Assuming unit vector?

• Subject: Assuming unit vector?
• From: Iai Masafumi ax
• Date: Thu, 07 Mar 2013 08:24:58 +0900

I want to know how to let Maxima know a relationship,
bx^2+by^^2+bz^2==1, when simplifying formula.

My calculation is below. The resulting matrix A has its (2,1) element being
(by*bz^2+by^3+bx^2*by)/bx
and its (2,2) element being
-bz^2-by^2-bx^2

I need them to be simplified to by/bx  and -1, respectively.


S : matrix(
 [0, bz, -by],
 [-bz, 0, bx],
 [by, -bx, 0]
);
e1 : [-by/bx, 1, 0];
e2 : [-bz, -by*bz/bx, (bx^2+by^2)/bx];
C : matrix(
 e1,
 e2
 );
A : ratsimp(C . S,bx^2+by^2+bz^2);


Thanks,
Iai

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