(* open TextIO; *)
open Real; 
open Real.Math; 
(* open String; *)
   
   val a = { 
   name = "a",
   x = valOf(Real.fromString("4.0")) , 
   y = valOf(Real.fromString("-3.0")) , 
   z = valOf(Real.fromString("0.0"))
   };
   val b = { 
   name = "b",
   x = valOf(Real.fromString("6.0")) , 
   y = valOf(Real.fromString("8.0")) , 
   z = valOf(Real.fromString("0.0"))
   };
   val f = { 
   name = "f",
   x = valOf(Real.fromString("2.0")) , 
   y = valOf(Real.fromString("-3.0")) , 
   z = valOf(Real.fromString("7.0"))
   };
   val g = { 
   name = "g",
   x = valOf(Real.fromString("12.0")) , 
   y = valOf(Real.fromString("45.0")) , 
   z = valOf(Real.fromString("-8.0"))
   };
   val h = { 
   name = "h",
   x = valOf(Real.fromString("-5.0")) , 
   y = valOf(Real.fromString("-3.0")) , 
   z = valOf(Real.fromString("42.0"))
   };

   fun add(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real},b : {name: string, x: Real.real, y: Real.real, z: Real.real}) = 
   { 
   name = name,
   x = (#x(a) + #x(b)), 
   y = (#y(a) + #y(b)),
   z = (#z(a) + #z(b)) 
   };
   
   fun subtract(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real},b : {name: string, x: Real.real, y: Real.real, z: Real.real}) = { 
   name = name,
   x = (#x(a) - #x(b)), 
   y = (#y(a) - #y(b)),
   z = (#z(a) - #z(b)) 
   };
  
   fun cross(name: string, a : { name: string, x: Real.real, y: Real.real, z: Real.real},b : {name: string, x: Real.real, y: Real.real, z: Real.real}) = { 
   name = name,
   x = #y(a) * #z(b) - #y(b) * #x(a),
   y = #x(b) * #z(a) - #x(a) * #z(b),
   z = #x(a) * #y(b) - #x(b) * #y(a)
   };
  
   fun dot(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real},b : {name: string, x: Real.real, y: Real.real, z: Real.real}) = {
   out = { 
   name = name,
   dot = (#x(a) * #x(b)) + (#y(a) * #y(b)) + (#z(a) + #z(b)) 
   }};
   
   fun magnitude(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real}) = {
   out = { 
   name = name,
   mag = sqrt((#x(a) * #x(a)) + (#y(a) * #y(a)) + (#z(a) + #z(a))) 
   }};

   fun direction_r(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real}) = {
   out = { 
   name = name,
   d_rad = atan2(#y(a), #x(a))
   }};

   fun direction_d(name: string, a :  {name: string, x: Real.real, y: Real.real, z: Real.real}) = {
   out = { 
   name = name,
   d_deg = atan2(#y(a), #x(a)) * 90.0 / asin(1.0)
   }};





   
val c = add("a+b",a, b); 

val d = subtract("b-a",b, a); 

val e = subtract("a-b",a, b); 

val ma = magnitude("ma",a);
val mb = magnitude("mb",b);
val mc = magnitude("mc",c);
val md = magnitude("md",d);
val me = magnitude("me",e);

val dar = direction_r("da_r",a);
val dbr = direction_r("db_r",b);
val dcr = direction_r("dc_r",c);
val ddr = direction_r("dd_r",d);
val der = direction_r("de_r",e);

val dad = direction_d("da_d",a);
val dbd = direction_d("db_d",b);
val dcd = direction_d("dc_d",c);
val ddd = direction_d("dd_d",d);
val ded = direction_d("de_d",e);

val ada = dot("a.a",a,a);
val adb = dot("a.b",a,b);
val bda = dot("b.a",b,a);
val adc = dot("a.c",a,c);
val dda = dot("d.a",d,a);
val ade = dot("a.e",a,e);
val eda = dot("e.a",e,a);

val aca = cross("aca",a,a);
val acb = cross("acb",a,b);
val bca = cross("bca",b,a);
val acc = cross("acc",a,c);
val dca = cross("dca",d,a);
val ace = cross("ace",a,e);
val eca = cross("eca",e,a);

val fcg = cross("fcg",f,g);
val fcg = cross("fch",f,h);
val fcg = cross("gch",g,g);
val fcg = cross("gcf",g,f);
val fcg = cross("hcf",h,f);
val fcg = cross("hcg",h,g);