Examples
User documentation
There are several functions for computing a factorization of a ring
element: the factorizations produced have different properties (see below).
For each function, the result is an object of type factorization; see
the corresponding manual page for accessor functions into this type.
factor(f)factorization into irreduciblesSqFreeFactor(f)factorization into coprime squarefree factors (NB may not be the coarsest such factorization)ContentFreeFactor(f)polynomial factorization into (coprime) content-free factors
NOTE The irreducible factorization of a polynomial with rational coefficients produces factors with integer coefficients (and integer content = 1) having positive leading coefficient. The remaining factor is the unique rational number (actually a polynomial of degree 0) which makes the factorization correct.
Maintainer documentation
SqFreeFactor is new code; should be reasonably clean and efficient.
Originally written by d'Ali` but then considerably modified by JAA.
The code is based on Bernardin's paper "On square-free factorization
of multivariate polynomials over a finite field" in Theoretical Computer
Science (special volume on algebra) Volume 187 Issue 1-2, Nov. 15, 1997
Pages 105 - 116.
ContentFreeFactor is a fairly simplistic recursive method; most of the
work is done by ContentFreeFactorLoop.
factor is still only a prototype -- just uses old C4 code to do the work.
Bugs, shortcomings and other ideas
factor still only a prototype -- just uses old C4 code to do the work.
Main changes
2014
- september: updated doc (new fns have been there for quite a while) 2013
- aprile (v0.9953): first doc