AngouriMath

Navigation

Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug ~~Donate~~ Contacts

FactorAfterTakingOutTheContent(AngouriMath.Entity,AngouriMath.Entity.Variable)

Method (no overloads)

Summary

The factorisation of a polynomial whose coefficients in variable are themselves polynomials, where taking out their common divisor leaves something
this can factor — or null where it does not.

Remarks

PolynomialFactorization works over ℚ, so a coefficient that is not a
rational number stops it before it starts and every polynomial in more than one
variable was refused. Some of them do not need factorising over a bigger ring at
all: x * y + y is y times something univariate, and only the y was in the way.
So the content in variable — the greatest common divisor of the
coefficients, which is a polynomial in the other variables — is taken out first,
using the same multivariate machinery Gcd(AngouriMath.Entity,AngouriMath.Entity) is built from, and what
remains goes down the ordinary path. Where the content is a constant that path
has nothing to offer, and KroneckerFactorization answers instead —
x ^ 2 - y ^ 2 is (x + y) * (x - y), which is a factorisation over
ℚ(y) reached by substitution rather than by lifting.

AngouriMath

Table of contents

AngouriMath

FactorAfterTakingOutTheContent​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

FactorAfterTakingOutTheContent(AngouriMath.Entity,AngouriMath.Entity.Variable)