D.7.5.2 Factor

Procedure from library zeroset.lib (see zeroset_lib).

Usage:

Factor(f); where f is a polynomial

Purpose:

compute the factorization of the squarefree poly f over Q(a)[t]

Return:

list with two entries

_[1] = factors (monic), first entry is the leading coefficient _[2] = multiplicities (not yet implemented)

Assume:

basering must be the univariate polynomial ring over a field, which is Q or a simple extension of Q given by a minpoly.

Note:

if basering = Q[t] then this is the built-in factorize

Example:

LIB "zeroset.lib";
ring R = (0,a), x, lp;
minpoly = a2+1;
poly f =  x4 - 1;
list fl = Factor(f);
fl;
→ [1]:
→    _[1]=1
→    _[2]=(40a+60)*x+(40a+60)
→    _[3]=(1/65a-29/130)*x+(-1/65a+29/130)
→    _[4]=(4a)*x+4
→    _[5]=(7/520a+1/130)*x+(1/130a-7/520)
→ [2]:
→    _[1]=1
→    _[2]=1
→    _[3]=1
→    _[4]=1
→    _[5]=1
fl[1][1]*fl[1][2]*fl[1][3]*fl[1][4]*fl[1][5] - f;
→ 0