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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


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            User manual for Singular version 3-0-1, October 2005, generated by texi2html.