%% load file
load("glob.lf")?

add_vectors(C,A,B) -> vector(name=>C, x => (A.x + B.x),y => (A.y + B.y), z =>(A.z + B.z)).

subtract_vectors(C,A,B) -> vector(name=>C, x => (A.x - B.x),y => (A.y - B.y), z =>(A.z - B.z)).

cross_vectors(C,A,B) -> vector(name=>C, x => (A.y * B.z - A.z * B.x) , y => - (A.x * B.z - B.x * A.z), z => (A.x * B.y - A.y * B.x)).  

% I could not get dot to work as a function.

dot_vectors(X,A,B) :- 
    X = A.x * B.x + A.y * B.y + A.z + B.z.

magnitude(N,A) -> sqrt((A.x * A.x) + (A.y * A.y) + (A.z * A.z)).

direction_2d(N,A) -> my_arctan2(A.y, A.x).

add_and_write(X,N,A,B) :-
    X = add_vectors(N,A,B),write(X),  nl.

subtract_and_write(X,N,A,B) :-
    X = subtract_vectors(N,A,B),write(X),  nl.

cross_and_write(X,N,A,B) :-
    X = cross_vectors(N,A,B),write(X),  nl.

dot_and_write(X,N,A,B) :-
    dot_vectors(X,A,B), write(N,X).

magnitude_and_write(N,A) :-
    X = magnitude(N,A),write("magnitude of ",N," = ",X),  nl.

direction_2d_and_write_r(N,A) :-
  X = direction_2d(N,A),write("direction of ",N," = ",X),  nl.
 
global(a)?
global(b)?
global(c)?
global(d)?
global(e)?

prob05 :-
    a = vector(name => "a", x => 4.0, y => -3.0, z => 0.0),
    b = vector(name => "b", x => 6.0, y => 8.0, z => 0.0),

%   TROUBLE whe add following
%    f = vector(name => "f", x => 2.0, y => -3.0, z => 7.0),
%    g = vector(name => "g", x => 12.0, y => 45.0, z => -8.0),
%    h = vector(name => "h", x => -5.0, y => -3.0, z => 42.0),
    
    write(a),nl,
    write(b),nl,
    
    add_and_write(C,"c",a,b),
    subtract_and_write(D,"d",b,a),
    subtract_and_write(E,"e",a,b),
    
    magnitude_and_write("a",a),
    magnitude_and_write("b",b),
    magnitude_and_write("c",C),
    magnitude_and_write("d",D),
    magnitude_and_write("e",E),

    my_arctan2(Ra,a.y,a.x), write("Direction of a is ", Ra , " radians"),nl,
    my_arctan2(Rb,b.y,b.x), write("Direction of b is ", Rb , " radians"),nl,
    my_arctan2(Rc,C.y,C.x), write("Direction of c is ", Rc , " radians"),nl,
    my_arctan2(Rd,D.y,D.x), write("Direction of d is ", Rd , " radians"),nl,
    my_arctan2(Re,E.y,E.x), write("Direction of e is ", Re , " radians"),nl,

    my_arctan(PiD4, 1.0), 
    Da = 45.0 / PiD4 * Ra,
    Db = 45.0 / PiD4 * Rb,
    Dc = 45.0 / PiD4 * Rc,
    Dd = 45.0 / PiD4 * Rd,
    De = 45.0 / PiD4 * Re,

    write("Direction of a is ", Da , " degrees"),nl,
    write("Direction of b is ", Db , " degrees"),nl,
    write("Direction of c is ", Dc , " degrees"),nl,
    write("Direction of d is ", Dd , " degrees"),nl,
    write("Direction of e is ", De , " degrees"),nl,

    dot_and_write(Xd1,"a dot a = ",a,a),nl,
    dot_and_write(Xd2,"a dot b = ",a,b),nl,
    dot_and_write(Xd3,"b dot a = ",a,a),nl,
    dot_and_write(Xd4,"a dot C = ",a,C),nl,
    dot_and_write(Xd5,"D dot a = ",D,a),nl,
    dot_and_write(Xd6,"a dot E = ",a,E),nl,
    dot_and_write(Xd7,"E dot a = ",E,a),nl,

%    cross_and_write(CXd8,"f cross g = ",f,g),nl,
%    cross_and_write(CXd9,"f cross h = ",f,h),nl,
%    cross_and_write(CXd10,"g cross h = ",g,h),nl,
%   cross_and_write(CXd11,"g cross f = ",g,f),nl,
%    cross_and_write(CXd12,"h cross f = ",h,f),nl,
%    cross_and_write(CXd13,"h cross g = ",h,g),nl,

    cross_and_write(CXd1,"a cross a = ",a,a),nl,
    cross_and_write(CXd2,"a cross b = ",a,b),nl,
    cross_and_write(CXd3,"b cross a = ",a,a),nl,
    cross_and_write(CXd4,"a cross C = ",a,C),nl,
    cross_and_write(CXd5,"D cross a = ",D,a),nl,
    cross_and_write(CXd6,"a cross E = ",a,E),nl,
    cross_and_write(CXd7,"E cross a = ",E,a),nl.



prob05?