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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, Mathematica 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.

ReferenceReference

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 ▪ ...