Polynomial Factoring & Decomposition

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of sophisticated algorithms, carefully tuned at Wolfram Research over the course of two decades.

ReferenceReference

Factor fully factor any polynomial

FactorSquareFree pull out only factors that occur as squares or higher powers

FactorTerms pull out only overall numerical factors

FactorList, FactorSquareFreeList, FactorTermsList give lists of factors

IrreduciblePolynomialQ ▪ SquareFreeQ

Modulus specify a modulus for a finite field

Extension specify a general algebraic extension field

GaussianIntegers factor over Gaussian integers

Expand expand out polynomials

MonomialList the list of monomials in a specified ordering

Decompose decompose into a composition of polynomials

HornerForm rearrange a polynomial into Horner form

SymmetricReduction reduce a polynomial into a symmetric and nonsymmetric part

InterpolatingPolynomial construct a polynomial that goes through a list of points

Rational Functions

Apart ▪ Together ▪ ApartSquareFree

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