 absolute error = 7.188e-06 relative error = 0.000636 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0127 0.473 h = 0.001 0.001 y[1] (numeric) = -1.12685728648 0.0906470621386 y[1] (closed_form) = -1.12685951722 0.0906539642185 absolute error = 7.254e-06 relative error = 0.0006416 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0117 0.474 h = 0.001 0.003 y[1] (numeric) = -1.12674903905 0.0908971347288 y[1] (closed_form) = -1.12675103461 0.0909040746531 absolute error = 7.221e-06 relative error = 0.0006388 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0107 0.477 h = 0.0001 0.004 y[1] (numeric) = -1.12678275724 0.0915062180115 y[1] (closed_form) = -1.12678522932 0.0915130605438 absolute error = 7.275e-06 relative error = 0.0006436 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0106 0.481 h = 0.003 0.006 y[1] (numeric) = -1.12705137312 0.0922300933088 y[1] (closed_form) = -1.12705398138 0.0922365447816 absolute error = 6.959e-06 relative error = 0.0006154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0076 0.487 h = 0.0001 0.005 y[1] (numeric) = -1.12694824876 0.0935193955818 y[1] (closed_form) = -1.12695199127 0.0935272681825 absolute error = 8.717e-06 relative error = 0.0007708 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0075 0.492 h = 0.0001 0.003 y[1] (numeric) = -1.12729777168 0.0944208452458 y[1] (closed_form) = -1.12730062284 0.0944279394634 absolute error = 7.646e-06 relative error = 0.0006759 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0074 0.495 h = 0.001 0.001 y[1] (numeric) = -1.12750184599 0.0949630935779 y[1] (closed_form) = -1.12750429402 0.0949704142962 absolute error = 7.719e-06 relative error = 0.0006822 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0064 0.496 h = 0.001 0.003 y[1] (numeric) = -1.1273979478 0.0952154695811 y[1] (closed_form) = -1.12740016092 0.0952228341527 absolute error = 7.690e-06 relative error = 0.0006797 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0054 0.499 h = 0.0001 0.004 y[1] (numeric) = -1.12744268562 0.0958248088976 y[1] (closed_form) = -1.12744537418 0.0958320638384 absolute error = 7.737e-06 relative error = 0.0006838 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0053 0.503 h = 0.003 0.006 y[1] (numeric) = -1.12772472089 0.0965448532556 y[1] (closed_form) = -1.1277275362 0.0965517126116 absolute error = 7.415e-06 relative error = 0.0006551 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0023 0.509 h = 0.0001 0.005 y[1] (numeric) = -1.12764468862 0.0978377786396 y[1] (closed_form) = -1.12764867705 0.097846034596 absolute error = 9.169e-06 relative error = 0.0008101 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.062 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0022 0.514 h = 0.0001 0.003 y[1] (numeric) = -1.12801094541 0.0987341188073 y[1] (closed_form) = -1.12801402045 0.0987416166572 absolute error = 8.104e-06 relative error = 0.0007157 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0021 0.517 h = 0.001 0.001 y[1] (numeric) = -1.12822506848 0.0992733920759 y[1] (closed_form) = -1.12822774498 0.0992811271892 absolute error = 8.185e-06 relative error = 0.0007227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0011 0.518 h = 0.0001 0.004 y[1] (numeric) = -1.12812558952 0.0995279686297 y[1] (closed_form) = -1.12812803158 0.0995357536276 absolute error = 8.159e-06 relative error = 0.0007204 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.058 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.001 0.522 h = 0.003 0.006 y[1] (numeric) = -1.12841854908 0.100244600695 y[1] (closed_form) = -1.12842163796 0.100251663677 absolute error = 7.709e-06 relative error = 0.0006805 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.057 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.998 0.528 h = 0.0001 0.005 y[1] (numeric) = -1.12835855179 0.101539910239 y[1] (closed_form) = -1.12836284651 0.101548347196 absolute error = 9.467e-06 relative error = 0.0008356 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.053 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9979 0.533 h = 0.0001 0.003 y[1] (numeric) = -1.12873907819 0.10243130565 y[1] (closed_form) = -1.12874244121 0.102439002835 absolute error = 8.400e-06 relative error = 0.0007411 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.052 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9978 0.536 h = 0.001 0.001 y[1] (numeric) = -1.12896177296 0.102967690051 y[1] (closed_form) = -1.12896474181 0.102975633634 absolute error = 8.480e-06 relative error = 0.000748 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.051 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9968 0.537 h = 0.001 0.003 y[1] (numeric) = -1.12886617635 0.103224022625 y[1] (closed_form) = -1.12886891138 0.103232021288 absolute error = 8.453e-06 relative error = 0.0007457 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9958 0.54 h = 0.0001 0.004 y[1] (numeric) = -1.12893150697 0.103832968921 y[1] (closed_form) = -1.12893471425 0.103840835135 absolute error = 8.495e-06 relative error = 0.0007493 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.048 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9957 0.544 h = 0.003 0.006 y[1] (numeric) = -1.12923829114 0.104544800356 y[1] (closed_form) = -1.12924160707 0.104552263399 absolute error = 8.167e-06 relative error = 0.0007201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.047 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9927 0.55 h = 0.0001 0.005 y[1] (numeric) = -1.12920165274 0.105842662778 y[1] (closed_form) = -1.1292062123 0.105851472821 absolute error = 9.920e-06 relative error = 0.0008747 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.043 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9926 0.555 h = 0.0001 0.003 y[1] (numeric) = -1.12959874119 0.106728139874 y[1] (closed_form) = -1.12960234799 0.106736231865 absolute error = 8.859e-06 relative error = 0.0007808 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9925 0.558 h = 0.001 0.001 y[1] (numeric) = -1.12983138532 0.107261064096 y[1] (closed_form) = -1.1298346032 0.10726941307 absolute error = 8.948e-06 relative error = 0.0007884 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.041 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9915 0.559 h = 0.001 0.003 y[1] (numeric) = -1.12974032934 0.107519397988 y[1] (closed_form) = -1.12974331422 0.107527808097 absolute error = 8.924e-06 relative error = 0.0007864 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9905 0.562 h = 0.0001 0.004 y[1] (numeric) = -1.12981676034 0.108127803139 y[1] (closed_form) = -1.12982021528 0.108136068514 absolute error = 8.958e-06 relative error = 0.0007893 % Correct digits = 5 memory used=219.9MB, alloc=44.3MB, time=2.80 Radius of convergence (given) for eq 1 = 2.038 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9904 0.566 h = 0.003 0.006 y[1] (numeric) = -1.13013676091 0.108834809239 y[1] (closed_form) = -1.13014031455 0.108842667706 absolute error = 8.625e-06 relative error = 0.0007596 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.037 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9874 0.572 h = 0.0001 0.005 y[1] (numeric) = -1.130123604 0.110134639899 y[1] (closed_form) = -1.13012843841 0.110143817086 absolute error = 1.037e-05 relative error = 0.0009135 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9873 0.577 h = 0.0001 0.003 y[1] (numeric) = -1.13053714501 0.111013764466 y[1] (closed_form) = -1.13054100618 0.11102224608 absolute error = 9.319e-06 relative error = 0.0008204 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.032 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9872 0.58 h = 0.001 0.001 y[1] (numeric) = -1.13077967481 0.111542968011 y[1] (closed_form) = -1.13078315267 0.111551717082 absolute error = 9.415e-06 relative error = 0.0008286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.031 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9862 0.581 h = 0.001 0.003 y[1] (numeric) = -1.13069322108 0.111803192927 y[1] (closed_form) = -1.13069646695 0.111812009191 absolute error = 9.395e-06 relative error = 0.0008269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9852 0.584 h = 0.0001 0.004 y[1] (numeric) = -1.1307807654 0.112410774153 y[1] (closed_form) = -1.13078447875 0.112419433407 absolute error = 9.422e-06 relative error = 0.0008291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.028 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9851 0.588 h = 0.003 0.006 y[1] (numeric) = -1.13111389134 0.11311260812 y[1] (closed_form) = -1.13111769328 0.113120857022 absolute error = 9.083e-06 relative error = 0.000799 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9821 0.594 h = 0.0001 0.005 y[1] (numeric) = -1.13112432094 0.114413815703 y[1] (closed_form) = -1.13112944008 0.114423353747 absolute error = 1.082e-05 relative error = 0.0009521 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.023 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.982 0.599 h = 0.0001 0.003 y[1] (numeric) = -1.13155419092 0.115286154823 y[1] (closed_form) = -1.13155831695 0.115295020524 absolute error = 9.779e-06 relative error = 0.0008597 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.022 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9819 0.602 h = 0.001 0.001 y[1] (numeric) = -1.13180653426 0.115811377924 y[1] (closed_form) = -1.13181028294 0.115820521431 absolute error = 9.882e-06 relative error = 0.0008686 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.021 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9809 0.603 h = 0.001 0.003 y[1] (numeric) = -1.13172474125 0.116073381113 y[1] (closed_form) = -1.13172825915 0.116082597868 absolute error = 9.865e-06 relative error = 0.0008672 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9799 0.606 h = 0.0001 0.004 y[1] (numeric) = -1.13182340306 0.116679853862 y[1] (closed_form) = -1.13182738545 0.116688901352 absolute error = 9.885e-06 relative error = 0.0008688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.019 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9798 0.61 h = 0.003 0.006 y[1] (numeric) = -1.13216955207 0.117376170074 y[1] (closed_form) = -1.13217361278 0.117384804069 absolute error = 9.541e-06 relative error = 0.0008382 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.018 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9768 0.616 h = 0.0001 0.005 y[1] (numeric) = -1.13220365517 0.11867815715 y[1] (closed_form) = -1.13220906876 0.118688049426 absolute error = 1.128e-05 relative error = 0.0009906 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.014 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9767 0.621 h = 0.0001 0.003 y[1] (numeric) = -1.1326497164 0.119543279721 y[1] (closed_form) = -1.13265411763 0.119552523617 absolute error = 1.024e-05 relative error = 0.0008989 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9766 0.624 h = 0.001 0.001 y[1] (numeric) = -1.13291179263 0.120064263645 y[1] (closed_form) = -1.13291582285 0.120073795556 absolute error = 1.035e-05 relative error = 0.0009084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.012 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9756 0.625 h = 0.0001 0.004 y[1] (numeric) = -1.13283471556 0.120327929987 y[1] (closed_form) = -1.13283851639 0.120337541192 absolute error = 1.034e-05 relative error = 0.0009072 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.011 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9755 0.629 h = 0.003 0.006 y[1] (numeric) = -1.1331914217 0.121019458085 y[1] (closed_form) = -1.13319578266 0.121028263255 absolute error = 9.826e-06 relative error = 0.0008622 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.01 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9725 0.635 h = 0.0001 0.005 y[1] (numeric) = -1.13324595731 0.122321350414 y[1] (closed_form) = -1.13325170083 0.122331385872 absolute error = 1.156e-05 relative error = 0.001014 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.006 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9724 0.64 h = 0.0001 0.003 y[1] (numeric) = -1.13370574134 0.123179727405 y[1] (closed_form) = -1.13371045677 0.123189135906 absolute error = 1.052e-05 relative error = 0.0009228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.005 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9723 0.643 h = 0.001 0.001 y[1] (numeric) = -1.13397606959 0.123696741753 y[1] (closed_form) = -1.13398041984 0.123706446852 absolute error = 1.064e-05 relative error = 0.0009324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.004 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9713 0.644 h = 0.001 0.003 y[1] (numeric) = -1.13390311138 0.123961688752 y[1] (closed_form) = -1.13390723368 0.123971478316 absolute error = 1.062e-05 relative error = 0.0009312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.003 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9703 0.647 h = 0.0001 0.004 y[1] (numeric) = -1.1340224194 0.124565204584 y[1] (closed_form) = -1.13402699943 0.124574802237 absolute error = 1.063e-05 relative error = 0.0009322 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.002 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9702 0.651 h = 0.003 0.006 y[1] (numeric) = -1.13439241473 0.125250187699 y[1] (closed_form) = -1.13439705356 0.125259366963 absolute error = 1.028e-05 relative error = 0.0009012 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.001 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9672 0.657 h = 0.0001 0.005 y[1] (numeric) = -1.13447072924 0.126551733083 y[1] (closed_form) = -1.13447678475 0.126562109438 absolute error = 1.201e-05 relative error = 0.001052 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.997 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9671 0.662 h = 0.0001 0.003 y[1] (numeric) = -1.13494640521 0.127402100022 y[1] (closed_form) = -1.13495141467 0.127411874698 absolute error = 1.098e-05 relative error = 0.0009617 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.996 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.967 0.665 h = 0.001 0.001 y[1] (numeric) = -1.13522629056 0.127914398798 y[1] (closed_form) = -1.13523094181 0.127924479979 absolute error = 1.110e-05 relative error = 0.0009718 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=266.0MB, alloc=44.3MB, time=3.38 x[1] = -1.966 0.666 h = 0.001 0.003 y[1] (numeric) = -1.13515814049 0.12818078821 y[1] (closed_form) = -1.13516256556 0.128190959862 absolute error = 1.109e-05 relative error = 0.000971 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.994 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.965 0.669 h = 0.0001 0.004 y[1] (numeric) = -1.13528852476 0.128782374757 y[1] (closed_form) = -1.13529340344 0.128792342394 absolute error = 1.110e-05 relative error = 0.0009713 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.993 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9649 0.673 h = 0.003 0.006 y[1] (numeric) = -1.13567118362 0.1294608633 y[1] (closed_form) = -1.13567611044 0.129470410312 absolute error = 1.074e-05 relative error = 0.0009399 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.992 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9619 0.679 h = 0.0001 0.005 y[1] (numeric) = -1.13577331041 0.130761450377 y[1] (closed_form) = -1.13577968711 0.13077216005 absolute error = 1.246e-05 relative error = 0.00109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.988 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9618 0.684 h = 0.0001 0.003 y[1] (numeric) = -1.13626469977 0.13160338447 y[1] (closed_form) = -1.13627001318 0.131613518425 absolute error = 1.144e-05 relative error = 0.001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.987 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9617 0.687 h = 0.001 0.001 y[1] (numeric) = -1.13655403711 0.132110713776 y[1] (closed_form) = -1.13655899964 0.132121163963 absolute error = 1.157e-05 relative error = 0.001011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.987 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9607 0.688 h = 0.001 0.003 y[1] (numeric) = -1.1364907404 0.132378424299 y[1] (closed_form) = -1.13649547872 0.132388970933 absolute error = 1.156e-05 relative error = 0.001011 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9597 0.691 h = 0.0001 0.004 y[1] (numeric) = -1.13663216993 0.132977793165 y[1] (closed_form) = -1.13663735732 0.13298812376 absolute error = 1.156e-05 relative error = 0.00101 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.984 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9596 0.695 h = 0.003 0.006 y[1] (numeric) = -1.13702734602 0.133649450174 y[1] (closed_form) = -1.13703257077 0.133659358241 absolute error = 1.120e-05 relative error = 0.0009784 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.983 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9566 0.701 h = 0.0001 0.005 y[1] (numeric) = -1.13715329904 0.134948463883 y[1] (closed_form) = -1.13716000591 0.134959498969 absolute error = 1.291e-05 relative error = 0.001128 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.979 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9565 0.706 h = 0.0001 0.003 y[1] (numeric) = -1.13766020893 0.135781546249 y[1] (closed_form) = -1.13766583605 0.135792032242 absolute error = 1.190e-05 relative error = 0.001039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9564 0.709 h = 0.001 0.001 y[1] (numeric) = -1.13795888459 0.136283654484 y[1] (closed_form) = -1.13796416848 0.136294466241 absolute error = 1.203e-05 relative error = 0.00105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9554 0.71 h = 0.001 0.003 y[1] (numeric) = -1.13790048275 0.136552562858 y[1] (closed_form) = -1.13790554459 0.136563476998 absolute error = 1.203e-05 relative error = 0.00105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.977 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9544 0.713 h = 0.0001 0.004 y[1] (numeric) = -1.13805291715 0.137149425419 y[1] (closed_form) = -1.13805842313 0.137160111593 absolute error = 1.202e-05 relative error = 0.001049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9543 0.717 h = 0.003 0.006 y[1] (numeric) = -1.13846045272 0.137813917219 y[1] (closed_form) = -1.13846598519 0.1378241793 absolute error = 1.166e-05 relative error = 0.001017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9513 0.723 h = 0.0001 0.005 y[1] (numeric) = -1.13861022621 0.139110739492 y[1] (closed_form) = -1.13861727202 0.139122091765 absolute error = 1.336e-05 relative error = 0.001165 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.971 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9512 0.728 h = 0.0001 0.003 y[1] (numeric) = -1.13913244949 0.139934555737 y[1] (closed_form) = -1.13913839986 0.139945386182 absolute error = 1.236e-05 relative error = 0.001077 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9511 0.731 h = 0.001 0.001 y[1] (numeric) = -1.13944034119 0.140431193939 y[1] (closed_form) = -1.13944595634 0.140442359471 absolute error = 1.250e-05 relative error = 0.001089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9501 0.732 h = 0.0001 0.004 y[1] (numeric) = -1.13938687192 0.14070117506 y[1] (closed_form) = -1.1393922674 0.140712448866 absolute error = 1.250e-05 relative error = 0.001089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.95 0.736 h = 0.003 0.006 y[1] (numeric) = -1.13980437819 0.141359542968 y[1] (closed_form) = -1.1398102329 0.141369939254 absolute error = 1.193e-05 relative error = 0.001039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.947 0.742 h = 0.0001 0.005 y[1] (numeric) = -1.1399745995 0.142653698944 y[1] (closed_form) = -1.13998199312 0.142665152439 absolute error = 1.363e-05 relative error = 0.001187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9469 0.747 h = 0.0001 0.003 y[1] (numeric) = -1.14050971024 0.143469032452 y[1] (closed_form) = -1.14051599594 0.143479988255 absolute error = 1.263e-05 relative error = 0.001099 