D.8.6.4 sqfrNorm

Usage:

sqfrNorm(f); where f is a polynomial

Purpose:

compute the norm of the squarefree polynomial f in Q(a)[x].

Return:

list with 3 entries

_[1] = squarefree norm of g (poly) _[2] = g (= f(x - s*a)) (poly) _[3] = s (int)

Assume:

f must be squarefree, basering = Q(a)[x] and minpoly != 0.

Note:

the norm is an element of Q[x]

LIB "zeroset.lib";
ring R = (0,a), x, lp;
minpoly = a2+1;
poly f =  x4 - 2*x + 1;
sqfrNorm(f);
==> [1]:
==>    x8+4*x6-4*x5+8*x4+8*x3-4*x2+8*x+8
==> [2]:
==>    x4+(-4a)*x3-6*x2+(4a-2)*x+(2a+2)
==> [3]:
==>    1