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7.7.13.0. facShift
Procedure from library ncfactor.lib (see ncfactor_lib).

Usage:
facShift(h); h a polynomial in the n'th shift algebra

Return:
list

Purpose:
compute all factorizations of a polynomial in the nth shift algebra

Theory:
h is mapped to the $n$th Weyl algebra and then factorized there. The factorizations are mapped back (S_n in subalgebra of Weyl algebra).

Assume:
basering is the nth shift algebra

Note:
Every entry of the output list is a list with factors for one possible factorization.

Example:
 
LIB "ncfactor.lib";
ring R = 0,(x1,x2,s1,s2),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,s1,0,
0,0,0,s2,
-s1,0,0,0,
0,-s2,0,0;
def r = nc_algebra(C,D);
setring(r);
poly h = x1*(x1+1)*s1^2-2*x1*(x1+100)*s1+(x1+99)*(x1+100);
facShift(h);
==> [1]:
==>    [1]:
==>       1
==>    [2]:
==>       x1*s1-x1+s1-100
==>    [3]:
==>       x1*s1-x1-s1-99
==> [2]:
==>    [1]:
==>       1
==>    [2]:
==>       x1*s1-x1-100
==>    [3]:
==>       x1*s1-x1-99
==> [3]:
==>    [1]:
==>       1
==>    [2]:
==>       x1*s1-x1-99
==>    [3]:
==>       x1*s1-x1-100
See also: facFirstWeyl; facSubWeyl; testNCfac.