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9468 0.75 h = 0.001 0.001 y[1] (numeric) = -1.14082536123 0.143960657501 y[1] (closed_form) = -1.14083131897 0.143971956136 absolute error = 1.277e-05 relative error = 0.001111 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9458 0.751 h = 0.001 0.003 y[1] (numeric) = -1.14077617568 0.144231401222 y[1] (closed_form) = -1.14078191601 0.144242813126 absolute error = 1.277e-05 relative error = 0.001111 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9448 0.754 h = 0.0001 0.004 y[1] (numeric) = -1.14094890962 0.144822703149 y[1] (closed_form) = -1.14095508367 0.144833865272 absolute error = 1.276e-05 relative error = 0.001109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9447 0.758 h = 0.0001 0.004 y[1] (numeric) = -1.14137888985 0.14547284499 y[1] (closed_form) = -1.14138506988 0.145483581169 absolute error = 1.239e-05 relative error = 0.001077 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9446 0.762 h = 0.003 0.006 y[1] (numeric) = -1.14181063884 0.146120743037 y[1] (closed_form) = -1.14181681888 0.146131479217 absolute error = 1.239e-05 relative error = 0.001076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.959 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9416 0.768 h = 0.0001 0.005 y[1] (numeric) = -1.14200856921 0.147410031738 y[1] (closed_form) = -1.14201632078 0.147421778287 absolute error = 1.407e-05 relative error = 0.001222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=312.1MB, alloc=44.3MB, time=3.97 x[1] = -1.9415 0.773 h = 0.0001 0.003 y[1] (numeric) = -1.14256073222 0.148213026064 y[1] (closed_form) = -1.14256736046 0.148224308766 absolute error = 1.309e-05 relative error = 0.001136 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9414 0.776 h = 0.001 0.001 y[1] (numeric) = -1.14288665535 0.148697350557 y[1] (closed_form) = -1.1428929661 0.148708986163 absolute error = 1.324e-05 relative error = 0.001149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9404 0.777 h = 0.001 0.003 y[1] (numeric) = -1.1428433538 0.148968874971 y[1] (closed_form) = -1.14284945059 0.148980630512 absolute error = 1.324e-05 relative error = 0.001149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.953 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9394 0.78 h = 0.0001 0.004 y[1] (numeric) = -1.14302865574 0.149555843267 y[1] (closed_form) = -1.14303517864 0.149567335724 absolute error = 1.321e-05 relative error = 0.001146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.952 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9393 0.784 h = 0.003 0.006 y[1] (numeric) = -1.14347219638 0.15019602406 y[1] (closed_form) = -1.14347871221 0.150207090372 absolute error = 1.284e-05 relative error = 0.001114 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.951 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9363 0.79 h = 0.0001 0.005 y[1] (numeric) = -1.14369377575 0.151481239212 y[1] (closed_form) = -1.14370189086 0.151493275713 absolute error = 1.452e-05 relative error = 0.001258 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.948 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9362 0.795 h = 0.0001 0.003 y[1] (numeric) = -1.14426051748 0.152273756359 y[1] (closed_form) = -1.14426749622 0.152285358017 absolute error = 1.354e-05 relative error = 0.001173 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9361 0.798 h = 0.001 0.001 y[1] (numeric) = -1.14459522199 0.152751882768 y[1] (closed_form) = -1.14460189221 0.152763845911 absolute error = 1.370e-05 relative error = 0.001186 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9351 0.799 h = 0.001 0.003 y[1] (numeric) = -1.14455693664 0.153024089352 y[1] (closed_form) = -1.14456339588 0.15303617812 absolute error = 1.371e-05 relative error = 0.001187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.946 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9341 0.802 h = 0.0001 0.004 y[1] (numeric) = -1.14475296962 0.1536073963 y[1] (closed_form) = -1.1447598484 0.15361921063 absolute error = 1.367e-05 relative error = 0.001184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.944 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.934 0.806 h = 0.003 0.006 y[1] (numeric) = -1.14520810274 0.154239119052 y[1] (closed_form) = -1.14521496329 0.154250507112 absolute error = 1.329e-05 relative error = 0.001151 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.944 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.931 0.812 h = 0.0001 0.005 y[1] (numeric) = -1.14545324317 0.155519639007 y[1] (closed_form) = -1.14546172952 0.155531956022 absolute error = 1.496e-05 relative error = 0.001294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9309 0.817 h = 0.0001 0.003 y[1] (numeric) = -1.14603429981 0.156301289346 y[1] (closed_form) = -1.14604163766 0.156313201053 absolute error = 1.399e-05 relative error = 0.00121 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9308 0.82 h = 0.001 0.001 y[1] (numeric) = -1.14637762945 0.156772983355 y[1] (closed_form) = -1.14638466808 0.156785264857 absolute error = 1.416e-05 relative error = 0.001223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9298 0.821 h = 0.001 0.003 y[1] (numeric) = -1.14634438158 0.15704574116 y[1] (closed_form) = -1.14635121239 0.157058153897 absolute error = 1.417e-05 relative error = 0.001224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9288 0.824 h = 0.0001 0.004 y[1] (numeric) = -1.14655105691 0.157625103016 y[1] (closed_form) = -1.14655830031 0.157637230142 absolute error = 1.413e-05 relative error = 0.001221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.937 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9287 0.828 h = 0.003 0.006 y[1] (numeric) = -1.14701756822 0.158248058257 y[1] (closed_form) = -1.14702478218 0.158259759357 absolute error = 1.375e-05 relative error = 0.001187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.936 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9257 0.834 h = 0.0001 0.005 y[1] (numeric) = -1.1472861609 0.159523262224 y[1] (closed_form) = -1.1472950259 0.159535850034 absolute error = 1.540e-05 relative error = 0.001329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.933 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9256 0.839 h = 0.0001 0.003 y[1] (numeric) = -1.1478812549 0.160293663611 y[1] (closed_form) = -1.14788896021 0.160305876142 absolute error = 1.444e-05 relative error = 0.001246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9255 0.842 h = 0.001 0.001 y[1] (numeric) = -1.14823304513 0.160758695335 y[1] (closed_form) = -1.14824046082 0.16077128569 absolute error = 1.461e-05 relative error = 0.00126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9245 0.843 h = 0.001 0.003 y[1] (numeric) = -1.14820485171 0.161031872289 y[1] (closed_form) = -1.14821206295 0.161044599401 absolute error = 1.463e-05 relative error = 0.001262 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9235 0.846 h = 0.0001 0.004 y[1] (numeric) = -1.14842207103 0.161607007351 y[1] (closed_form) = -1.14842968751 0.161619437875 absolute error = 1.458e-05 relative error = 0.001257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9234 0.85 h = 0.003 0.006 y[1] (numeric) = -1.14889973526 0.162220891759 y[1] (closed_form) = -1.14890731107 0.162232896877 absolute error = 1.420e-05 relative error = 0.001223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9204 0.856 h = 0.0001 0.005 y[1] (numeric) = -1.1491916504 0.16349016064 y[1] (closed_form) = -1.14920090115 0.163503009254 absolute error = 1.583e-05 relative error = 0.001364 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9203 0.861 h = 0.0001 0.003 y[1] (numeric) = -1.14980049058 0.164248939019 y[1] (closed_form) = -1.14980857142 0.164261442847 absolute error = 1.489e-05 relative error = 0.001282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.925 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9202 0.864 h = 0.001 0.001 y[1] (numeric) = -1.15016056871 0.164707083377 y[1] (closed_form) = -1.15016836982 0.164719972758 absolute error = 1.507e-05 relative error = 0.001297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.925 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9192 0.865 h = 0.0001 0.004 y[1] (numeric) = -1.15013744238 0.164980546448 y[1] (closed_form) = -1.15014504261 0.164993578011 absolute error = 1.509e-05 relative error = 0.001298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=358.3MB, alloc=44.3MB, time=4.57 x[1] = -1.9191 0.869 h = 0.003 0.006 y[1] (numeric) = -1.15062403794 0.165586775113 y[1] (closed_form) = -1.15063195509 0.165598863273 absolute error = 1.445e-05 relative error = 0.001243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9161 0.875 h = 0.0001 0.005 y[1] (numeric) = -1.15093582756 0.166850166116 y[1] (closed_form) = -1.15094543858 0.166863059573 absolute error = 1.608e-05 relative error = 0.001383 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.916 0.88 h = 0.0001 0.003 y[1] (numeric) = -1.15155611227 0.167598488117 y[1] (closed_form) = -1.15156454575 0.167611063483 absolute error = 1.514e-05 relative error = 0.001301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9159 0.883 h = 0.001 0.001 y[1] (numeric) = -1.15192309432 0.168050431977 y[1] (closed_form) = -1.15193125692 0.168063399179 absolute error = 1.532e-05 relative error = 0.001316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9149 0.884 h = 0.001 0.003 y[1] (numeric) = -1.15190433755 0.16832397371 y[1] (closed_form) = -1.15191230255 0.168337087633 absolute error = 1.534e-05 relative error = 0.001318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.918 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9139 0.887 h = 0.0001 0.004 y[1] (numeric) = -1.15214082357 0.168890380223 y[1] (closed_form) = -1.15214917897 0.168903177817 absolute error = 1.528e-05 relative error = 0.001313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.917 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9138 0.891 h = 0.003 0.006 y[1] (numeric) = -1.15263848811 0.169486475698 y[1] (closed_form) = -1.15264678194 0.169498850179 absolute error = 1.490e-05 relative error = 0.001279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.917 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9108 0.897 h = 0.0001 0.005 y[1] (numeric) = -1.15297329522 0.170742789206 y[1] (closed_form) = -1.15298330421 0.170755924109 absolute error = 1.651e-05 relative error = 0.001417 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.914 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9107 0.902 h = 0.0001 0.003 y[1] (numeric) = -1.15360674471 0.171478819633 y[1] (closed_form) = -1.15361556782 0.171491667692 absolute error = 1.559e-05 relative error = 0.001336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9106 0.905 h = 0.001 0.001 y[1] (numeric) = -1.15398166952 0.17192347361 y[1] (closed_form) = -1.15399023216 0.171936720639 absolute error = 1.577e-05 relative error = 0.001352 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9096 0.906 h = 0.001 0.003 y[1] (numeric) = -1.1539679899 0.172197051919 y[1] (closed_form) = -1.15397635886 0.172210450888 absolute error = 1.580e-05 relative error = 0.001354 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9086 0.909 h = 0.0001 0.004 y[1] (numeric) = -1.15421468176 0.172758442215 y[1] (closed_form) = -1.15422343267 0.172771514544 absolute error = 1.573e-05 relative error = 0.001348 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.911 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9085 0.913 h = 0.003 0.006 y[1] (numeric) = -1.15472279245 0.173344640546 y[1] (closed_form) = -1.15473147059 0.173357291471 absolute error = 1.534e-05 relative error = 0.001314 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9055 0.919 h = 0.0001 0.005 y[1] (numeric) = -1.15508042688 0.174593267336 y[1] (closed_form) = -1.15509083997 0.174606632983 absolute error = 1.694e-05 relative error = 0.00145 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9054 0.924 h = 0.0001 0.003 y[1] (numeric) = -1.15572671255 0.175316658798 y[1] (closed_form) = -1.15573593247 0.175329769199 absolute error = 1.603e-05 relative error = 0.001371 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9053 0.927 h = 0.001 0.001 y[1] (numeric) = -1.15610938492 0.175753813652 y[1] (closed_form) = -1.15611835506 0.175767329819 absolute error = 1.622e-05 relative error = 0.001387 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9043 0.928 h = 0.001 0.003 y[1] (numeric) = -1.15610078224 0.176027293762 y[1] (closed_form) = -1.1561095628 0.176040966967 absolute error = 1.625e-05 relative error = 0.00139 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.906 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9033 0.931 h = 0.0001 0.004 y[1] (numeric) = -1.15635754435 0.176583397969 y[1] (closed_form) = -1.15636669805 0.176596734488 absolute error = 1.618e-05 relative error = 0.001383 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9032 0.935 h = 0.003 0.006 y[1] (numeric) = -1.15687583545 0.177159424261 y[1] (closed_form) = -1.15688490518 0.17717234147 absolute error = 1.578e-05 relative error = 0.001349 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9002 0.941 h = 0.0001 0.005 y[1] (numeric) = -1.15725608589 0.178399760196 y[1] (closed_form) = -1.15726690887 0.178413345653 absolute error = 1.737e-05 relative error = 0.001483 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9001 0.946 h = 0.0001 0.003 y[1] (numeric) = -1.15791486657 0.179110175729 y[1] (closed_form) = -1.15792449014 0.179123537856 absolute error = 1.647e-05 relative error = 0.001405 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9 0.949 h = 0.001 0.001 y[1] (numeric) = -1.15830508377 0.179539628422 y[1] (closed_form) = -1.15831446851 0.179553402759 absolute error = 1.667e-05 relative error = 0.001422 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.899 0.95 h = 0.001 0.003 y[1] (numeric) = -1.15830155322 0.179812875282 y[1] (closed_form) = -1.15831075266 0.179826811626 absolute error = 1.670e-05 relative error = 0.001425 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.898 0.953 h = 0.0001 0.004 y[1] (numeric) = -1.15856824051 0.18036342758 y[1] (closed_form) = -1.15857780391 0.180377017473 absolute error = 1.662e-05 relative error = 0.001417 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.899 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8979 0.957 h = 0.003 0.006 y[1] (numeric) = -1.15909643632 0.180929015437 y[1] (closed_form) = -1.15910590462 0.1809421885 absolute error = 1.622e-05 relative error = 0.001383 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.898 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8949 0.963 h = 0.0001 0.005 y[1] (numeric) = -1.15949907042 0.182160462377 y[1] (closed_form) = -1.1595103087 0.182174256501 absolute error = 1.779e-05 relative error = 0.001516 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8948 0.968 h = 0.0001 0.003 y[1] (numeric) = -1.16016999274 0.182857576042 y[1] (closed_form) = -1.16018002647 0.182871179022 absolute error = 1.690e-05 relative error = 0.001439 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8947 0.971 h = 0.001 0.001 y[1] (numeric) = -1.16056754471 0.183279130095 y[1] (closed_form) = -1.16057735078 0.183293151366 absolute error = 1.711e-05 relative error = 0.001456 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=404.6MB, alloc=44.3MB, time=5.16 x[1] = -1.8937 0.972 h = 0.0001 0.004 y[1] (numeric) = -1.16056907685 0.183552008566 y[1] (closed_form) = -1.16057870209 0.183566196673 absolute error = 1.714e-05 relative error = 0.001459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8936 0.976 h = 0.003 0.006 y[1] (numeric) = -1.16110514449 0.184108853343 y[1] (closed_form) = -1.16111496231 0.184122065397 absolute error = 1.646e-05 relative error = 0.0014 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8906 0.982 h = 0.0001 0.005 y[1] (numeric) = -1.1615267282 0.185331912742 y[1] (closed_form) = -1.16153832855 0.18534570454 absolute error = 1.802e-05 relative error = 0.001532 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8905 0.987 h = 0.0001 0.003 y[1] (numeric) = -1.16220764612 0.186017185761 y[1] (closed_form) = -1.16221803877 0.186030814348 absolute error = 1.714e-05 relative error = 0.001456 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8904 0.99 h = 0.001 0.001 y[1] (numeric) = -1.16261124082 0.186431705023 y[1] (closed_form) = -1.16262141567 0.186445756698 absolute error = 1.735e-05 relative error = 0.001473 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8894 0.991 h = 0.001 0.003 y[1] (numeric) = -1.16261711305 0.186704098193 y[1] (closed_form) = -1.16262711111 0.186718320687 absolute error = 1.739e-05 relative error = 0.001476 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.889 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8884 0.994 h = 0.0001 0.004 y[1] (numeric) = -1.16290177724 0.18724351412 y[1] (closed_form) = -1.16291212115 0.187257372917 absolute error = 1.729e-05 relative error = 0.001468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.888 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8883 0.998 h = 0.003 0.006 y[1] (numeric) = -1.16344750544 0.187788890738 y[1] (closed_form) = -1.16345773376 0.187802338483 absolute error = 1.690e-05 relative error = 0.001434 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.888 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8853 1.004 h = 0.0001 0.005 y[1] (numeric) = -1.16389097792 0.189001970618 y[1] (closed_form) = -1.1639030025 0.189015949777 absolute error = 1.844e-05 relative error = 0.001564 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8852 1.009 h = 0.0001 0.003 y[1] (numeric) = -1.16458334529 0.189673371131 y[1] (closed_form) = -1.16459415908 0.189687219638 absolute error = 1.757e-05 relative error = 0.001489 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8851 1.012 h = 0.001 0.001 y[1] (numeric) = -1.164993863 0.190079647497 y[1] (closed_form) = -1.16500447058 0.19009392446 absolute error = 1.779e-05 relative error = 0.001507 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8841 1.013 h = 0.001 0.003 y[1] (numeric) = -1.16500476632 0.190351421499 y[1] (closed_form) = -1.16501520188 0.190365873829 absolute error = 1.783e-05 relative error = 0.00151 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.884 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8831 1.016 h = 0.0001 0.004 y[1] (numeric) = -1.16529888636 0.190884553325 y[1] (closed_form) = -1.16530965762 0.190898633095 absolute error = 1.773e-05 relative error = 0.001501 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.883 1.02 h = 0.003 0.006 y[1] (numeric) = -1.16585367565 0.19141878418 y[1] (closed_form) = -1.16586432044 0.191432456482 absolute error = 1.733e-05 relative error = 0.001467 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.88 1.026 h = 0.0001 0.005 y[1] (numeric) = -1.16631874524 0.192621308907 y[1] (closed_form) = -1.16633119835 0.192635463761 absolute error = 1.885e-05 relative error = 0.001595 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8799 1.031 h = 0.0001 0.003 y[1] (numeric) = -1.16702217619 0.193278545812 y[1] (closed_form) = -1.16703341656 0.193292602716 absolute error = 1.800e-05 relative error = 0.001522 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8798 1.034 h = 0.001 0.001 y[1] (numeric) = -1.1674393873 0.193676403547 y[1] (closed_form) = -1.16745043324 0.193690893877 absolute error = 1.822e-05 relative error = 0.00154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8788 1.035 h = 0.001 0.003 y[1] (numeric) = -1.16745529886 0.19394742414 y[1] (closed_form) = -1.16746617772 0.193962094222 absolute error = 1.826e-05 relative error = 0.001543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.879 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8778 1.038 h = 0.0001 0.004 y[1] (numeric) = -1.16775869433 0.194474025757 y[1] (closed_form) = -1.16776989843 0.194488314761 absolute error = 1.816e-05 relative