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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)
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- 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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