D.11.4.7 magnitude

Usage:

magnitude(P); P a poly

Return:

poly

Purpose:

compute the square of the magnitude of a complex expression

Assume:

i is the variable of a basering

LIB "findifs.lib";
ring r = (0,d),(g,i,sin,cos),dp;
poly P = d*i*sin - g*cos +d^2*i;
NF( magnitude(P), std(i^2+1) );
==> g^2*cos^2+(d^2)*sin^2+(2*d^3)*sin+(d^4)