error = 0.001534 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8777 1.042 h = 0.003 0.006 y[1] (numeric) = -1.16832223379 0.194996881702 y[1] (closed_form) = -1.16833330063 0.195010767206 absolute error = 1.776e-05 relative error = 0.001499 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8747 1.048 h = 0.0001 0.005 y[1] (numeric) = -1.1688085885 0.196188285214 y[1] (closed_form) = -1.16882147403 0.196202603946 absolute error = 1.926e-05 relative error = 0.001625 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8746 1.053 h = 0.0001 0.003 y[1] (numeric) = -1.16952268666 0.1968310806 y[1] (closed_form) = -1.16953435864 0.196845334176 absolute error = 1.842e-05 relative error = 0.001553 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8745 1.056 h = 0.001 0.001 y[1] (numeric) = -1.16994635524 0.197220351828 y[1] (closed_form) = -1.16995784475 0.197235043392 absolute error = 1.865e-05 relative error = 0.001572 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8735 1.057 h = 0.001 0.003 y[1] (numeric) = -1.16996724749 0.197490485455 y[1] (closed_form) = -1.16997857502 0.197505360987 absolute error = 1.870e-05 relative error = 0.001576 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.874 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8725 1.06 h = 0.0001 0.004 y[1] (numeric) = -1.17027972923 0.19801031685 y[1] (closed_form) = -1.17029137123 0.198024803146 absolute error = 1.858e-05 relative error = 0.001566 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8724 1.064 h = 0.003 0.006 y[1] (numeric) = -1.17085169969 0.198521579422 y[1] (closed_form) = -1.17086319378 0.198535666566 absolute error = 1.818e-05 relative error = 0.001531 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8694 1.07 h = 0.0001 0.005 y[1] (numeric) = -1.17135900752 0.199701306156 y[1] (closed_form) = -1.17137232895 0.199715776813 absolute error = 1.967e-05 relative error = 0.001655 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8693 1.075 h = 0.0001 0.003 y[1] (numeric) = -1.17208336654 0.200329395823 y[1] (closed_form) = -1.17209547476 0.200343834163 absolute error = 1.884e-05 relative error = 0.001585 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=450.8MB, alloc=44.3MB, time=5.76 x[1] = -1.8692 1.078 h = 0.001 0.001 y[1] (numeric) = -1.17251325062 0.200709920837 y[1] (closed_form) = -1.1725251885 0.200724801309 absolute error = 1.908e-05 relative error = 0.001604 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8682 1.079 h = 0.0001 0.004 y[1] (numeric) = -1.17253909133 0.200979034836 y[1] (closed_form) = -1.17255087249 0.200994103314 absolute error = 1.913e-05 relative error = 0.001608 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8681 1.083 h = 0.003 0.006 y[1] (numeric) = -1.17311769568 0.201480649279 y[1] (closed_form) = -1.17312954016 0.201494730124 absolute error = 1.840e-05 relative error = 0.001546 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8651 1.089 h = 0.0001 0.005 y[1] (numeric) = -1.17364261053 0.202649644999 y[1] (closed_form) = -1.17365628779 0.202664066232 absolute error = 1.988e-05 relative error = 0.001669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.865 1.094 h = 0.0001 0.003 y[1] (numeric) = -1.17437528994 0.203264760279 y[1] (closed_form) = -1.1743877556 0.203279177436 absolute error = 1.906e-05 relative error = 0.001599 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8649 1.097 h = 0.001 0.001 y[1] (numeric) = -1.1748102194 0.203637565405 y[1] (closed_form) = -1.17482252533 0.203652427772 absolute error = 1.930e-05 relative error = 0.001618 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8639 1.098 h = 0.001 0.003 y[1] (numeric) = -1.17484027592 0.203905638009 y[1] (closed_form) = -1.1748524298 0.203920691646 absolute error = 1.935e-05 relative error = 0.001623 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8629 1.101 h = 0.0001 0.004 y[1] (numeric) = -1.17516904557 0.204412152836 y[1] (closed_form) = -1.17518149302 0.204426803203 absolute error = 1.922e-05 relative error = 0.001612 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8628 1.105 h = 0.003 0.006 y[1] (numeric) = -1.17575568446 0.204901208585 y[1] (closed_form) = -1.17576796466 0.204915469009 absolute error = 1.882e-05 relative error = 0.001577 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8598 1.111 h = 0.0001 0.005 y[1] (numeric) = -1.17630087644 0.206057529332 y[1] (closed_form) = -1.1763149948 0.206072079922 absolute error = 2.027e-05 relative error = 0.001698 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8597 1.116 h = 0.0001 0.003 y[1] (numeric) = -1.17704303317 0.206657490551 y[1] (closed_form) = -1.17705594243 0.206672069837 absolute error = 1.947e-05 relative error = 0.001629 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8596 1.119 h = 0.001 0.001 y[1] (numeric) = -1.1774837114 0.207021278082 y[1] (closed_form) = -1.17749647331 0.207036305919 absolute error = 1.972e-05 relative error = 0.001649 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8586 1.12 h = 0.001 0.003 y[1] (numeric) = -1.17751864244 0.207288087813 y[1] (closed_form) = -1.17753125781 0.207303310607 absolute error = 1.977e-05 relative error = 0.001654 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8576 1.123 h = 0.0001 0.004 y[1] (numeric) = -1.17785590847 0.207787185649 y[1] (closed_form) = -1.17786880584 0.207801998129 absolute error = 1.964e-05 relative error = 0.001642 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8575 1.127 h = 0.003 0.006 y[1] (numeric) = -1.17845002149 0.208264089724 y[1] (closed_form) = -1.17846274146 0.208278517668 absolute error = 1.923e-05 relative error = 0.001607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8545 1.133 h = 0.0001 0.005 y[1] (numeric) = -1.17901510376 0.209407215226 y[1] (closed_form) = -1.17902966547 0.209421882938 absolute error = 2.067e-05 relative error = 0.001726 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8544 1.138 h = 0.0001 0.003 y[1] (numeric) = -1.17976630623 0.209991800161 y[1] (closed_form) = -1.1797796625 0.21000652924 absolute error = 1.988e-05 relative error = 0.001659 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8543 1.141 h = 0.001 0.001 y[1] (numeric) = -1.18021247607 0.210346435418 y[1] (closed_form) = -1.18022569749 0.210361615948 absolute error = 2.013e-05 relative error = 0.001679 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8533 1.142 h = 0.001 0.003 y[1] (numeric) = -1.18025223611 0.210611853382 y[1] (closed_form) = -1.18026531663 0.210627232359 absolute error = 2.019e-05 relative error = 0.001684 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8523 1.145 h = 0.0001 0.004 y[1] (numeric) = -1.18059777803 0.211103321584 y[1] (closed_form) = -1.18061112874 0.211118283619 absolute error = 2.005e-05 relative error = 0.001672 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8522 1.149 h = 0.003 0.006 y[1] (numeric) = -1.18119901855 0.211567900504 y[1] (closed_form) = -1.18121218189 0.211582483766 absolute error = 1.965e-05 relative error = 0.001637 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8492 1.155 h = 0.0001 0.005 y[1] (numeric) = -1.18178358595 0.212697324455 y[1] (closed_form) = -1.18179859283 0.212712096992 absolute error = 2.106e-05 relative error = 0.001754 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8491 1.16 h = 0.0001 0.003 y[1] (numeric) = -1.18254339494 0.213266326361 y[1] (closed_form) = -1.1825572012 0.21328119278 absolute error = 2.029e-05 relative error = 0.001688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.849 1.163 h = 0.001 0.001 y[1] (numeric) = -1.1829947946 0.213611683893 y[1] (closed_form) = -1.1830084786 0.213627004217 absolute error = 2.054e-05 relative error = 0.001709 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.848 1.164 h = 0.001 0.003 y[1] (numeric) = -1.1830393336 0.213875582898 y[1] (closed_form) = -1.18305288245 0.213891104955 absolute error = 2.060e-05 relative error = 0.001714 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.855 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.847 1.167 h = 0.0001 0.004 y[1] (numeric) = -1.18339292347 0.214359216812 y[1] (closed_form) = -1.18340673049 0.214374315724 absolute error = 2.046e-05 relative error = 0.001701 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.855 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8469 1.171 h = 0.003 0.006 y[1] (numeric) = -1.18400093893 0.214811309559 y[1] (closed_form) = -1.18401454881 0.214826035814 absolute error = 2.005e-05 relative error = 0.001666 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.855 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8439 1.177 h = 0.0001 0.005 y[1] (numeric) = -1.1846045686 0.215926540482 y[1] (closed_form) = -1.18462002203 0.215941405502 absolute error = 2.144e-05 relative error = 0.001781 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=497.1MB, alloc=44.3MB, time=6.34 x[1] = -1.8438 1.182 h = 0.0001 0.003 y[1] (numeric) = -1.18537253787 0.216479768471 y[1] (closed_form) = -1.18538679665 0.216494759683 absolute error = 2.069e-05 relative error = 0.001717 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8437 1.185 h = 0.001 0.001 y[1] (numeric) = -1.18582890134 0.21681573229 y[1] (closed_form) = -1.18584305053 0.216831179406 absolute error = 2.095e-05 relative error = 0.001738 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8427 1.186 h = 0.0001 0.004 y[1] (numeric) = -1.18587816475 0.217077987056 y[1] (closed_form) = -1.18589218464 0.217093638983 absolute error = 2.101e-05 relative error = 0.001743 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8426 1.19 h = 0.003 0.006 y[1] (numeric) = -1.18649143539 0.217519748015 y[1] (closed_form) = -1.1865053889 0.217534422956 absolute error = 2.025e-05 relative error = 0.001679 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8396 1.196 h = 0.0001 0.005 y[1] (numeric) = -1.18711094482 0.218622160522 y[1] (closed_form) = -1.18712673981 0.218636930832 absolute error = 2.163e-05 relative error = 0.001792 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8395 1.201 h = 0.0001 0.003 y[1] (numeric) = -1.18788538534 0.219161580508 y[1] (closed_form) = -1.18789999214 0.219176504525 absolute error = 2.088e-05 relative error = 0.001729 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8394 1.204 h = 0.001 0.001 y[1] (numeric) = -1.18834569196 0.219489318284 y[1] (closed_form) = -1.18836020012 0.219504699408 absolute error = 2.114e-05 relative error = 0.00175 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.851 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8384 1.205 h = 0.001 0.003 y[1] (numeric) = -1.18839895334 0.219750003724 y[1] (closed_form) = -1.18841333739 0.219765592064 absolute error = 2.121e-05 relative error = 0.001755 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8374 1.208 h = 0.0001 0.004 y[1] (numeric) = -1.18876678929 0.220218454836 y[1] (closed_form) = -1.18878140852 0.22023360981 absolute error = 2.106e-05 relative error = 0.001742 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8373 1.212 h = 0.003 0.006 y[1] (numeric) = -1.18938630225 0.220646858552 y[1] (closed_form) = -1.1894007069 0.22066165326 absolute error = 2.065e-05 relative error = 0.001707 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8343 1.218 h = 0.0001 0.005 y[1] (numeric) = -1.19002403673 0.221734211287 y[1] (closed_form) = -1.19004027949 0.221749051064 absolute error = 2.200e-05 relative error = 0.001817 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8342 1.223 h = 0.0001 0.003 y[1] (numeric) = -1.19080578918 0.222257551029 y[1] (closed_form) = -1.19082085186 0.222272576285 absolute error = 2.128e-05 relative error = 0.001756 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8341 1.226 h = 0.001 0.001 y[1] (numeric) = -1.19127055371 0.222575708414 y[1] (closed_form) = -1.19128553049 0.222591191924 absolute error = 2.154e-05 relative error = 0.001778 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8331 1.227 h = 0.001 0.003 y[1] (numeric) = -1.1913284249 0.222834523062 y[1] (closed_form) = -1.1913432836 0.22285021646 absolute error = 2.161e-05 relative error = 0.001783 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8321 1.23 h = 0.0001 0.004 y[1] (numeric) = -1.19170361681 0.22329460459 y[1] (closed_form) = -1.19171869814 0.223309859698 absolute error = 2.145e-05 relative error = 0.001769 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.832 1.234 h = 0.003 0.006 y[1] (numeric) = -1.1923288669 0.223710137285 y[1] (closed_form) = -1.19234372459 0.22372503919 absolute error = 2.104e-05 relative error = 0.001735 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.829 1.24 h = 0.0001 0.005 y[1] (numeric) = -1.19298435672 0.224781985845 y[1] (closed_form) = -1.19300104735 0.224796882739 absolute error = 2.237e-05 relative error = 0.001843 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8289 1.245 h = 0.0001 0.003 y[1] (numeric) = -1.19377295901 0.225289101694 y[1] (closed_form) = -1.1937884788 0.22530421548 absolute error = 2.166e-05 relative error = 0.001783 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8288 1.248 h = 0.001 0.001 y[1] (numeric) = -1.19424190582 0.225597590883 y[1] (closed_form) = -1.19425735246 0.225613163608 absolute error = 2.193e-05 relative error = 0.001805 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8278 1.249 h = 0.001 0.003 y[1] (numeric) = -1.19430431991 0.225854416104 y[1] (closed_form) = -1.1943196546 0.225870201165 absolute error = 2.201e-05 relative error = 0.001811 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8268 1.252 h = 0.0001 0.004 y[1] (numeric) = -1.19468661469 0.226305957455 y[1] (closed_form) = -1.19470215929 0.226321299768 absolute error = 2.184e-05 relative error = 0.001796 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8267 1.256 h = 0.003 0.006 y[1] (numeric) = -1.19531723188 0.226708508816 y[1] (closed_form) = -1.19533254407 0.226723505299 absolute error = 2.143e-05 relative error = 0.001762 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8237 1.262 h = 0.0001 0.005 y[1] (numeric) = -1.19598999231 0.227764426646 y[1] (closed_form) = -1.19600713046 0.227779368339 absolute error = 2.274e-05 relative error = 0.001868 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8236 1.267 h = 0.0001 0.003 y[1] (numeric) = -1.19678497818 0.228255191945 y[1] (closed_form) = -1.19680095584 0.228270381535 absolute error = 2.205e-05 relative error = 0.001809 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8235 1.27 h = 0.001 0.001 y[1] (numeric) = -1.19725782908 0.228553935272 y[1] (closed_form) = -1.19727374635 0.228569584024 absolute error = 2.232e-05 relative error = 0.001831 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8225 1.271 h = 0.001 0.003 y[1] (numeric) = -1.19732471506 0.228808655119 y[1] (closed_form) = -1.19734052657 0.228824518429 absolute error = 2.240e-05 relative error = 0.001837 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8215 1.274 h = 0.0001 0.004 y[1] (numeric) = -1.19771385405 0.229251495229 y[1] (closed_form) = -1.19772986262 0.229266911802 absolute error = 2.222e-05 relative error = 0.001822 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8214 1.278 h = 0.003 0.006 y[1] (numeric) = -1.19834946522 0.229640968565 y[1] (closed_form) = -1.1983652329 0.22965604698 absolute error = 2.182e-05 relative error = 0.001788 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=543.4MB, alloc=44.3MB, time=6.93 x[1] = -1.8184 1.284 h = 0.0001 0.005 y[1] (numeric) = -1.19903899728 0.230680547652 y[1] (closed_form) = -1.19905658218 0.230695521881 absolute error = 2.310e-05 relative error = 0.001892 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8183 1.289 h = 0.0001 0.003 y[1] (numeric) = -1.19983989709 0.231154852934 y[1] (closed_form) = -1.19985633293 0.231170105606 absolute error = 2.242e-05 relative error = 0.001835 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8182 1.292 h = 0.001 0.001 y[1] (numeric) = -1.20031637184 0.231443782994 y[1] (closed_form) = -1.20033276001 0.231459494589 absolute error = 2.270e-05 relative error = 0.001857 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8172 1.293 h = 0.0001 0.004 y[1] (numeric) = -1.20038765468 0.231696284394 y[1] (closed_form) = -1.20040394336 0.231712212538 absolute error = 2.278e-05 relative error = 0.001863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8171 1.297 h = 0.003 0.006 y[1] (numeric) = -1.20102705053 0.232074993208 y[1] (closed_form) = -1.20104314753 0.232089977202 absolute error = 2.199e-05 relative error = 0.001798 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8141 1.303 h = 0.0001 0.005 y[1] (numeric) = -1.20173040841 0.233100004916 y[1] (closed_form) = -1.2017483131 0.233114842708 absolute error = 2.325e-05 relative error = 0.0019 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.814 1.308 h = 0.0001 0.003 y[1] (numeric) = -1.20253582312 0.233560004758 y[1] (closed_form) = -1.20255258981 0.233575146725 absolute error = 2.259e-05 relative error = 0.001844 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8139 1.311 h = 0.001 0.001 y[1] (numeric) = -1.20301507371 0.233840403215 y[1] (closed_form) = -1.20303180364 0.233856003381 absolute error = 2.287e-05 relative error = 0.001866 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8129 1.312 h = 0.001 0.003 y[1] (numeric) = -1.20309004998 0.234090855749 y[1] (closed_form) = -1.20310668587 0.234106673914 absolute error = 2.296e-05 relative error = 0.001873 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8119 1.315 h = 0.0001 0.004 y[1] (numeric) = -1.20349111099 0.234517035867 y[1] (closed_form) = -1.20350791973 0.234532401301 absolute error = 2.277e-05 relative error = 0.001857 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8118 1.319 h = 0.003 0.006 y[1] (numeric) = -1.20413485582 0.234881915042 y[1] (closed_form) = -1.20415140879 0.234896957433 absolute error = 2.237e-05 relative error = 0.001823 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8088 1.325 h = 0.0001 0.005 y[1] (numeric) = -1.2048540177 0.235889886642 y[1] (closed_form) = -1.20487236636 0.235904734386 absolute error = 2.360e-05 relative error = 0.001923 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8087 1.33 h = 0.0001 0.003 y[1] (numeric) = -1.20566446531 0.236333274665 y[1] (closed_form) = -1.20568168938 0.236348456131 absolute error = 2.296e-05 relative error = 0.001869 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8086 1.333 h = 0.001 0.001 y[1] (numeric) = -1.20614681386 0.236603765407 y[1] (closed_form) = -1.20616401377 0.236619403979 absolute error = 2.325e-05 relative error = 0.001891 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8076 1.334 h = 0.001 0.003 y[1] (numeric) = -1.20622603594 0.23685179837 y[1] (closed_form) = -1.20624314818 0.236867656494 absolute error = 2.333e-05 relative error = 0.001898 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8066 1.337 h = 0.0001 0.004 y[1] (numeric) = -1.20663317283 0.237268874564 y[1] (closed_form) = -1.20665044482 0.237284277343 absolute error = 2.314e-05 relative error = 0.001882 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8065 1.341 h = 0.003 0.006 y[1] (numeric) = -1.20728083211 0.237620479981 y[1] (closed_form) = -1.20729784074 0.237635568164 absolute error = 2.274e-05 relative error = 0.001848 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8035 1.347 h = 0.0001 0.005 y[1] (numeric) = -1.20801526345 0.238611060073 y[1] (closed_form) = -1.20803405405 0.238625905779 absolute error = 2.395e-05 relative error = 0.001945 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8034 1.352 h = 0.0001 0.003 y[1] (numeric) = -1.20883026922 0.239037776681 y[1] (closed_form) = -1.20884794968 0.239052985053 absolute error = 2.332e-05 relative error = 0.001893 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8033 1.355 h = 0.001 0.001 y[1] (numeric) = -1.20931543229 0.239298322076 y[1] (closed_form) = -1.20933310111 0.239313986007 absolute error = 2.361e-05 