Singular Manual: ncfactor

| ##### 7.7.13.0. ncfactor Procedure from library `ncfactor.lib` (see ncfactor_lib). Usage: ncfactor(h); h is a polynomial in a non-commutative polynomial algebra over a field k. Return: list(list) Purpose: Compute all factorizations of h. Theory: Implements an ansatz-driven factorization method as outlined by Bell, Heinle and Levandovskyy in "On Noncommutative Finite Factorization Domains". Assume: - k is a ring, such that factorize can factor any univariate and multivariate commutative polynomial over k. - There exists at least one variable in the ring. 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). Example:
    LIB "ncfactor.lib";
    def R = makeUsl2();
    setring(R);
    poly p = e^3*f+e^2*f^2-e^3+e^2*f+2*e*f^2-3*e^2*h-2*e*f*h-8*e^2
    +e*f+f^2-4*e*h-2*f*h-7*e+f-h;
    ncfactor(p);
    ==> [1]:
    ==>    [1]:
    ==>       1
    ==>    [2]:
    ==>       e+1
    ==>    [3]:
    ==>       ef-e+f-2h-3
    ==>    [4]:
    ==>       e+f
    ==> [2]:
    ==>    [1]:
    ==>       1
    ==>    [2]:
    ==>       e2f+ef2-e2+f2-2eh-3e-f-2h
    ==>    [3]:
    ==>       e+1
See also: facSubWeyl; facWeyl; testNCfac.

User manual for Singular version 4-0-3p3, 2016, generated by texi2html.