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These are answers submitted by james_is_stuck

Thanks for the help.

I think I can accept that maple will want to display trig in weird ways, eg. 1-cos^2 instead of sin. I can always change it later


It works.

But, one more question.

My output know is giving me for the first fundamental form;

 I = dt2 + (1-cos^2(t)) ds2

I'd like it to simplify to sin^2.


Know, I can use simplify(I,1-cos^2=sin^2) but I am needing to write a procedure that takes in parametised three-dimensional graoh. Clearly not all of these will have the same problem, and some will have a different problem regarding simplifcation. If i could just sort out all the trig identities it would be something. Any ideas?

Also, does anyone know how to extract the coefficients of the dt and ds?





> X:=Vector(3,[sin(s)*cos(t),sin(s)*sin(t),cos(s)]);


Vector[column](%id = 135619380) (1)

> Xs:=Vector(3,[diff(X[1],s),diff(X[2],s),diff(X[3],s)]);

Vector[column](%id = 136007568) (2)

> Xt:=Vector(3,[diff(X[1],t),diff(X[2],t),diff(X[3],t)]);

Vector[column](%id = 136015428) (3)

> E:=Xs.Xs;

`+`(`*`(conjugate(`*`(cos(s), `*`(cos(t)))), `*`(cos(s), `*`(cos(t)))), `*`(conjugate(`*`(cos(s), `*`(sin(t)))), `*`(cos(s), `*`(sin(t)))), `*`(sin(conjugate(s)), `*`(sin(s)))) (4)

> E:=simplify(E,{sin(t)^2+cos(t)^2=1});

`+`(`*`(cos(conjugate(s)), `*`(cos(conjugate(t)), `*`(cos(s), `*`(cos(t))))), `*`(cos(conjugate(s)), `*`(sin(conjugate(t)), `*`(cos(s), `*`(sin(t))))), `*`(sin(conjugate(s)), `*`(sin(s)))) (5)


Ok, that didn't format as i meant it too, i'll try again later

[ posting edited to change Input format to Filtered HTML instead of Plain Text]


But I'm still having trouble, I think it might be to do with these lines above some of the sines and cosines. I have no idea what they are.

Here's my input and output;


                       Vector[column](%id = 136901428)
                       Vector[column](%id = 136946480)
  _____________                 _____________                    / __\      
  cos(s) cos(t) cos(s) cos(t) + cos(s) sin(t) cos(s) sin(t) + sin\s/ sin(s)

     /_\    /_\                    /_\    /_\                    /_\      
  cos\s/ cos\t/ cos(s) cos(t) + cos\s/ sin\t/ cos(s) sin(t) + sin\s/ sin(s)

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