relative error = 0.001915 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8023 1.356 h = 0.001 0.003 y[1] (numeric) = -1.20939881454 0.23954383165 y[1] (closed_form) = -1.20941640205 0.23955971645 absolute error = 2.370e-05 relative error = 0.001922 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8013 1.359 h = 0.0001 0.004 y[1] (numeric) = -1.20981175148 0.239951681875 y[1] (closed_form) = -1.20982948561 0.239967109204 absolute error = 2.351e-05 relative error = 0.001906 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8012 1.363 h = 0.003 0.006 y[1] (numeric) = -1.21046294618 0.240289970467 y[1] (closed_form) = -1.21048040972 0.240305091886 absolute error = 2.310e-05 relative error = 0.001872 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7982 1.369 h = 0.0001 0.005 y[1] (numeric) = -1.21121210174 0.241262828427 y[1] (closed_form) = -1.21123133183 0.241277660234 absolute error = 2.429e-05 relative error = 0.001966 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7981 1.374 h = 0.0001 0.003 y[1] (numeric) = -1.21203119066 0.241672831538 y[1] (closed_form) = -1.21204932604 0.241688054309 absolute error = 2.368e-05 relative error = 0.001916 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.798 1.377 h = 0.001 0.001 y[1] (numeric) = -1.2125188846 0.241923404412 y[1] (closed_form) = -1.21253702075 0.241939080747 absolute error = 2.397e-05 relative error = 0.001939 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.797 1.378 h = 0.001 0.003 y[1] (numeric) = -1.21260633793 0.242166290318 y[1] (closed_form) = -1.21262439917 0.242182188601 absolute error = 2.406e-05 relative error = 0.001946 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.796 1.381 h = 0.0001 0.004 y[1] (numeric) = -1.21302479576 0.242564803065 y[1] (closed_form) = -1.21304299047 0.242580242238 absolute error = 2.386e-05 relative error = 0.001929 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=589.7MB, alloc=44.3MB, time=7.51 x[1] = -1.7959 1.385 h = 0.003 0.006 y[1] (numeric) = -1.21367914691 0.242889745734 y[1] (closed_form) = -1.21369706412 0.24290488791 absolute error = 2.346e-05 relative error = 0.001895 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7929 1.391 h = 0.0001 0.005 y[1] (numeric) = -1.2144424717 0.243844572171 y[1] (closed_form) = -1.21446213841 0.243859378367 absolute error = 2.462e-05 relative error = 0.001987 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7928 1.396 h = 0.0001 0.003 y[1] (numeric) = -1.21526516929 0.244237837191 y[1] (closed_form) = -1.21528375768 0.244253061959 absolute error = 2.403e-05 relative error = 0.001938 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7927 1.399 h = 0.001 0.001 y[1] (numeric) = -1.21575511071 0.244478420815 y[1] (closed_form) = -1.21577371214 0.244494096709 absolute error = 2.433e-05 relative error = 0.001962 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7917 1.4 h = 0.003 0.006 y[1] (numeric) = -1.21584654278 0.244718586461 y[1] (closed_form) = -1.21586507573 0.244734485145 absolute error = 2.442e-05 relative error = 0.001969 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7887 1.406 h = 0.0001 0.005 y[1] (numeric) = -1.21661958366 0.245662751779 y[1] (closed_form) = -1.21664002156 0.245676711828 absolute error = 2.475e-05 relative error = 0.001994 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7886 1.411 h = 0.0001 0.003 y[1] (numeric) = -1.21744491081 0.246044574418 y[1] (closed_form) = -1.21746428152 0.246058972048 absolute error = 2.414e-05 relative error = 0.001943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7885 1.414 h = 0.001 0.001 y[1] (numeric) = -1.21793648598 0.246278330429 y[1] (closed_form) = -1.21795587818 0.246293177559 absolute error = 2.442e-05 relative error = 0.001965 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7875 1.415 h = 0.001 0.003 y[1] (numeric) = -1.2180306711 0.246516668152 y[1] (closed_form) = -1.2180499992 0.246531738675 absolute error = 2.451e-05 relative error = 0.001972 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7865 1.418 h = 0.0001 0.004 y[1] (numeric) = -1.21845804727 0.246899320615 y[1] (closed_form) = -1.21847748667 0.246913930033 absolute error = 2.432e-05 relative error = 0.001956 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7864 1.422 h = 0.003 0.006 y[1] (numeric) = -1.21911720524 0.247201768397 y[1] (closed_form) = -1.21913635607 0.247216096174 absolute error = 2.392e-05 relative error = 0.001923 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7834 1.428 h = 0.0001 0.005 y[1] (numeric) = -1.21990363295 0.248125844004 y[1] (closed_form) = -1.21992450201 0.248139758976 absolute error = 2.508e-05 relative error = 0.002015 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7833 1.433 h = 0.0001 0.003 y[1] (numeric) = -1.22073177105 0.248490914623 y[1] (closed_form) = -1.22075159086 0.248505293544 absolute error = 2.449e-05 relative error = 0.001966 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7832 1.436 h = 0.001 0.001 y[1] (numeric) = -1.22122511717 0.24871466962 y[1] (closed_form) = -1.22124497049 0.248729494869 absolute error = 2.478e-05 relative error = 0.001988 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7822 1.437 h = 0.001 0.003 y[1] (numeric) = -1.22132312054 0.248950130314 y[1] (closed_form) = -1.22134291617 0.248965179395 absolute error = 2.487e-05 relative error = 0.001995 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7812 1.44 h = 0.0001 0.004 y[1] (numeric) = -1.22175525668 0.249323191468 y[1] (closed_form) = -1.2217751505 0.249337779111 absolute error = 2.467e-05 relative error = 0.001978 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7811 1.444 h = 0.003 0.006 y[1] (numeric) = -1.22241655706 0.249612274521 y[1] (closed_form) = -1.22243615638 0.249626589967 absolute error = 2.427e-05 relative error = 0.001945 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7781 1.45 h = 0.0001 0.005 y[1] (numeric) = -1.22321562805 0.250517580493 y[1] (closed_form) = -1.22323692431 0.250531439163 absolute error = 2.541e-05 relative error = 0.002035 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.778 1.455 h = 0.0001 0.003 y[1] (numeric) = -1.22404610764 0.250865921083 y[1] (closed_form) = -1.22406637347 0.250880269267 absolute error = 2.483e-05 relative error = 0.001987 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7779 1.458 h = 0.001 0.001 y[1] (numeric) = -1.22454094417 0.251079686163 y[1] (closed_form) = -1.22456125535 0.251094477083 absolute error = 2.513e-05 relative error = 0.00201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7769 1.459 h = 0.001 0.003 y[1] (numeric) = -1.22464266552 0.25131218375 y[1] (closed_form) = -1.2246629254 0.251327198707 absolute error = 2.522e-05 relative error = 0.002017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7759 1.462 h = 0.0001 0.004 y[1] (numeric) = -1.22507927435 0.251675581791 y[1] (closed_form) = -1.22509961937 0.251690135454 absolute error = 2.501e-05 relative error = 0.002 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7758 1.466 h = 0.003 0.006 y[1] (numeric) = -1.2257423434 0.251951322008 y[1] (closed_form) = -1.22576238838 0.251965613082 absolute error = 2.462e-05 relative error = 0.001967 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7728 1.472 h = 0.0001 0.005 y[1] (numeric) = -1.2265534752 0.252837630073 y[1] (closed_form) = -1.22657519433 0.252851421431 absolute error = 2.573e-05 relative error = 0.002054 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7727 1.477 h = 0.0001 0.003 y[1] (numeric) = -1.22738583032 0.253169279623 y[1] (closed_form) = -1.22740653866 0.253183585224 absolute error = 2.517e-05 relative error = 0.002008 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7726 1.48 h = 0.001 0.001 y[1] (numeric) = -1.22788187876 0.253373076042 y[1] (closed_form) = -1.22790264409 0.253387820376 absolute error = 2.547e-05 relative error = 0.002031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7716 1.481 h = 0.0001 0.004 y[1] (numeric) = -1.22798721529 0.253602528603 y[1] (closed_form) = -1.22800793568 0.253617496943 absolute error = 2.556e-05 relative error = 0.002039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7715 1.485 h = 0.003 0.006 y[1] (numeric) = -1.22865143457 0.253867380641 y[1] (closed_form) = -1.22867176745 0.253881510721 absolute error = 2.476e-05 relative error = 0.001974 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=635.9MB, alloc=44.3MB, time=8.10 x[1] = -1.7685 1.491 h = 0.0001 0.005 y[1] (numeric) = -1.22947224818 0.254737036254 y[1] (closed_form) = -1.22949423398 0.254750630827 absolute error = 2.585e-05 relative error = 0.002059 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7684 1.496 h = 0.0001 0.003 y[1] (numeric) = -1.23030564994 0.255054347864 y[1] (closed_form) = -1.23032664275 0.255068477021 absolute error = 2.530e-05 relative error = 0.002014 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7683 1.499 h = 0.001 0.001 y[1] (numeric) = -1.23080240223 0.255249578293 y[1] (closed_form) = -1.23082346182 0.255264142284 absolute error = 2.561e-05 relative error = 0.002037 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7673 1.5 h = 0.001 0.003 y[1] (numeric) = -1.23091072895 0.25547630609 y[1] (closed_form) = -1.23093174903 0.255491093801 absolute error = 2.570e-05 relative error = 0.002044 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7663 1.503 h = 0.0001 0.004 y[1] (numeric) = -1.23135477635 0.255821524357 y[1] (closed_form) = -1.23137585754 0.255835852458 absolute error = 2.549e-05 relative error = 0.002027 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7662 1.507 h = 0.003 0.006 y[1] (numeric) = -1.2320199949 0.256072530294 y[1] (closed_form) = -1.23204076687 0.256086614104 absolute error = 2.510e-05 relative error = 0.001994 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7632 1.513 h = 0.0001 0.005 y[1] (numeric) = -1.23285177138 0.2569228305 y[1] (closed_form) = -1.23287417092 0.256936337969 absolute error = 2.616e-05 relative error = 0.002077 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7631 1.518 h = 0.0001 0.003 y[1] (numeric) = -1.23368619456 0.257223573403 y[1] (closed_form) = -1.23370762214 0.257237638527 absolute error = 2.563e-05 relative error = 0.002034 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.763 1.521 h = 0.001 0.001 y[1] (numeric) = -1.23418364809 0.257408904476 y[1] (closed_form) = -1.23420515366 0.257423399703 absolute error = 2.593e-05 relative error = 0.002057 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.762 1.522 h = 0.001 0.003 y[1] (numeric) = -1.23429539177 0.257632447492 y[1] (closed_form) = -1.2343168641 0.257647165982 absolute error = 2.603e-05 relative error = 0.002065 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.761 1.525 h = 0.0001 0.004 y[1] (numeric) = -1.23474308618 0.257967860764 y[1] (closed_form) = -1.23476460687 0.257982121128 absolute error = 2.582e-05 relative error = 0.002047 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7609 1.529 h = 0.003 0.006 y[1] (numeric) = -1.23540902381 0.258205664573 y[1] (closed_form) = -1.23543023086 0.258219690607 absolute error = 2.543e-05 relative error = 0.002015 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7579 1.535 h = 0.0001 0.005 y[1] (numeric) = -1.23625117006 0.259036445987 y[1] (closed_form) = -1.236273978 0.259049856053 absolute error = 2.646e-05 relative error = 0.002095 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7578 1.54 h = 0.0001 0.003 y[1] (numeric) = -1.23708616318 0.259320706215 y[1] (closed_form) = -1.23710802088 0.259334696078 absolute error = 2.595e-05 relative error = 0.002053 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7577 1.543 h = 0.001 0.001 y[1] (numeric) = -1.23758404792 0.259496187308 y[1] (closed_form) = -1.23760599457 0.259510602171 absolute error = 2.626e-05 relative error = 0.002076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7567 1.544 h = 0.001 0.003 y[1] (numeric) = -1.23769909967 0.259716476037 y[1] (closed_form) = -1.23772101929 0.259731113481 absolute error = 2.636e-05 relative error = 0.002084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7557 1.547 h = 0.0001 0.004 y[1] (numeric) = -1.23815015317 0.260042054395 y[1] (closed_form) = -1.23817210855 0.26005623565 absolute error = 2.614e-05 relative error = 0.002066 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7556 1.551 h = 0.003 0.006 y[1] (numeric) = -1.23881645131 0.260266728724 y[1] (closed_form) = -1.23883808901 0.2602806857 absolute error = 2.575e-05 relative error = 0.002034 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7526 1.557 h = 0.0001 0.005 y[1] (numeric) = -1.23966837251 0.261077850675 y[1] (closed_form) = -1.23969158319 0.261091153314 absolute error = 2.675e-05 relative error = 0.002112 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7525 1.562 h = 0.0001 0.003 y[1] (numeric) = -1.24050349047 0.261345730056 y[1] (closed_form) = -1.24052577328 0.261359633681 absolute error = 2.626e-05 relative error = 0.002072 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7524 1.565 h = 0.001 0.001 y[1] (numeric) = -1.24100154018 0.261511419989 y[1] (closed_form) = -1.24102392263 0.26152574315 absolute error = 2.657e-05 relative error = 0.002095 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7514 1.566 h = 0.001 0.003 y[1] (numeric) = -1.2411197894 0.26172838939 y[1] (closed_form) = -1.24114215095 0.26174293423 absolute error = 2.668e-05 relative error = 0.002103 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7504 1.569 h = 0.0001 0.004 y[1] (numeric) = -1.24157391509 0.262044113596 y[1] (closed_form) = -1.24159629997 0.262058204627 absolute error = 2.645e-05 relative error = 0.002084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7503 1.573 h = 0.003 0.006 y[1] (numeric) = -1.24224022046 0.262255743577 y[1] (closed_form) = -1.24226228401 0.262269620449 absolute error = 2.606e-05 relative error = 0.002053 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7473 1.579 h = 0.0001 0.005 y[1] (numeric) = -1.24310132115 0.263047088033 y[1] (closed_form) = -1.2431249286 0.263060273508 absolute error = 2.704e-05 relative error = 0.002128 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7472 1.584 h = 0.0001 0.003 y[1] (numeric) = -1.24393612596 0.263298703779 y[1] (closed_form) = -1.2439588285 0.26331251045 absolute error = 2.657e-05 relative error = 0.00209 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7471 1.587 h = 0.001 0.001 y[1] (numeric) = -1.24443407857 0.263454670572 y[1] (closed_form) = -1.24445689116 0.263468890972 absolute error = 2.688e-05 relative error = 0.002113 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7461 1.588 h = 0.0001 0.004 y[1] (numeric) = -1.24455541316 0.263668260116 y[1] (closed_form) = -1.2445782109 0.263682701079 absolute error = 2.699e-05 relative error = 0.002121 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=682.2MB, alloc=44.3MB, time=8.69 x[1] = -1.746 1.592 h = 0.003 0.006 y[1] (numeric) = -1.24522144599 0.26386929475 y[1] (closed_form) = -1.24524376625 0.263882980535 absolute error = 2.618e-05 relative error = 0.002057 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.743 1.598 h = 0.0001 0.005 y[1] (numeric) = -1.24608973446 0.264643438362 y[1] (closed_form) = -1.24611357227 0.264656402296 absolute error = 2.713e-05 relative error = 0.00213 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7429 1.603 h = 0.0001 0.003 y[1] (numeric) = -1.24692373336 0.264881170872 y[1] (closed_form) = -1.24694668667 0.26489477232 absolute error = 2.668e-05 relative error = 0.002093 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7428 1.606 h = 0.001 0.001 y[1] (numeric) = -1.24742128147 0.26502883493 y[1] (closed_form) = -1.24744435348 0.265042844724 absolute error = 2.699e-05 relative error = 0.002117 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7418 1.607 h = 0.001 0.003 y[1] (numeric) = -1.24754513991 0.265239435295 y[1] (closed_form) = -1.24756820221 0.265253664452 absolute error = 2.710e-05 relative error = 0.002125 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7408 1.61 h = 0.0001 0.004 y[1] (numeric) = -1.24800410679 0.265536779454 y[1] (closed_form) = -1.24802716982 0.265550560512 absolute error = 2.687e-05 relative error = 0.002106 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7407 1.614 h = 0.003 0.006 y[1] (numeric) = -1.24866935335 0.26572441442 y[1] (closed_form) = -1.24869208945 0.265738000303 absolute error = 2.649e-05 relative error = 0.002075 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7377 1.62 h = 0.0001 0.005 y[1] (numeric) = -1.24954571442 0.266478627706 y[1] (closed_form) = -1.249569937 0.266491457241 absolute error = 2.741e-05 relative error = 0.002145 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7376 1.625 h = 0.0001 0.003 y[1] (numeric) = -1.25037860814 0.266700359053 y[1] (closed_form) = -1.25040197014 0.266713844437 absolute error = 2.697e-05 relative error = 0.00211 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7375 1.628 h = 0.001 0.001 y[1] (numeric) = -1.25087558505 0.266838453092 y[1] (closed_form) = -1.25089907559 0.266852340421 absolute error = 2.729e-05 relative error = 0.002134 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7365 1.629 h = 0.001 0.003 y[1] (numeric) = -1.25100231642 0.267045574458 y[1] (closed_form) = -1.25102580311 0.26705967965 absolute error = 2.740e-05 relative error = 0.002142 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7355 1.632 h = 0.0001 0.004 y[1] (numeric) = -1.25146354498 0.26733307051 y[1] (closed_form) = -1.25148702057 0.267346731182 absolute error = 2.716e-05 relative error = 0.002122 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7354 1.636 h = 0.003 0.006 y[1] (numeric) = -1.25212782368 0.267507974406 y[1] (closed_form) = -1.25215096982 0.267521450114 absolute error = 2.678e-05 relative error = 0.002092 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7324 1.642 h = 0.0001 0.005 y[1] (numeric) = -1.25301166613 0.268242203097 y[1] (closed_form) = -1.25303626671 0.268254889382 absolute error = 2.768e-05 relative error = 0.00216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7323 1.647 h = 0.0001 0.003 y[1] (numeric) = -1.25384304071 0.268448091794 y[1] (closed_form) = -1.25386680507 0.26846145124 absolute error = 2.726e-05 relative error = 0.002126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7322 1.65 h = 0.001 0.001 y[1] (numeric) = -1.25433919855 0.268576708553 y[1] (closed_form) = -1.25436310099 0.268590463245 absolute error = 2.758e-05 relative error = 0.00215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7312 1.651 h = 0.001 0.003 y[1] (numeric) = -1.25446868772 0.268780303458 y[1] (closed_form) = -1.25449259207 0.268794274315 absolute error = 2.769e-05 relative error = 0.002158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7302 1.654 h = 0.0001 0.004 y[1] (numeric) = -1.25493189969 0.269057971945 y[1] (closed_form) = -1.25495578132 0.269071502254 absolute error = 2.745e-05 relative error = 0.002139 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7301 1.658 h = 0.003 0.006 y[1] (numeric) = -1.25559488276 0.269220274575 y[1] (closed_form) = -1.25561843282 0.269233630129 absolute error = 2.707e-05 relative error = 0.002108 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.851 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7271 1.664 h = 0.0001 0.005 y[1] (numeric) = -1.2564856187 0.269934486167 y[1] (closed_form) = -1.25651059027 0.26994702068 absolute error = 2.794e-05 relative error = 0.002174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.727 1.669 h = 0.0001 0.003 y[1] (numeric) = -1.25731506968 0.270124704186 y[1] (closed_form) = -1.25733922978 0.270137928133 absolute error = 2.754e-05 relative error = 0.002142 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7269 1.672 h = 0.001 0.001 y[1] (numeric) = -1.25781016618 0.270243944462 y[1] (closed_form) = -1.25783447356 0.270257556677 absolute error = 2.786e-05 relative