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?

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]

Thanks

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;

Xs:=Vector(3,[diff(X[1],s),diff(X[2],s),diff(X[3],s)]);
                       Vector[column](%id = 136901428)
Xt:=Vector(3,[diff(X[1],t),diff(X[2],t),diff(X[3],t)]);
                       Vector[column](%id = 136946480)
E:=Xs.Xs;
  _____________                 _____________                    / __\      
  cos(s) cos(t) cos(s) cos(t) + cos(s) sin(t) cos(s) sin(t) + sin\s/ sin(s)

E:=simplify(E,{sin(t)^2+cos(t)^2=1});
     /_\    /_\                    /_\    /_\                    /_\      
  cos\s/ cos\t/ cos(s) cos(t) + cos\s/ sin\t/ cos(s) sin(t) + sin\s/ sin(s)