Singular

7.5.12.0. facWeyl

Usage:

facWeyl(h); h a polynomial in the nth Weyl algebra

Return:

list

Purpose:

compute all factorizations of a polynomial in the first Weyl algebra

Theory:

Implements the new algorithm by A. Heinle and V. Levandovskyy, see the thesis of A. Heinle

Assume:

basering is the nth Weyl algebra, where n in NN.

Note:

Every entry of the output list is a list with factors for one possible factorization. The first factor is always a constant (1, if no nontrivial constant could be excluded).

LIB "ncfactor.lib";
ring R = 0,(x1,x2,d1,d2),dp;
matrix C[4][4] = 1,1,1,1,
1,1,1,1,
1,1,1,1,
1,1,1,1;
matrix D[4][4] = 0,0,1,0,
0,0,0,1,
-1,0,0,0,
0,-1,0,0;
def r = nc_algebra(C,D);
setring(r);
poly h = (d1+1)^2*(d1 + x1*d2);
facWeyl(h);
==> [1]:
==>    [1]:
==> 1
==>    [2]:
==>       d1+1
==>    [3]:
==>       d1+1
==>    [4]:
==>       x1*d2+d1
==> [2]:
==>    [1]:
==> 1
==>    [2]:
==>       x1*d1*d2+d1^2+x1*d2+d1+2*d2
==>    [3]:
==>       d1+1