error = 0.002165 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7259 1.673 h = 0.001 0.003 y[1] (numeric) = -1.25794229739 0.270443970018 y[1] (closed_form) = -1.25796661233 0.270457796509 absolute error = 2.797e-05 relative error = 0.002174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7249 1.676 h = 0.0001 0.004 y[1] (numeric) = -1.25840721779 0.270711841296 y[1] (closed_form) = -1.25843149866 0.270725231591 absolute error = 2.773e-05 relative error = 0.002154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7248 1.68 h = 0.003 0.006 y[1] (numeric) = -1.25906858516 0.270861683036 y[1] (closed_form) = -1.25909253271 0.270874908763 absolute error = 2.736e-05 relative error = 0.002124 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.854 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7218 1.686 h = 0.0001 0.005 y[1] (numeric) = -1.25996563105 0.271555866429 y[1] (closed_form) = -1.25999096636 0.271568240981 absolute error = 2.820e-05 relative error = 0.002188 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7217 1.691 h = 0.0001 0.003 y[1] (numeric) = -1.26079276396 0.271730598627 y[1] (closed_form) = -1.26081731291 0.271743677842 absolute error = 2.782e-05 relative error = 0.002157 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.855 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7216 1.694 h = 0.001 0.001 y[1] (numeric) = -1.2612865628 0.271840570936 y[1] (closed_form) = -1.26131126787 0.271854031181 absolute error = 2.813e-05 relative error = 0.00218 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=728.6MB, alloc=44.3MB, time=9.29 x[1] = -1.7206 1.695 h = 0.0001 0.004 y[1] (numeric) = -1.26142121984 0.272036988814 y[1] (closed_form) = -1.26144593801 0.272050661261 absolute error = 2.825e-05 relative error = 0.002189 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7205 1.699 h = 0.003 0.006 y[1] (numeric) = -1.2620810147 0.272176754433 y[1] (closed_form) = -1.26210518418 0.272189765691 absolute error = 2.745e-05 relative error = 0.002126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.857 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7175 1.705 h = 0.0001 0.005 y[1] (numeric) = -1.26298279033 0.272853639563 y[1] (closed_form) = -1.26300831759 0.272865775326 absolute error = 2.827e-05 relative error = 0.002187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.857 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7174 1.71 h = 0.0001 0.003 y[1] (numeric) = -1.26380743883 0.273015233323 y[1] (closed_form) = -1.26383220173 0.273028085713 absolute error = 2.790e-05 relative error = 0.002158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7173 1.713 h = 0.001 0.001 y[1] (numeric) = -1.26429982768 0.273117339778 y[1] (closed_form) = -1.26432475395 0.273130566673 absolute error = 2.822e-05 relative error = 0.002182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7163 1.714 h = 0.001 0.003 y[1] (numeric) = -1.26443652215 0.273310596853 y[1] (closed_form) = -1.26446146615 0.273324033959 absolute error = 2.833e-05 relative error = 0.00219 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7153 1.717 h = 0.0001 0.004 y[1] (numeric) = -1.26490378734 0.273560338365 y[1] (closed_form) = -1.26492867691 0.273573348459 absolute error = 2.808e-05 relative error = 0.00217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7152 1.721 h = 0.003 0.006 y[1] (numeric) = -1.26556118048 0.273687429046 y[1] (closed_form) = -1.26558573462 0.273700293423 absolute error = 2.772e-05 relative error = 0.002141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7122 1.727 h = 0.0001 0.005 y[1] (numeric) = -1.26646819541 0.274344327613 y[1] (closed_form) = -1.26649407228 0.274356289183 absolute error = 2.851e-05 relative error = 0.0022 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7121 1.732 h = 0.0001 0.003 y[1] (numeric) = -1.26728982271 0.274490816165 y[1] (closed_form) = -1.26731496081 0.274503507634 absolute error = 2.816e-05 relative error = 0.002172 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.712 1.735 h = 0.001 0.001 y[1] (numeric) = -1.26778049238 0.274583878537 y[1] (closed_form) = -1.26780580207 0.27459693684 absolute error = 2.848e-05 relative error = 0.002195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.711 1.736 h = 0.001 0.003 y[1] (numeric) = -1.26791949575 0.274773470024 y[1] (closed_form) = -1.26794482844 0.274786736146 absolute error = 2.860e-05 relative error = 0.002204 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.71 1.739 h = 0.0001 0.004 y[1] (numeric) = -1.26838770542 0.275013556153 y[1] (closed_form) = -1.26841297311 0.275026400609 absolute error = 2.834e-05 relative error = 0.002184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7099 1.743 h = 0.003 0.006 y[1] (numeric) = -1.2690426154 0.275128645167 y[1] (closed_form) = -1.26906754701 0.275141353934 absolute error = 2.798e-05 relative error = 0.002155 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7069 1.749 h = 0.0001 0.005 y[1] (numeric) = -1.26995430382 0.275765604748 y[1] (closed_form) = -1.26998052252 0.27577738493 absolute error = 2.874e-05 relative error = 0.002212 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7068 1.754 h = 0.0001 0.003 y[1] (numeric) = -1.27077254684 0.275897206314 y[1] (closed_form) = -1.27079805254 0.275909728616 absolute error = 2.841e-05 relative error = 0.002185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7067 1.757 h = 0.001 0.001 y[1] (numeric) = -1.2712612796 0.275981353125 y[1] (closed_form) = -1.27128696472 0.275994234383 absolute error = 2.873e-05 relative error = 0.002209 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7057 1.758 h = 0.001 0.003 y[1] (numeric) = -1.27140247566 0.276167253539 y[1] (closed_form) = -1.27142818894 0.276180340062 absolute error = 2.885e-05 relative error = 0.002218 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7047 1.761 h = 0.0001 0.004 y[1] (numeric) = -1.27187137148 0.276397749942 y[1] (closed_form) = -1.2718970095 0.276410420461 absolute error = 2.860e-05 relative error = 0.002197 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7046 1.765 h = 0.003 0.006 y[1] (numeric) = -1.2725235117 0.276501013872 y[1] (closed_form) = -1.27254881333 0.276513558645 absolute error = 2.824e-05 relative error = 0.002169 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7016 1.771 h = 0.0001 0.005 y[1] (numeric) = -1.2734393156 0.277118101566 y[1] (closed_form) = -1.27346586815 0.277129693519 absolute error = 2.897e-05 relative error = 0.002223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7015 1.776 h = 0.0001 0.003 y[1] (numeric) = -1.27425382293 0.27723504484 y[1] (closed_form) = -1.27427968842 0.277247390088 absolute error = 2.866e-05 relative error = 0.002198 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7014 1.779 h = 0.001 0.001 y[1] (numeric) = -1.27474040795 0.277310410897 y[1] (closed_form) = -1.27476646034 0.277323107034 absolute error = 2.898e-05 relative error = 0.002222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7004 1.78 h = 0.001 0.003 y[1] (numeric) = -1.27488368091 0.277492599135 y[1] (closed_form) = -1.27490976644 0.27750549783 absolute error = 2.910e-05 relative error = 0.00223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6994 1.783 h = 0.0001 0.004 y[1] (numeric) = -1.27535300971 0.277713579875 y[1] (closed_form) = -1.27537901005 0.277726068527 absolute error = 2.884e-05 relative error = 0.00221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6993 1.787 h = 0.003 0.006 y[1] (numeric) = -1.27600210297 0.277805203471 y[1] (closed_form) = -1.27602776697 0.277817576217 absolute error = 2.849e-05 relative error = 0.002182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6963 1.793 h = 0.0001 0.005 y[1] (numeric) = -1.2769214729 0.278402505308 y[1] (closed_form) = -1.27694835122 0.278413902547 absolute error = 2.919e-05 relative error = 0.002234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6962 1.798 h = 0.0001 0.003 y[1] (numeric) = -1.27773190518 0.278505028792 y[1] (closed_form) = -1.27775812245 0.278517189462 absolute error = 2.890e-05 relative error = 0.00221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=774.9MB, alloc=44.3MB, time=9.88 x[1] = -1.6961 1.801 h = 0.001 0.001 y[1] (numeric) = -1.27821613878 0.278571754793 y[1] (closed_form) = -1.27824255006 0.278584258114 absolute error = 2.922e-05 relative error = 0.002234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.876 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6951 1.802 h = 0.0001 0.004 y[1] (numeric) = -1.27836137339 0.278750214066 y[1] (closed_form) = -1.27838782265 0.278762917096 absolute error = 2.934e-05 relative error = 0.002243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.695 1.806 h = 0.003 0.006 y[1] (numeric) = -1.27900775793 0.278832465966 y[1] (closed_form) = -1.27903360716 0.278844607939 absolute error = 2.856e-05 relative error = 0.002182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.877 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.692 1.812 h = 0.0001 0.005 y[1] (numeric) = -1.27992953056 0.279412785933 y[1] (closed_form) = -1.27995656206 0.279423934551 absolute error = 2.924e-05 relative error = 0.002232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.877 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6919 1.817 h = 0.0001 0.003 y[1] (numeric) = -1.28073602509 0.279503149133 y[1] (closed_form) = -1.28076241809 0.279515068769 absolute error = 2.896e-05 relative error = 0.002209 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.879 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6918 1.82 h = 0.001 0.001 y[1] (numeric) = -1.28121797659 0.279562586108 y[1] (closed_form) = -1.28124456932 0.279574841106 absolute error = 2.928e-05 relative error = 0.002233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6908 1.821 h = 0.001 0.003 y[1] (numeric) = -1.2813647634 0.279737803888 y[1] (closed_form) = -1.28139139811 0.279750255977 absolute error = 2.940e-05 relative error = 0.002242 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6898 1.824 h = 0.0001 0.004 y[1] (numeric) = -1.2818341322 0.27994130439 y[1] (closed_form) = -1.28186066417 0.279953358366 absolute error = 2.914e-05 relative error = 0.002221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6897 1.828 h = 0.003 0.006 y[1] (numeric) = -1.28247671816 0.280011829138 y[1] (closed_form) = -1.28250291492 0.280023785191 absolute error = 2.880e-05 relative error = 0.002194 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6867 1.834 h = 0.0001 0.005 y[1] (numeric) = -1.28340106138 0.280572577806 y[1] (closed_form) = -1.28342840318 0.280583520697 absolute error = 2.945e-05 relative error = 0.002242 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6866 1.839 h = 0.0001 0.003 y[1] (numeric) = -1.28420288543 0.280648992497 y[1] (closed_form) = -1.2842296148 0.280660714634 absolute error = 2.919e-05 relative error = 0.00222 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.884 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6865 1.842 h = 0.001 0.001 y[1] (numeric) = -1.28468212789 0.280700067749 y[1] (closed_form) = -1.2847090634 0.28071211675 absolute error = 2.951e-05 relative error = 0.002244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6855 1.843 h = 0.001 0.003 y[1] (numeric) = -1.284830664 0.280871537863 y[1] (closed_form) = -1.28485764603 0.280883780862 absolute error = 2.963e-05 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6845 1.846 h = 0.0001 0.004 y[1] (numeric) = -1.28529977403 0.281065780689 y[1] (closed_form) = -1.28532664433 0.281077632283 absolute error = 2.937e-05 relative error = 0.002232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6844 1.85 h = 0.003 0.006 y[1] (numeric) = -1.28593857663 0.281125236839 y[1] (closed_form) = -1.28596511272 0.281136999978 absolute error = 2.903e-05 relative error = 0.002205 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6814 1.856 h = 0.0001 0.005 y[1] (numeric) = -1.28686496974 0.281666550679 y[1] (closed_form) = -1.28689261344 0.281677282385 absolute error = 2.965e-05 relative error = 0.002251 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6813 1.861 h = 0.0001 0.003 y[1] (numeric) = -1.28766181992 0.281729279531 y[1] (closed_form) = -1.28768887721 0.281740797703 absolute error = 2.941e-05 relative error = 0.002231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.889 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6812 1.864 h = 0.001 0.001 y[1] (numeric) = -1.28813817099 0.281772148299 y[1] (closed_form) = -1.28816544046 0.281783984722 absolute error = 2.973e-05 relative error = 0.002254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6802 1.865 h = 0.001 0.003 y[1] (numeric) = -1.28828834387 0.2819398658 y[1] (closed_form) = -1.28831566423 0.28195189301 absolute error = 2.985e-05 relative error = 0.002263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6792 1.868 h = 0.0001 0.004 y[1] (numeric) = -1.28875696478 0.28212495409 y[1] (closed_form) = -1.28878416477 0.28213659683 absolute error = 2.959e-05 relative error = 0.002243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6791 1.872 h = 0.003 0.006 y[1] (numeric) = -1.28939174531 0.282173552754 y[1] (closed_form) = -1.28941861242 0.282185116352 absolute error = 2.925e-05 relative error = 0.002216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.892 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6761 1.878 h = 0.0001 0.005 y[1] (numeric) = -1.29031967885 0.282695584559 y[1] (closed_form) = -1.29034761598 0.282706099978 absolute error = 2.985e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.892 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.676 1.883 h = 0.0001 0.003 y[1] (numeric) = -1.29111126469 0.282744897421 y[1] (closed_form) = -1.29113864134 0.282756205537 absolute error = 2.962e-05 relative error = 0.002241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6759 1.886 h = 0.001 0.001 y[1] (numeric) = -1.2915845497 0.282779719276 y[1] (closed_form) = -1.29161214419 0.282791336932 absolute error = 2.994e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.896 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6749 1.887 h = 0.001 0.003 y[1] (numeric) = -1.29173624806 0.282943683162 y[1] (closed_form) = -1.29176389766 0.282955488283 absolute error = 3.006e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6739 1.89 h = 0.0001 0.004 y[1] (numeric) = -1.29220415599 0.283119726697 y[1] (closed_form) = -1.29223167693 0.283131154493 absolute error = 2.980e-05 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.896 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6738 1.894 h = 0.003 0.006 y[1] (numeric) = -1.29283468609 0.283157684524 y[1] (closed_form) = -1.29286187577 0.283169042325 absolute error = 2.947e-05 relative error = 0.002226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.898 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6708 1.9 h = 0.0001 0.005 y[1] (numeric) = -1.2937636624 0.283660602669 y[1] (closed_form) = -1.29379188441 0.283670897053 absolute error = 3.004e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.898 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=821.3MB, alloc=44.3MB, time=10.47 x[1] = -1.6707 1.905 h = 0.0001 0.003 y[1] (numeric) = -1.29454970645 0.283696775889 y[1] (closed_form) = -1.2945773938 0.28370786823 absolute error = 2.983e-05 relative error = 0.002251 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6706 1.908 h = 0.001 0.001 y[1] (numeric) = -1.29501975848 0.283723714325 y[1] (closed_form) = -1.29504766896 0.283735107416 absolute error = 3.015e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6696 1.909 h = 0.0001 0.004 y[1] (numeric) = -1.29517287246 0.283883927425 y[1] (closed_form) = -1.29520084209 0.28389550456 absolute error = 3.027e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6695 1.913 h = 0.003 0.006 y[1] (numeric) = -1.29579974804 0.283913354579 y[1] (closed_form) = -1.29582708597 0.283924472277 absolute error = 2.951e-05 relative error = 0.002225 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.903 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6665 1.919 h = 0.0001 0.005 y[1] (numeric) = -1.29672900812 0.284399961909 y[1] (closed_form) = -1.29675734578 0.284410004716 absolute error = 3.006e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.903 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6664 1.924 h = 0.0001 0.003 y[1] (numeric) = -1.29750991793 0.284425120982 y[1] (closed_form) = -1.29753774306 0.284435965206 absolute error = 2.986e-05 relative error = 0.002248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6663 1.927 h = 0.001 0.001 y[1] (numeric) = -1.29797696821 0.284445448324 y[1] (closed_form) = -1.29800502062 0.284456585626 absolute error = 3.018e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6653 1.928 h = 0.001 0.003 y[1] (numeric) = -1.29813116936 0.284602422864 y[1] (closed_form) = -1.29815928422 0.284613741147 absolute error = 3.031e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.906 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6643 1.931 h = 0.0001 0.004 y[1] (numeric) = -1.29859707344 0.284761964015 y[1] (closed_form) = -1.29862504524 0.284772918842 absolute error = 3.004e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6642 1.935 h = 0.003 0.006 y[1] (numeric) = -1.29921900196 0.284780771622 y[1] (closed_form) = -1.2992466464 0.284791672969 absolute error = 2.972e-05 relative error = 0.002234 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6612 1.941 h = 0.0001 0.005 y[1] (numeric) = -1.3001484143 0.285248623045 y[1] (closed_form) = -1.30017702082 0.285258437017 absolute error = 3.024e-05 relative error = 0.002272 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6611 1.946 h = 0.0001 0.003 y[1] (numeric) = -1.30092330455 0.285261174604 y[1] (closed_form) = -1.30095142399 0.285271793504 absolute error = 3.006e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.661 1.949 h = 0.001 0.001 y[1] (numeric) = -1.30138683408 0.285273933583 y[1] (closed_form) = -1.3014151854 0.285284836674 absolute error = 3.038e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.66 1.95 h = 0.001 0.003 y[1] (numeric) = -1.30154225082 0.285427173644 y[1] (closed_form) = -1.30157066831 0.285438254134 absolute error = 3.050e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.659 1.953 h = 0.0001 0.004 y[1] (numeric) = -1.30200684056 0.285578019685 y[1] (closed_form) = -1.30203510773 0.285588744351 absolute error = 3.023e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6589 1.957 h = 0.003 0.006 y[1] (numeric) = -1.30262392582 0.285586834279 y[1] (closed_form) = -1.30265186805 0.285597514078 absolute error = 2.991e-05 relative error = 0.002243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.915 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6559 1.963 h = 0.0001 0.005 y[1] (numeric) = -1.30355302932 0.28603613836 y[1] (closed_form) = -1.3035818961 0.286045719742 absolute error = 3.042e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.916 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6558 1.968 h = 0.0001 0.003 y[1] (numeric) = -1.30432166032 0.286036373463 y[1] (closed_form) = -1.30435006524 0.286046762377 absolute error = 3.025e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.918 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6557 1.971 h = 0.001 0.001 y[1] (numeric) = -1.30478152461 0.286041736492 y[1] (closed_form) = -1.30481016565 0.286052400681 absolute error = 3.056e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6547 1.972 h = 0.001 0.003 y[1] (numeric) = -1.30493805195 0.286191255153 y[1] (closed_form) = -1.30496676271 0.286202093086 absolute error = 3.069e-05 relative error = 0.002297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6537 1.975 h = 0.0001 0.004 y[1] (numeric) = -1.30540113025 0.286333537754 y[1] (closed_form) = -1.30542968378 0.286344027629 absolute error = 3.042e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6536 1.979 h = 0.003 0.006 