Singular

7.5.12.0. homogfacNthQWeyl

Usage:

homogfacNthQWeyl(h); h is a homogeneous polynomial in the n'th q-Weyl algebra with respect to the weight vector
@ [-1,...,-1,1,...,1].
@ \__ __/ \__ __/ @ \/ \/ @ n/2 n/2

Return:

list

Purpose:

Computes a factorization of a homogeneous polynomial h in the n'th q-Weyl algebra

Theory:

homogfacNthQWeyl returns a list with a factorization of the given, [-1,1]-homogeneous polynomial. For every i in 1..n: If the degree of the polynomial in [d_i,x_i] is k with k positive, the last entries in the output list are the second variable. If k is positive, the last k entries will be x_i. The other entries will be irreducible polynomials of degree zero or 1 resp. -1. resp. other variables

General assumptions:

- The basering is the nth Weyl algebra and has the form, that the first n variables represent x1, ..., xn, and the second n variables do represent the d1, ..., dn.
- We have n parameters q_1,..., q_n given.

LIB "ncfactor.lib";
ring R = (0,q1,q2,q3),(x1,x2,x3,d1,d2,d3),dp;
matrix C[6][6] = 1,1,1,q1,1,1,
1,1,1,1,q2,1,
1,1,1,1,1,q3,
1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1;
matrix D[6][6] = 0,0,0,1,0,0,
0,0,0,0,1,0,
0,0,0,0,0,1,
-1,0,0,0,0,0,
0,-1,0,0,0,0,
0,0,-1,0,0,0;
def r = nc_algebra(C,D);
setring(r);
poly h =x1*x2^2*x3^3*d1*d2^2+x2*x3^3*d2;
homogfacNthQWeyl(h);
==> [1]:
==>    1/(q2)
==> [2]:
==>    x1*x2*d1*d2-x1*d1+(q2)
==> [3]:
==>    x2
==> [4]:
==>    d2
==> [5]:
==>    x3
==> [6]:
==>    x3
==> [7]:
==>    x3