Module multivariate 

Multivariate polynomial factorization.

Currently implements bivariate factorization over $\mathbb{Z}$ and $\mathbb{F}_p$ via evaluation and Hensel lifting (Wang’s algorithm).

The bivariate polynomial is treated as a univariate polynomial in the main variable $x$ with coefficients in $\mathbb{Z}[y]$ (or $\mathbb{F}_p[y]$). It is evaluated at $y = \alpha$ to obtain a univariate image over the base domain, factored there, and the factors are lifted back to bivariate polynomials by linear Hensel lifting in the ideal $(y - \alpha)$.

References: Wang (1978), “An Improved Multivariate Polynomial Factoring Algorithm”; Geddes, Czapor, Labahn, Algorithms for Computer Algebra.

Functions

bivariate_factor_fp

Factor a bivariate polynomial over a prime finite field into irreducible factors with multiplicities.

bivariate_factor_z

Factor a bivariate polynomial over the integers into irreducible factors with multiplicities.

Type Aliases

FpMPoly

Bivariate polynomial over a prime finite field with lexicographic order.

FpPoly

Univariate polynomial over a prime finite field.

QPoly

Univariate polynomial over the rationals.

ZMPoly

Bivariate polynomial over the integers with lexicographic order.

ZPoly

Univariate polynomial over the integers.