Originally Posted by

**Deveno** is -x1^2 - x2^2 of either form (a+b)^2 or (a-b)^2? no, it is not.

however: (a+b)^2 - (a-b)^2 = 4ab, that is:

ab = ((a+b)/2)^2 - ((a-b)/2)^2 and these terms are of the required form (using a' = a/2, b' = b/2).

if you have a term like:

kab, then you use a' = a√k/2, b' = b√k/2.

your way gves you too many variables to be able to come up with a 4x4 matrix.

the goal is to replace each variable x1,x2,x3,x4 with some other variables u1,u2,u3,u4,

so that q(u1,u2,u3,u4) = ±(c1u1)^2 ± (c2u2)^2 ± (c3u3)^3 ± (c4u4)^2, so that the matrix for q

in the variables (u1,u2,u3,u4) is diag(±c1,±c2,±c3,±c4).