Singular

7.7.5.0. bFactor

Usage:

bFactor(f); f poly

Return:

list of ideal and intvec and possibly a string

Purpose:

tries to compute the roots of a univariate poly f

Note:

The output list consists of two or three entries:
roots of f as an ideal, their multiplicities as intvec, and,
if present, a third one being the product of all irreducible factors
of degree greater than one, given as string.
If f is the zero polynomial or if f has no roots in the ground field,
this is encoded as root 0 with multiplicity 0.

Display:

If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.

LIB "dmodapp.lib";
ring r = 0,(x,y),dp;
bFactor((x^2-1)^2);
==> [1]:
==>    _[1]=1
==>    _[2]=-1
==> [2]:
==>    2,2
bFactor((x^2+1)^2);
==> [1]:
==>    _[1]=0
==> [2]:
==>    0
==> [3]:
==>    x4+2x2+1
bFactor((y^2+1/2)*(y+9)*(y-7));
==> [1]:
==>    _[1]=7
==>    _[2]=-9
==> [2]:
==>    1,1
==> [3]:
==>    2y2+1
bFactor(1);
==> [1]:
==>    _[1]=0
==> [2]:
==>    0
==> [3]:
==>    1
bFactor(0);
==> [1]:
==>    _[1]=0
==> [2]:
==>    0
==> [3]:
==>    0