D.7.5.6 SQFRNorm

Procedure from library zeroset.lib (see zeroset_lib).

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]

Example:

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