y[1] (numeric) = -1.3060131844 0.286332592192 y[1] (closed_form) = -1.30604141566 0.286343045609 absolute error = 3.010e-05 relative error = 0.002252 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.922 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6506 1.985 h = 0.0001 0.005 y[1] (numeric) = -1.30694153147 0.286763570077 y[1] (closed_form) = -1.3069706499 0.286772915452 absolute error = 3.058e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.922 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6505 1.99 h = 0.0001 0.003 y[1] (numeric) = -1.30770367672 0.286751783707 y[1] (closed_form) = -1.30773235824 0.286761938336 absolute error = 3.043e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.925 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6504 1.993 h = 0.001 0.001 y[1] (numeric) = -1.30815973912 0.286749925592 y[1] (closed_form) = -1.30818866063 0.286760346567 absolute error = 3.074e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6494 1.994 h = 0.001 0.003 y[1] (numeric) = -1.30831727401 0.286895739266 y[1] (closed_form) = -1.30834626862 0.286906330262 absolute error = 3.087e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6484 1.997 h = 0.0001 0.004 y[1] (numeric) = -1.30877865099 0.287029594825 y[1] (closed_form) = -1.30880748182 0.287039845652 absolute error = 3.060e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6483 2.001 h = 0.003 0.006 y[1] (numeric) = -1.30938549665 0.287019124921 y[1] (closed_form) = -1.30941400813 0.287029347485 absolute error = 3.029e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.928 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=867.6MB, alloc=44.3MB, time=11.05 x[1] = -1.6453 2.007 h = 0.0001 0.005 y[1] (numeric) = -1.31031265352 0.287432009543 y[1] (closed_form) = -1.31034201501 0.287441115826 absolute error = 3.074e-05 relative error = 0.002292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6452 2.012 h = 0.0001 0.003 y[1] (numeric) = -1.31106809966 0.287408499969 y[1] (closed_form) = -1.31109704887 0.287418416373 absolute error = 3.060e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6451 2.015 h = 0.001 0.001 y[1] (numeric) = -1.31152023131 0.28739959753 y[1] (closed_form) = -1.31154942405 0.287409771352 absolute error = 3.091e-05 relative error = 0.002302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.933 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6441 2.016 h = 0.0001 0.004 y[1] (numeric) = -1.31167867274 0.287541725821 y[1] (closed_form) = -1.31170794178 0.287552065885 absolute error = 3.104e-05 relative error = 0.002312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.933 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.644 2.02 h = 0.003 0.006 y[1] (numeric) = -1.31228112003 0.287523652167 y[1] (closed_form) = -1.31230974393 0.287533631766 absolute error = 3.031e-05 relative error = 0.002256 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.641 2.026 h = 0.0001 0.005 y[1] (numeric) = -1.31320670427 0.287921178594 y[1] (closed_form) = -1.31323614635 0.287930036341 absolute error = 3.075e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6409 2.031 h = 0.0001 0.003 y[1] (numeric) = -1.31395608837 0.287887901987 y[1] (closed_form) = -1.3139851391 0.287897569651 absolute error = 3.062e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6408 2.034 h = 0.001 0.001 y[1] (numeric) = -1.3144046583 0.287873127653 y[1] (closed_form) = -1.31443395522 0.287883045028 absolute error = 3.093e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6398 2.035 h = 0.001 0.003 y[1] (numeric) = -1.31456375727 0.288012092517 y[1] (closed_form) = -1.31459313306 0.288022172805 absolute error = 3.106e-05 relative error = 0.002308 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6388 2.038 h = 0.0001 0.004 y[1] (numeric) = -1.31502139189 0.288130670182 y[1] (closed_form) = -1.31505059275 0.288140425301 absolute error = 3.079e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6387 2.042 h = 0.003 0.006 y[1] (numeric) = -1.31561800265 0.288103179905 y[1] (closed_form) = -1.31564689028 0.288112921389 absolute error = 3.049e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.942 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6357 2.048 h = 0.0001 0.005 y[1] (numeric) = -1.31654163028 0.288483079903 y[1] (closed_form) = -1.31657129952 0.288491693778 absolute error = 3.089e-05 relative error = 0.002292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.943 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6356 2.053 h = 0.0001 0.003 y[1] (numeric) = -1.31728395649 0.288438643905 y[1] (closed_form) = -1.31731325835 0.288448067052 absolute error = 3.078e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.945 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6355 2.056 h = 0.001 0.001 y[1] (numeric) = -1.31772837868 0.288417159682 y[1] (closed_form) = -1.31775792961 0.288426823661 absolute error = 3.109e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6345 2.057 h = 0.001 0.003 y[1] (numeric) = -1.31788820234 0.288552484784 y[1] (closed_form) = -1.31791783501 0.288562307816 absolute error = 3.122e-05 relative error = 0.002314 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.946 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6335 2.06 h = 0.0001 0.004 y[1] (numeric) = -1.31834363479 0.288663050201 y[1] (closed_form) = -1.318373087 0.28867255619 absolute error = 3.095e-05 relative error = 0.002293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6334 2.064 h = 0.003 0.006 y[1] (numeric) = -1.31893458987 0.288626723758 y[1] (closed_form) = -1.3189637324 0.288636223669 absolute error = 3.065e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.949 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6304 2.07 h = 0.0001 0.005 y[1] (numeric) = -1.31985586811 0.288989259402 y[1] (closed_form) = -1.31988575604 0.288997627227 absolute error = 3.104e-05 relative error = 0.002297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6303 2.075 h = 0.0001 0.003 y[1] (numeric) = -1.32059096007 0.28893396815 y[1] (closed_form) = -1.3206205042 0.288943143834 absolute error = 3.094e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.953 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6302 2.078 h = 0.001 0.001 y[1] (numeric) = -1.32103112768 0.288905954516 y[1] (closed_form) = -1.32106092343 0.288915362196 absolute error = 3.125e-05 relative error = 0.002311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6292 2.079 h = 0.001 0.003 y[1] (numeric) = -1.32119158142 0.289037667765 y[1] (closed_form) = -1.32122146163 0.289047230601 absolute error = 3.137e-05 relative error = 0.00232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6282 2.082 h = 0.0001 0.004 y[1] (numeric) = -1.32164465034 0.289140371854 y[1] (closed_form) = -1.32167434491 0.289149625829 absolute error = 3.110e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6281 2.086 h = 0.003 0.006 y[1] (numeric) = -1.32222981217 0.289095451743 y[1] (closed_form) = -1.32225920078 0.289104706964 absolute error = 3.081e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.957 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6251 2.092 h = 0.0001 0.005 y[1] (numeric) = -1.32314836285 0.289440893827 y[1] (closed_form) = -1.32317846107 0.289449013729 absolute error = 3.117e-05 relative error = 0.002302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.958 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.625 2.097 h = 0.0001 0.003 y[1] (numeric) = -1.3238760568 0.289375052443 y[1] (closed_form) = -1.32390583439 0.289383978049 absolute error = 3.109e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.961 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6249 2.1 h = 0.001 0.001 y[1] (numeric) = -1.32431187052 0.289340690518 y[1] (closed_form) = -1.32434190196 0.289349839341 absolute error = 3.139e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6239 2.101 h = 0.001 0.003 y[1] (numeric) = -1.32447286213 0.289468822447 y[1] (closed_form) = -1.32450298058 0.289478122505 absolute error = 3.152e-05 relative error = 0.002325 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6229 2.104 h = 0.0001 0.004 y[1] (numeric) = -1.32492341358 0.289563818991 y[1] (closed_form) = -1.32495334154 0.289572818406 absolute error = 3.125e-05 relative error = 0.002304 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=914.0MB, alloc=44.3MB, time=11.64 x[1] = -1.6228 2.108 h = 0.003 0.006 y[1] (numeric) = -1.32550265459 0.289510548351 y[1] (closed_form) = -1.32553228049 0.2895195561 absolute error = 3.097e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.965 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6198 2.114 h = 0.0001 0.005 y[1] (numeric) = -1.3264181142 0.289839175613 y[1] (closed_form) = -1.32644841441 0.289847046012 absolute error = 3.131e-05 relative error = 0.002306 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.966 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6197 2.119 h = 0.0001 0.003 y[1] (numeric) = -1.32713825885 0.289763089655 y[1] (closed_form) = -1.32716826114 0.289771762894 absolute error = 3.123e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.969 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6196 2.122 h = 0.001 0.001 y[1] (numeric) = -1.32756962677 0.289722560873 y[1] (closed_form) = -1.32759988482 0.28973144862 absolute error = 3.154e-05 relative error = 0.002321 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6186 2.123 h = 0.0001 0.004 y[1] (numeric) = -1.32773106649 0.289847144493 y[1] (closed_form) = -1.32776141392 0.289856179535 absolute error = 3.166e-05 relative error = 0.00233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6185 2.127 h = 0.003 0.006 y[1] (numeric) = -1.328305365 0.289787234943 y[1] (closed_form) = -1.32833506984 0.289796002516 absolute error = 3.097e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6155 2.133 h = 0.0001 0.005 y[1] (numeric) = -1.32921768848 0.290101659713 y[1] (closed_form) = -1.32924803762 0.29010928953 absolute error = 3.129e-05 relative error = 0.0023 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.973 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6154 2.138 h = 0.0001 0.003 y[1] (numeric) = -1.32993110602 0.290017092344 y[1] (closed_form) = -1.32996117639 0.290025521731 absolute error = 3.123e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.976 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6153 2.141 h = 0.001 0.001 y[1] (numeric) = -1.33035850858 0.289971454949 y[1] (closed_form) = -1.330388836 0.289980091394 absolute error = 3.153e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6143 2.142 h = 0.001 0.003 y[1] (numeric) = -1.33052022235 0.290093008589 y[1] (closed_form) = -1.33055064102 0.290101788902 absolute error = 3.166e-05 relative error = 0.002325 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.977 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6133 2.145 h = 0.0001 0.004 y[1] (numeric) = -1.33096561752 0.290174114759 y[1] (closed_form) = -1.33099583771 0.29018260982 absolute error = 3.139e-05 relative error = 0.002304 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6132 2.149 h = 0.003 0.006 y[1] (numeric) = -1.33153344268 0.290106026931 y[1] (closed_form) = -1.33156336858 0.290114542826 absolute error = 3.111e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6102 2.155 h = 0.0001 0.005 y[1] (numeric) = -1.3324420415 0.290404178001 y[1] (closed_form) = -1.33247257737 0.290411556224 absolute error = 3.141e-05 relative error = 0.002304 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.982 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6101 2.16 h = 0.0001 0.003 y[1] (numeric) = -1.33314766414 0.290309935466 y[1] (closed_form) = -1.33317794308 0.290318109167 absolute error = 3.136e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.984 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.61 2.163 h = 0.001 0.001 y[1] (numeric) = -1.33357047126 0.290258469493 y[1] (closed_form) = -1.33360100861 0.290266841706 absolute error = 3.166e-05 relative error = 0.00232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.986 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.609 2.164 h = 0.001 0.003 y[1] (numeric) = -1.33373247326 0.290376543329 y[1] (closed_form) = -1.33376310393 0.290385055457 absolute error = 3.179e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.986 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.608 2.167 h = 0.0001 0.004 y[1] (numeric) = -1.33417495314 0.290450396022 y[1] (closed_form) = -1.33420538145 0.290458631139 absolute error = 3.152e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.987 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6079 2.171 h = 0.003 0.006 y[1] (numeric) = -1.33473654913 0.290374654126 y[1] (closed_form) = -1.33476668748 0.290382916475 absolute error = 3.125e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.989 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6049 2.177 h = 0.0001 0.005 y[1] (numeric) = -1.33564110206 0.290656828619 y[1] (closed_form) = -1.33567181663 0.290663954458 absolute error = 3.153e-05 relative error = 0.002307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6048 2.182 h = 0.0001 0.003 y[1] (numeric) = -1.33633881274 0.290553214757 y[1] (closed_form) = -1.33636929173 0.290561131367 absolute error = 3.149e-05 relative error = 0.002303 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.993 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6047 2.185 h = 0.001 0.001 y[1] (numeric) = -1.33675695293 0.290496100779 y[1] (closed_form) = -1.33678769138 0.290504207455 absolute error = 3.179e-05 relative error = 0.002324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6037 2.186 h = 0.001 0.003 y[1] (numeric) = -1.3369191607 0.290610734055 y[1] (closed_form) = -1.33694999438 0.290618976694 absolute error = 3.192e-05 relative error = 0.002333 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6027 2.189 h = 0.0001 0.004 y[1] (numeric) = -1.33735859963 0.290677494689 y[1] (closed_form) = -1.3373892274 0.290685468542 absolute error = 3.165e-05 relative error = 0.002312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.996 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6026 2.193 h = 0.003 0.006 y[1] (numeric) = -1.3379138758 0.290594340355 y[1] (closed_form) = -1.33794421807 0.290602347594 absolute error = 3.138e-05 relative error = 0.002292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5996 2.199 h = 0.0001 0.005 y[1] (numeric) = -1.33881407628 0.290860840479 y[1] (closed_form) = -1.33884496162 0.290867713401 absolute error = 3.164e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.999 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5995 2.204 h = 0.0001 0.003 y[1] (numeric) = -1.33950376941 0.290748157672 y[1] (closed_form) = -1.33953444001 0.290755816074 absolute error = 3.161e-05 relative error = 0.002306 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.002 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5994 2.207 h = 0.001 0.001 y[1] (numeric) = -1.339917178 0.290685575447 y[1] (closed_form) = -1.33994810883 0.29069341558 absolute error = 3.191e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.004 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5984 2.208 h = 0.001 0.003 y[1] (numeric) = -1.34007951168 0.290796809311 y[1] (closed_form) = -1.34011053951 0.290804781464 absolute error = 3.204e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.004 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=960.6MB, alloc=44.3MB, time=12.26 x[1] = -1.5974 2.211 h = 0.0001 0.004 y[1] (numeric) = -1.34051579115 0.290856640493 y[1] (closed_form) = -1.34054660983 0.290864352055 absolute error = 3.177e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.005 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5973 2.215 h = 0.003 0.006 y[1] (numeric) = -1.3410646659 0.290766314079 y[1] (closed_form) = -1.34109520366 0.290774064939 absolute error = 3.151e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5943 2.221 h = 0.0001 0.005 y[1] (numeric) = -1.34196022196 0.291017446429 y[1] (closed_form) = -1.34199127026 0.291024066152 absolute error = 3.175e-05 relative error = 0.002312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.008 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5942 2.226 h = 0.0001 0.003 y[1] (numeric) = -1.34264180311 0.290895995167 y[1] (closed_form) = -1.342672657 0.290903394526 absolute error = 3.173e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.011 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5941 2.229 h = 0.001 0.001 y[1] (numeric) = -1.34305042208 0.290828123379 y[1] (closed_form) = -1.34308153671 0.290835696254 absolute error = 3.202e-05 relative error = 0.00233 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5931 2.23 h = 0.0001 0.004 y[1] (numeric) = -1.34321280445 0.290936000743 y[1] (closed_form) = -1.34324401769 0.290943701706 absolute error = 3.215e-05 relative error = 0.002339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.593 2.234 h = 0.003 0.006 y[1] (numeric) = -1.34375637893 0.290839996483 y[1] (closed_form) = -1.34378696531 0.290847514606 absolute error = 3.150e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.015 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.59 2.24 h = 0.0001 0.005 y[1] (numeric) = -1.34464753641 0.291078208921 y[1] (closed_form) = -1.34467860592 0.291084599775 absolute error = 3.172e-05 relative error = 0.002306 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5899 2.245 h = 0.0001 0.003 y[1] (numeric) = -1.34532196811 0.290949546901 y[1] (closed_form) = -1.34535286019 0.290956711712 absolute error = 3.171e-05 relative error = 0.002304 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.019 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5898 2.248 h = 0.001 0.001 y[1] (numeric) = -1.34572636269 0.290877321994 y[1] (closed_form) = -1.34575751565 0.29088465335 absolute error = 3.200e-05 relative error = 0.002324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.021 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5888 2.249 h = 0.001 0.003 y[1] (numeric) = -1.34588868792 0.290982346418 y[1] (closed_form) = -1.34591994071 0.290989802477 absolute error = 3.213e-05 relative error = 0.002333 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.021 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5878 2.252 h = 0.0001 0.004 y[1] (numeric) = -1.34631871909 0.291029759707 y[1] (closed_form) = -1.3463497576 0.291036970335 absolute error = 3.187e-05 relative error = 0.002313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.022 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5877 2.256 h = 0.003 0.006 y[1] (numeric) = -1.34685541636 0.290926799845 y[1] (closed_form) = -1.34688618279 0.290934060069 absolute error = 3.161e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5847 2.262 h = 0.0001 0.005 y[1] (numeric) = -1.34774142817 0.291150227472 y[1] (closed_form) = -1.34777264647 0.291156365313 absolute error = 3.182e-05 relative error = 0.002307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.026 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5846 2.267 h = 0.0001 0.003 y[1] (numeric) = -1.34840760435 0.291013350551 y[1] (closed_form) = -1.34843866454 0.291020255572 absolute error = 3.182e-05 relative error = 0.002307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.029 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5845 2.27 h = 0.001 0.001 y[1] (numeric) = -1.34880712055 0.290936165408 y[1] (closed_form) = -1.34883844165 0.290943229005 absolute error = 3.211e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.031 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5835 2.271 h = 0.001 0.003 y[1] (numeric) = -1.34896935841 0.291037918226 y[1] (closed_form) = -1.34900078068 0.291045102639 absolute error = 3.223e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5825 2.274 h = 0.0001 0.004 y[1] (numeric) = -1.34939593159 0.291078872197 y[1] (closed_form) = -1.3494271372 0.29108581922 