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

AsymptoticSolve asymptotic approximation to algebraic equations

Discriminant  ▪  Resultant  ▪  GroebnerBasis  ▪  CylindricalDecomposition  ▪  ...

Finite Fields

Modulus specify a modulus

PolynomialMod reduce coefficients in a polynomial

IrreduciblePolynomialQ  ▪  PrimitivePolynomialQ

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  ▪  ...