Polynomial Algebra

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, the Wolfram Language has the world's broadest and deepest integrated web of polynomial algorithms. Carefully tuned strategies automatically select optimal algorithms, allowing large-scale polynomial algebra to become a routine part of many types of computations.


Polynomial Elements

Coefficient  ▪  CoefficientList  ▪  CoefficientRules  ▪  Exponent  ▪  Variables

Basic Structural Operations

Expand  ▪  Collect  ▪  MonomialList

Polynomial Factoring & Decomposition »

Factor  ▪  FactorList  ▪  Decompose  ▪  SymmetricReduction  ▪  ...

Polynomial Division »

PolynomialQuotient  ▪  PolynomialGCD  ▪  PolynomialReduce  ▪  ...

Polynomial Systems »

Solve find generic solutions for variables

Eliminate eliminate variables between equations

Resolve eliminate general quantifiers

Reduce reduce systems of equations and inequalities to canonical form

Discriminant  ▪  Resultant  ▪  GroebnerBasis  ▪  CylindricalDecomposition  ▪  ...

Finite Fields

Modulus specify a modulus

PolynomialMod reduce coefficients in a polynomial

Algebraic Number Fields »

GaussianIntegers do operations over Gaussian integers

Extension specify a general algebraic extension field

Root general representation of a polynomial root

MinimalPolynomial minimal polynomial for a general algebraic number

RootSum  ▪  RootReduce  ▪  ToRadicals  ▪  Cyclotomic  ▪  SymmetricPolynomial  ▪  ...