absolute error = 3.197e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.032 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5824 2.278 h = 0.003 0.006 y[1] (numeric) = -1.34992604458 0.290969418539 y[1] (closed_form) = -1.34995698294 0.29097642038 absolute error = 3.172e-05 relative error = 0.002297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.034 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5794 2.284 h = 0.0001 0.005 y[1] (numeric) = -1.35080665967 0.29117837669 y[1] (closed_form) = -1.35083801935 0.291184261887 absolute error = 3.191e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.035 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5793 2.289 h = 0.0001 0.003 y[1] (numeric) = -1.35146451607 0.291033577665 y[1] (closed_form) = -1.3514957364 0.291040222807 absolute error = 3.192e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.039 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5792 2.292 h = 0.001 0.001 y[1] (numeric) = -1.35185911386 0.290951606539 y[1] (closed_form) = -1.3518905949 0.290958402429 absolute error = 3.221e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5782 2.293 h = 0.001 0.003 y[1] (numeric) = -1.35202119475 0.291050134895 y[1] (closed_form) = -1.35205277816 0.291057047741 absolute error = 3.233e-05 relative error = 0.002338 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5772 2.296 h = 0.0001 0.004 y[1] (numeric) = -1.35244421798 0.291084793848 y[1] (closed_form) = -1.35247558263 0.291091477274 absolute error = 3.207e-05 relative error = 0.002318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.041 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5771 2.3 h = 0.003 0.006 y[1] (numeric) = -1.35296769768 0.290969078766 y[1] (closed_form) = -1.35299879999 0.290975821992 absolute error = 3.182e-05 relative error = 0.0023 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.044 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5741 2.306 h = 0.0001 0.005 y[1] (numeric) = -1.35384267891 0.291163884692 y[1] (closed_form) = -1.35387417269 0.291169517824 absolute error = 3.199e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.045 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.574 2.311 h = 0.0001 0.003 y[1] (numeric) = -1.35449216117 0.291011453044 y[1] (closed_form) = -1.35452353382 0.291017838455 absolute error = 3.202e-05 relative error = 0.002311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.048 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5739 2.314 h = 0.001 0.001 y[1] (numeric) = -1.35488180645 0.290924868262 y[1] (closed_form) = -1.35491343938 0.290931396739 absolute error = 3.230e-05 relative error = 0.002331 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5729 2.315 h = 0.001 0.003 y[1] (numeric) = -1.35504366343 0.29102022053 y[1] (closed_form) = -1.35507539978 0.291026862139 memory used=1007.0MB, alloc=44.3MB, time=12.85 absolute error = 3.242e-05 relative error = 0.002339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5719 2.318 h = 0.0001 0.004 y[1] (numeric) = -1.3554630513 0.291048748559 y[1] (closed_form) = -1.35549456707 0.291055168638 absolute error = 3.216e-05 relative error = 0.00232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.051 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5718 2.322 h = 0.003 0.006 y[1] (numeric) = -1.35597985649 0.290927001707 y[1] (closed_form) = -1.35601111488 0.290933486333 absolute error = 3.192e-05 relative error = 0.002302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.054 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5688 2.328 h = 0.0001 0.005 y[1] (numeric) = -1.35684898041 0.291107973996 y[1] (closed_form) = -1.35688060117 0.291113355839 absolute error = 3.208e-05 relative error = 0.002311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.055 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5687 2.333 h = 0.0001 0.003 y[1] (numeric) = -1.35749004374 0.290948195574 y[1] (closed_form) = -1.35752156103 0.290954321634 absolute error = 3.211e-05 relative error = 0.002313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5686 2.336 h = 0.001 0.001 y[1] (numeric) = -1.35787470813 0.290857167353 y[1] (closed_form) = -1.35790648504 0.290863428951 absolute error = 3.239e-05 relative error = 0.002332 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5676 2.337 h = 0.0001 0.004 y[1] (numeric) = -1.35803627689 0.290949393008 y[1] (closed_form) = -1.35806815816 0.290955763952 absolute error = 3.251e-05 relative error = 0.002341 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5675 2.341 h = 0.003 0.006 y[1] (numeric) = -1.35854758931 0.290822892318 y[1] (closed_form) = -1.35857886968 0.290829155225 absolute error = 3.190e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.063 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5645 2.347 h = 0.0001 0.005 y[1] (numeric) = -1.35941134319 0.290992285945 y[1] (closed_form) = -1.35944296158 0.290997453273 absolute error = 3.204e-05 relative error = 0.002304 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.064 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5644 2.352 h = 0.0001 0.003 y[1] (numeric) = -1.360045048 0.290826510428 y[1] (closed_form) = -1.36007657758 0.290832414537 absolute error = 3.208e-05 relative error = 0.002306 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5643 2.355 h = 0.001 0.001 y[1] (numeric) = -1.36042535627 0.290731851697 y[1] (closed_form) = -1.36045714465 0.290737885002 absolute error = 3.236e-05 relative error = 0.002326 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5633 2.356 h = 0.001 0.003 y[1] (numeric) = -1.36058659102 0.290821430864 y[1] (closed_form) = -1.36061848441 0.290827570279 absolute error = 3.248e-05 relative error = 0.002334 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5623 2.359 h = 0.0001 0.004 y[1] (numeric) = -1.36099894038 0.29083903111 y[1] (closed_form) = -1.36103061059 0.290844963441 absolute error = 3.222e-05 relative error = 0.002315 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5622 2.363 h = 0.003 0.006 y[1] (numeric) = -1.36150317617 0.290706741804 y[1] (closed_form) = -1.36153459839 0.290712746841 absolute error = 3.199e-05 relative error = 0.002298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5592 2.369 h = 0.0001 0.005 y[1] (numeric) = -1.36236069635 0.290862898575 y[1] (closed_form) = -1.36239242889 0.290867816638 absolute error = 3.211e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5591 2.374 h = 0.0001 0.003 y[1] (numeric) = -1.36298592641 0.290690297857 y[1] (closed_form) = -1.36301758675 0.290695943984 absolute error = 3.216e-05 relative error = 0.002308 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.559 2.377 h = 0.001 0.001 y[1] (numeric) = -1.36336121742 0.290591506412 y[1] (closed_form) = -1.36339313553 0.290597274504 absolute error = 3.244e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.558 2.378 h = 0.001 0.003 y[1] (numeric) = -1.36352205187 0.290678054226 y[1] (closed_form) = -1.36355407568 0.290683924727 absolute error = 3.256e-05 relative error = 0.002335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.557 2.381 h = 0.0001 0.004 y[1] (numeric) = -1.36393055825 0.290689990469 y[1] (closed_form) = -1.36396235778 0.290695661493 absolute error = 3.230e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5569 2.385 h = 0.003 0.006 y[1] (numeric) = -1.36442804478 0.290552309514 y[1] (closed_form) = -1.36445960141 0.290558057335 absolute error = 3.208e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5539 2.391 h = 0.0001 0.005 y[1] (numeric) = -1.36527914552 0.290695548719 y[1] (closed_form) = -1.36531098553 0.290700218805 absolute error = 3.218e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.086 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5538 2.396 h = 0.0001 0.003 y[1] (numeric) = -1.36589588139 0.290516396682 y[1] (closed_form) = -1.36592766525 0.290521785804 absolute error = 3.224e-05 relative error = 0.002308 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.089 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5537 2.399 h = 0.001 0.001 y[1] (numeric) = -1.3662661419 0.290413635746 y[1] (closed_form) = -1.36629818232 0.290419139768 absolute error = 3.251e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5527 2.4 h = 0.001 0.003 y[1] (numeric) = -1.3664265192 0.290497204128 y[1] (closed_form) = -1.3664586659 0.290502806904 absolute error = 3.263e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5517 2.403 h = 0.0001 0.004 y[1] (numeric) = -1.36683112096 0.290503637403 y[1] (closed_form) = -1.36686304254 0.290509048198 absolute error = 3.238e-05 relative error = 0.002317 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.092 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5516 2.407 h = 0.003 0.006 y[1] (numeric) = -1.36732184447 0.29036078181 y[1] (closed_form) = -1.36735352823 0.290366273272 absolute error = 3.216e-05 relative error = 0.0023 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5486 2.413 h = 0.0001 0.005 y[1] (numeric) = -1.36816635265 0.290491422082 y[1] (closed_form) = -1.36819829362 0.290495845644 absolute error = 3.225e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.096 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5485 2.418 h = 0.0001 0.003 y[1] (numeric) = -1.36877458307 0.290305988021 y[1] (closed_form) = -1.36880648338 0.290311121303 absolute error = 3.231e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5484 2.421 h = 0.001 0.001 y[1] (numeric) = -1.36913980474 0.290199418126 y[1] (closed_form) = -1.36917196023 0.290204659411 absolute error = 3.258e-05 relative error = 0.002328 % Correct digits = 5 memory used=1053.4MB, alloc=44.3MB, time=13.44 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5474 2.422 h = 0.001 0.003 y[1] (numeric) = -1.36929967058 0.290280059635 y[1] (closed_form) = -1.3693319328 0.290285396074 absolute error = 3.270e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5464 2.425 h = 0.0001 0.004 y[1] (numeric) = -1.36970031185 0.290281149704 y[1] (closed_form) = -1.36973234832 0.290286301539 absolute error = 3.245e-05 relative error = 0.002317 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5463 2.429 h = 0.003 0.006 y[1] (numeric) = -1.37018426497 0.290133332783 y[1] (closed_form) = -1.37021606873 0.290138568938 absolute error = 3.223e-05 relative error = 0.002301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5433 2.435 h = 0.0001 0.005 y[1] (numeric) = -1.37102201978 0.290251691657 y[1] (closed_form) = -1.37105405536 0.290255870295 absolute error = 3.231e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.107 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5432 2.44 h = 0.0001 0.003 y[1] (numeric) = -1.37162174131 0.29006024008 y[1] (closed_form) = -1.37165375117 0.290065118865 absolute error = 3.238e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5431 2.443 h = 0.001 0.001 y[1] (numeric) = -1.3719819205 0.289950018951 y[1] (closed_form) = -1.37201418397 0.289954999012 absolute error = 3.265e-05 relative error = 0.002328 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5421 2.444 h = 0.0001 0.004 y[1] (numeric) = -1.37214122308 0.290027786682 y[1] (closed_form) = -1.37217359365 0.290032858352 absolute error = 3.277e-05 relative error = 0.002336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.542 2.448 h = 0.003 0.006 y[1] (numeric) = -1.37261963084 0.289876078661 y[1] (closed_form) = -1.37265143387 0.289881106653 absolute error = 3.220e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.115 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.539 2.454 h = 0.0001 0.005 y[1] (numeric) = -1.37345131176 0.289984202063 y[1] (closed_form) = -1.3734833255 0.289988182176 absolute error = 3.226e-05 relative error = 0.002298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.117 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5389 2.459 h = 0.0001 0.003 y[1] (numeric) = -1.3740436446 0.289787880112 y[1] (closed_form) = -1.37407564492 0.289792551776 absolute error = 3.234e-05 relative error = 0.002303 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5388 2.462 h = 0.001 0.001 y[1] (numeric) = -1.3743994429 0.289674700247 y[1] (closed_form) = -1.37443169528 0.289679467556 absolute error = 3.260e-05 relative error = 0.002321 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5378 2.463 h = 0.001 0.003 y[1] (numeric) = -1.37455818769 0.289750044675 y[1] (closed_form) = -1.37459054734 0.289754900586 absolute error = 3.272e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5368 2.466 h = 0.0001 0.004 y[1] (numeric) = -1.37495127036 0.289741660867 y[1] (closed_form) = -1.37498340375 0.289746345572 absolute error = 3.247e-05 relative error = 0.002311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5367 2.47 h = 0.003 0.006 y[1] (numeric) = -1.37542257333 0.289585247108 y[1] (closed_form) = -1.37545448356 0.289590022307 absolute error = 3.227e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.127 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5337 2.476 h = 0.0001 0.005 y[1] (numeric) = -1.37624723696 0.289681677184 y[1] (closed_form) = -1.37627933396 0.289685415799 absolute error = 3.231e-05 relative error = 0.002298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5336 2.481 h = 0.0001 0.003 y[1] (numeric) = -1.37683107714 0.28947981643 y[1] (closed_form) = -1.37686317463 0.289484236616 absolute error = 3.240e-05 relative error = 0.002303 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5335 2.484 h = 0.001 0.001 y[1] (numeric) = -1.37718183971 0.289363270924 y[1] (closed_form) = -1.37721418742 0.289367780351 absolute error = 3.266e-05 relative error = 0.002321 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5325 2.485 h = 0.001 0.003 y[1] (numeric) = -1.37733993205 0.289435841986 y[1] (closed_form) = -1.37737238719 0.289440436582 absolute error = 3.278e-05 relative error = 0.002329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5315 2.488 h = 0.0001 0.004 y[1] (numeric) = -1.37772892627 0.289422563846 y[1] (closed_form) = -1.37776115513 0.289426994247 absolute error = 3.253e-05 relative error = 0.002311 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.135 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5314 2.492 h = 0.003 0.006 y[1] (numeric) = -1.37819347314 0.289261777159 y[1] (closed_form) = -1.37822548393 0.289266301112 absolute error = 3.233e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5284 2.498 h = 0.0001 0.005 y[1] (numeric) = -1.37901099197 0.289346825908 y[1] (closed_form) = -1.37904316636 0.289350325006 absolute error = 3.236e-05 relative error = 0.002297 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5283 2.503 h = 0.0001 0.003 y[1] (numeric) = -1.37958635642 0.289139676206 y[1] (closed_form) = -1.37961854465 0.289143846712 absolute error = 3.246e-05 relative error = 0.002303 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5282 2.506 h = 0.001 0.001 y[1] (numeric) = -1.37993209181 0.289019914172 y[1] (closed_form) = -1.37996452828 0.28902416769 absolute error = 3.271e-05 relative error = 0.00232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.146 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5272 2.507 h = 0.001 0.003 y[1] (numeric) = -1.38008948684 0.289089765905 y[1] (closed_form) = -1.38012203082 0.28909410122 absolute error = 3.283e-05 relative error = 0.002328 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.146 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5262 2.51 h = 0.0001 0.004 y[1] (numeric) = -1.38047435718 0.289071746625 y[1] (closed_form) = -1.38050667503 0.28907592462 absolute error = 3.259e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5261 2.514 h = 0.003 0.006 y[1] (numeric) = -1.38093216268 0.288906784731 y[1] (closed_form) = -1.38096426755 0.288911059139 absolute error = 3.239e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5231 2.52 h = 0.0001 0.005 y[1] (numeric) = -1.38174242018 0.288980761562 y[1] (closed_form) = -1.38177466626 0.288984023243 absolute error = 3.241e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.523 2.525 h = 0.0001 0.003 y[1] (numeric) = -1.38230933228 0.288768567434 y[1] (closed_form) = -1.38234160503 0.288772490196 absolute error = 3.251e-05 relative error = 0.002302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1099.9MB, alloc=44.3MB, time=14.04 x[1] = -1.5229 2.528 h = 0.001 0.001 y[1] (numeric) = -1.38265005292 0.288645734845 y[1] (closed_form) = -1.3826825718 0.288649734566 absolute error = 3.276e-05 relative error = 0.00232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5219 2.529 h = 0.001 0.003 y[1] (numeric) = -1.38280670816 0.288712921444 y[1] (closed_form) = -1.38283933451 0.288716999655 absolute error = 3.288e-05 relative error = 0.002328 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5209 2.532 h = 0.0001 0.004 y[1] (numeric) = -1.38318742398 0.288690312185 y[1] (closed_form) = -1.38321982456 0.288694239812 absolute error = 3.264e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5208 2.536 h = 0.003 0.006 y[1] (numeric) = -1.38363850792 0.288521368539 y[1] (closed_form) = -1.38367070057 0.288525395245 absolute error = 3.244e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5178 2.542 h = 0.0001 0.005 y[1] (numeric) = -1.3844413982 0.288584579951 y[1] (closed_form) = -1.38447371042 0.288587606421 absolute error = 3.245e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.164 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5177 2.547 h = 0.0001 0.003 y[1] (numeric) = -1.38499988745 0.288367580485 y[1] (closed_form) = -1.38503223864 0.288371257571 absolute error = 3.256e-05 relative error = 0.002301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.167 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5176 2.55 h = 0.001 0.001 y[1] (numeric) = -1.38533560943 0.288241820112 y[1] (closed_form) = -1.38536820453 0.288245568279 absolute error = 3.281e-05 relative error = 0.002319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5166 2.551 h = 0.0001 0.004 y[1] (numeric) = -1.38549148465 0.288306395848 y[1] (closed_form) = -1.38552418711 0.288310219264 absolute error = 3.293e-05 relative error = 0.002327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5165 2.555 h = 0.003 0.006 y[1] (numeric) = -1.38593708386 0.288134346986 y[1] (closed_form) = -1.38596925692 0.288138180683 absolute error = 3.240e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.172 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5135 2.561 h = 0.0001 0.005 y[1] (numeric) = -1.38673343241 0.288188624162 y[1] (closed_form) = -1.38676570716 0.288191468884 absolute error = 3.240e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5134 2.566 h = 0.0001 0.003 y[1] (numeric) = -1.38728464612 0.287967775417 y[1] (closed_form) = -1.3873169699 0.287971261512 absolute error = 3.251e-05 relative error = 0.002295 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5133 2.569 h = 0.001 0.001 y[1] (numeric) = -1.38761604836 0.287839665973 y[1] (closed_form) = -1.38764861396 0.287843218259 absolute error = 3.276e-05 relative error = 0.002312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5123 2.57 h = 0.001 0.003 y[1] (numeric) = -1.38777119145 0.287902047723 y[1] (closed_form) = -1.38780386421 0.287905672525 absolute error = 3.287e-05 relative error = 0.002319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5113 2.573 h = 0.0001 0.004 y[1] (numeric) = -1.38814406052 0.28787134259 y[1] (closed_form) = -1.38817650867 0.287874828951 absolute error = 3.263e-05 relative error = 0.002302 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.181 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5112 2.577 h = 0.003 0.006 y[1] (numeric) = -1.38858266387 0.287695569108 y[1] (closed_form) = -1.38861491347 0.287699158958 absolute error = 3.245e-05 relative error = 0.002288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5082 2.583 h = 0.0001 0.005 y[1] (numeric) = -1.38937147875 0.287739643418 y[1] (closed_form) = -1.38940380982 0.287742257356 absolute