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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
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- 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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