Singular Manual: homogfacNthQWeyl

  | ##### 7.7.13.0. homogfacNthQWeyl Procedure from library `ncfactor.lib` (see ncfactor_lib). 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. Example:
    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
See also: homogfacFirstQWeyl; homogfacFirstQWeyl_all; homogfacNthQWeyl_all.

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