error = 3.244e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5081 2.588 h = 0.0001 0.003 y[1] (numeric) = -1.38991434233 0.287514418998 y[1] (closed_form) = -1.38994673376 0.287517663646 absolute error = 3.255e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.508 2.591 h = 0.001 0.001 y[1] (numeric) = -1.39024078657 0.287383638475 y[1] (closed_form) = -1.3902734174 0.287386943763 absolute error = 3.280e-05 relative error = 0.00231 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.507 2.592 h = 0.001 0.003 y[1] (numeric) = -1.39039508136 0.287443510689 y[1] (closed_form) = -1.39042781908 0.287446885379 absolute error = 3.291e-05 relative error = 0.002318 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.506 2.595 h = 0.0001 0.004 y[1] (numeric) = -1.39076373512 0.287408635954 y[1] (closed_form) = -1.39079624905 0.287411878525 absolute error = 3.268e-05 relative error = 0.002301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5059 2.599 h = 0.003 0.006 y[1] (numeric) = -1.3911957012 0.287229409586 y[1] (closed_form) = -1.39122802152 0.287232757792 absolute error = 3.249e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.196 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5029 2.605 h = 0.0001 0.005 y[1] (numeric) = -1.39197690487 0.287263577523 y[1] (closed_form) = -1.39200928718 0.287265963147 absolute error = 3.247e-05 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.199 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5028 2.61 h = 0.0001 0.003 y[1] (numeric) = -1.39251146341 0.287034200536 y[1] (closed_form) = -1.39254391691 0.287037206127 absolute error = 3.259e-05 relative error = 0.002292 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5027 2.613 h = 0.001 0.001 y[1] (numeric) = -1.39283297513 0.286900882281 y[1] (closed_form) = -1.39286566551 0.286903943134 absolute error = 3.283e-05 relative error = 0.002309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5017 2.614 h = 0.001 0.003 y[1] (numeric) = -1.39298638764 0.286958298989 y[1] (closed_form) = -1.39301918457 0.2869614262 absolute error = 3.295e-05 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5007 2.617 h = 0.0001 0.004 y[1] (numeric) = -1.39335081238 0.286919396898 y[1] (closed_form) = -1.39338338649 0.286922398163 absolute error = 3.271e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5006 2.621 h = 0.003 0.006 y[1] (numeric) = -1.39377617795 0.286736894023 y[1] (closed_form) = -1.39380856336 0.286740002899 absolute error = 3.253e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4976 2.627 h = 0.0001 0.005 y[1] (numeric) = -1.39454970211 0.286761448156 y[1] (closed_form) = -1.39458213077 0.286763608012 absolute error = 3.250e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1146.3MB, alloc=44.3MB, time=14.64 x[1] = -1.4975 2.632 h = 0.0001 0.003 y[1] (numeric) = -1.39507600554 0.286528136064 y[1] (closed_form) = -1.39510851573 0.286530905083 absolute error = 3.263e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.215 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4974 2.635 h = 0.001 0.001 y[1] (numeric) = -1.39539261313 0.286392410091 y[1] (closed_form) = -1.39542535759 0.286395229168 absolute error = 3.287e-05 relative error = 0.002307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4964 2.636 h = 0.001 0.003 y[1] (numeric) = -1.39554511147 0.28644742511 y[1] (closed_form) = -1.39557796207 0.28645030757 absolute error = 3.298e-05 relative error = 0.002315 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4954 2.639 h = 0.0001 0.004 y[1] (numeric) = -1.39590529742 0.286404635404 y[1] (closed_form) = -1.39593792629 0.286407397942 absolute error = 3.275e-05 relative error = 0.002298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.219 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4953 2.643 h = 0.003 0.006 y[1] (numeric) = -1.39632410304 0.28621902791 y[1] (closed_form) = -1.39635654808 0.28622189987 absolute error = 3.257e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4923 2.649 h = 0.0001 0.005 y[1] (numeric) = -1.39708988824 0.286234256669 y[1] (closed_form) = -1.39712235851 0.286236193374 absolute error = 3.253e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.224 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4922 2.654 h = 0.0001 0.003 y[1] (numeric) = -1.39760799106 0.285997221271 y[1] (closed_form) = -1.39764055271 0.28599975629 absolute error = 3.266e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4921 2.657 h = 0.001 0.001 y[1] (numeric) = -1.39791972566 0.285859214247 y[1] (closed_form) = -1.39795251889 0.285861794292 absolute error = 3.289e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4911 2.658 h = 0.0001 0.004 y[1] (numeric) = -1.39807127992 0.285911881121 y[1] (closed_form) = -1.39810417882 0.285914521644 absolute error = 3.300e-05 relative error = 0.002313 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.491 2.662 h = 0.003 0.006 y[1] (numeric) = -1.39848474885 0.285723869309 y[1] (closed_form) = -1.39851715909 0.285726564215 absolute error = 3.252e-05 relative error = 0.002278 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.233 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.488 2.668 h = 0.0001 0.005 y[1] (numeric) = -1.39924372504 0.285731391759 y[1] (closed_form) = -1.39927614573 0.285733163603 absolute error = 3.247e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.235 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4879 2.673 h = 0.0001 0.003 y[1] (numeric) = -1.3997547749 0.285491413458 y[1] (closed_form) = -1.39978729494 0.285493774146 absolute error = 3.261e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4878 2.676 h = 0.001 0.001 y[1] (numeric) = -1.4000623167 0.28535159935 y[1] (closed_form) = -1.40009506589 0.285354000901 absolute error = 3.284e-05 relative error = 0.002298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4868 2.677 h = 0.001 0.003 y[1] (numeric) = -1.40021300878 0.285402299335 y[1] (closed_form) = -1.40024586314 0.285404758929 absolute error = 3.295e-05 relative error = 0.002305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4858 2.68 h = 0.0001 0.004 y[1] (numeric) = -1.40056525155 0.285352689345 y[1] (closed_form) = -1.40059788664 0.285355039811 absolute error = 3.272e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.243 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4857 2.684 h = 0.003 0.006 y[1] (numeric) = -1.40097193817 0.285161823774 y[1] (closed_form) = -1.40100439836 0.285164286554 absolute error = 3.255e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4827 2.69 h = 0.0001 0.005 y[1] (numeric) = -1.40172309049 0.285160546387 y[1] (closed_form) = -1.40175554442 0.285162100166 absolute error = 3.249e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4826 2.695 h = 0.0001 0.003 y[1] (numeric) = -1.40222605455 0.284917223034 y[1] (closed_form) = -1.40225861682 0.284919354776 absolute error = 3.263e-05 relative error = 0.002281 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.252 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4825 2.698 h = 0.001 0.001 y[1] (numeric) = -1.40252878937 0.284775354215 y[1] (closed_form) = -1.40256157799 0.284777522103 absolute error = 3.286e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.254 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4815 2.699 h = 0.001 0.003 y[1] (numeric) = -1.40267848755 0.284823805061 y[1] (closed_form) = -1.40271138074 0.284826028219 absolute error = 3.297e-05 relative error = 0.002303 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.254 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4805 2.702 h = 0.0001 0.004 y[1] (numeric) = -1.40302648525 0.284770692789 y[1] (closed_form) = -1.40305916062 0.284772812413 absolute error = 3.274e-05 relative error = 0.002287 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4804 2.706 h = 0.003 0.006 y[1] (numeric) = -1.40342674858 0.284577188838 y[1] (closed_form) = -1.40345925375 0.284579422146 absolute error = 3.258e-05 relative error = 0.002275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4774 2.712 h = 0.0001 0.005 y[1] (numeric) = -1.40417004092 0.284567387147 y[1] (closed_form) = -1.40420252382 0.28456872564 absolute error = 3.251e-05 relative error = 0.002269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.261 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4773 2.717 h = 0.0001 0.003 y[1] (numeric) = -1.40466498497 0.284320914297 y[1] (closed_form) = -1.40469758474 0.284322819875 absolute error = 3.266e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4772 2.72 h = 0.001 0.001 y[1] (numeric) = -1.40496295079 0.284177107832 y[1] (closed_form) = -1.40499577403 0.284179045003 absolute error = 3.288e-05 relative error = 0.002294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.267 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4762 2.721 h = 0.001 0.003 y[1] (numeric) = -1.40511163059 0.284223361963 y[1] (closed_form) = -1.40514455776 0.284225351705 absolute error = 3.299e-05 relative error = 0.002301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.267 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4752 2.724 h = 0.0001 0.004 y[1] (numeric) = -1.40545538692 0.284166876885 y[1] (closed_form) = -1.40548809782 0.284168768535 absolute error = 3.277e-05 relative error = 0.002285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4751 2.728 h = 0.003 0.006 y[1] (numeric) = -1.40584927986 0.283970889037 y[1] (closed_form) = -1.40588182521 0.2839728956 absolute error = 3.261e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.272 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1192.8MB, alloc=44.3MB, time=15.22 x[1] = -1.4721 2.734 h = 0.0001 0.005 y[1] (numeric) = -1.40658468364 0.283952833824 y[1] (closed_form) = -1.40661719136 0.283953959857 absolute error = 3.253e-05 relative error = 0.002267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.275 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.472 2.739 h = 0.0001 0.003 y[1] (numeric) = -1.40707167689 0.283703401412 y[1] (closed_form) = -1.40710430958 0.283705083666 absolute error = 3.268e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4719 2.742 h = 0.001 0.001 y[1] (numeric) = -1.40736491374 0.283557771039 y[1] (closed_form) = -1.40739776698 0.283559480496 absolute error = 3.290e-05 relative error = 0.002291 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4709 2.743 h = 0.001 0.003 y[1] (numeric) = -1.40751255248 0.283601880402 y[1] (closed_form) = -1.40754550894 0.283603639802 absolute error = 3.300e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4699 2.746 h = 0.0001 0.004 y[1] (numeric) = -1.40785207423 0.283542149245 y[1] (closed_form) = -1.40788481608 0.283543815847 absolute error = 3.278e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.282 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4698 2.75 h = 0.003 0.006 y[1] (numeric) = -1.40823965237 0.283343827525 y[1] (closed_form) = -1.40827223324 0.283345610129 absolute error = 3.263e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4668 2.756 h = 0.0001 0.005 y[1] (numeric) = -1.40896714614 0.283317784706 y[1] (closed_form) = -1.40899967471 0.283318701141 absolute error = 3.254e-05 relative error = 0.002264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4667 2.761 h = 0.0001 0.003 y[1] (numeric) = -1.40944626099 0.283065577078 y[1] (closed_form) = -1.40947892219 0.283067038902 absolute error = 3.269e-05 relative error = 0.002274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4666 2.764 h = 0.001 0.001 y[1] (numeric) = -1.40973481082 0.282918233227 y[1] (closed_form) = -1.40976768961 0.282919718026 absolute error = 3.291e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.294 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4656 2.765 h = 0.0001 0.004 y[1] (numeric) = -1.40988138753 0.282960249248 y[1] (closed_form) = -1.40991436879 0.282961781431 absolute error = 3.302e-05 relative error = 0.002296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.294 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4655 2.769 h = 0.003 0.006 y[1] (numeric) = -1.41026384103 0.282760136935 y[1] (closed_form) = -1.41029637521 0.282761758598 absolute error = 3.257e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.297 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4625 2.775 h = 0.0001 0.005 y[1] (numeric) = -1.41098442326 0.282727522244 y[1] (closed_form) = -1.41101689318 0.282728290308 absolute error = 3.248e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4624 2.78 h = 0.0001 0.003 y[1] (numeric) = -1.41145678666 0.282473161813 y[1] (closed_form) = -1.41148939536 0.28247446589 absolute error = 3.263e-05 relative error = 0.002267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4623 2.783 h = 0.001 0.001 y[1] (numeric) = -1.41174131834 0.282324484101 y[1] (closed_form) = -1.41177414199 0.282325807674 absolute error = 3.285e-05 relative error = 0.002282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.306 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4613 2.784 h = 0.001 0.003 y[1] (numeric) = -1.41188694125 0.282364751954 y[1] (closed_form) = -1.41191986666 0.282366120777 absolute error = 3.295e-05 relative error = 0.002289 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.306 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4603 2.787 h = 0.0001 0.004 y[1] (numeric) = -1.41221857613 0.282299358498 y[1] (closed_form) = -1.41225129031 0.282300643955 absolute error = 3.274e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.308 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4602 2.791 h = 0.003 0.006 y[1] (numeric) = -1.41259453632 0.282097151682 y[1] (closed_form) = -1.41262709786 0.28209855477 absolute error = 3.259e-05 relative error = 0.002263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.311 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4572 2.797 h = 0.0001 0.005 y[1] (numeric) = -1.4133071896 0.282057030983 y[1] (closed_form) = -1.41333967339 0.282057594908 absolute error = 3.249e-05 relative error = 0.002254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.314 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4571 2.802 h = 0.0001 0.003 y[1] (numeric) = -1.41377181891 0.281800222722 y[1] (closed_form) = -1.41380444837 0.281801311918 absolute error = 3.265e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.317 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.457 2.805 h = 0.001 0.001 y[1] (numeric) = -1.41405174747 0.28165002776 y[1] (closed_form) = -1.41408458885 0.281651132517 absolute error = 3.286e-05 relative error = 0.002279 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.456 2.806 h = 0.001 0.003 y[1] (numeric) = -1.41419627429 0.281688296642 y[1] (closed_form) = -1.41422921661 0.281689444222 absolute error = 3.296e-05 relative error = 0.002286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.32 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.455 2.809 h = 0.0001 0.004 y[1] (numeric) = -1.41452371096 0.28162000408 y[1] (closed_form) = -1.41455644395 0.281621073164 absolute error = 3.275e-05 relative error = 0.002271 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4549 2.813 h = 0.003 0.006 y[1] (numeric) = -1.41489352988 0.281415867496 y[1] (closed_form) = -1.4149261146 0.281417054938 absolute error = 3.261e-05 relative error = 0.00226 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.325 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4519 2.819 h = 0.0001 0.005 y[1] (numeric) = -1.41559825137 0.28136849222 y[1] (closed_form) = -1.41563074546 0.281368854952 absolute error = 3.250e-05 relative error = 0.002251 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4518 2.824 h = 0.0001 0.003 y[1] (numeric) = -1.41605522659 0.281109404747 y[1] (closed_form) = -1.41608787287 0.281110282072 absolute error = 3.266e-05 relative error = 0.002262 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.331 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4517 2.827 h = 0.001 0.001 y[1] (numeric) = -1.41633059863 0.280957793649 y[1] (closed_form) = -1.41636345376 0.280958682749 absolute error = 3.287e-05 relative error = 0.002276 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4507 2.828 h = 0.001 0.003 y[1] (numeric) = -1.41647401297 0.280994113265 y[1] (closed_form) = -1.41650696817 0.280995042832 absolute error = 3.297e-05 relative error = 0.002283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4497 2.831 h = 0.0001 0.004 y[1] (numeric) = -1.41679726856 0.280923037505 y[1] (closed_form) = -1.4168300164 0.2809238933 absolute error = 3.276e-05 relative error = 0.002268 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.335 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1239.2MB, alloc=44.3MB, time=15.83 x[1] = -1.4496 2.835 h = 0.003 0.006 y[1] (numeric) = -1.41716101018 0.280717104287 y[1] (closed_form) = -1.41719361405 0.280718079051 absolute error = 3.262e-05 relative error = 0.002258 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.338 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4466 2.841 h = 0.0001 0.005 y[1] (numeric) = -1.41785780293 0.280662720706 y[1] (closed_form) = -1.41789030389 0.280662885209 absolute error = 3.250e-05 relative error = 0.002249 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4465 2.846 h = 0.0001 0.003 y[1] (numeric) = -1.41830720632 0.280401517276 y[1] (closed_form) = -1.4183398656 0.280402185766 absolute error = 3.267e-05 relative error = 0.002259 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.345 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4464 2.849 h = 0.001 0.001 y[1] (numeric) = -1.4185780698 0.280248587972 y[1] (closed_form) = -1.41861093484 0.280249264602 absolute error = 3.287e-05 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.348 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4454 2.85 h = 0.001 0.003 y[1] (numeric) = -1.41872035676 0.280283007373 y[1] (closed_form) = -1.41875332097 0.280283722182 absolute error = 3.297e-05 relative error = 0.00228 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.348 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4444 2.853 h = 0.0001 0.004 y[1] (numeric) = -1.41903945072 0.280209261514 y[1] (closed_form) = -1.41907220962 0.280209907131 absolute error = 3.277e-05 relative error = 0.002265 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.349 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4443 2.857 h = 0.003 0.006 y[1] (numeric) = -1.41939718073 0.280001660546 y[1] (closed_form) = -1.41942979988 0.280002425633 absolute error = 3.263e-05 relative error = 0.002255 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.353 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4413 2.863 h = 0.0001 0.005 y[1] (numeric) = -1.4200860534 0.279940509734 y[1] (closed_form) = -1.42011855796 0.279940478988 absolute error = 3.250e-05 relative error = 0.002246 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.355 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4412 2.868 h = 0.0001 0.003 y[1] (numeric) = -1.42052796923 0.279677348311 y[1] (closed_form) = -1.42056063786 0.279677811027 absolute error = 3.267e-05 relative error = 0.002257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.359 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4411 2.871 h = 0.001 0.001 y[1] (numeric) = -1.42079437335 0.279523195594 y[1] (closed_form) = -1.42082724464 0.279523662961 absolute error = 3.287e-05 relative error = 0.00227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.362 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4401 2.872 h = 0.001 0.003 y[1] (numeric) = -1.42093551946 0.279555763145 y[1] (closed_form) = -1.42096848898 0.279556266472 absolute error = 3.297e-05 relative error = 0.002277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.362 Order of pole (given) = 1 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations = 754 Total Elapsed Time = 15 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 15 Seconds > quit memory used=1258.4MB, alloc=44.3MB, time=16.06