List of polynomial topics

This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.

Terminology

 * Degree: The maximum exponents among the monomials.
 * Factor: An expression being multiplied.
 * Linear factor: A factor of degree one.
 * Coefficient: An expression multiplying one of the monomials of the polynomial.
 * Root (or zero) of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 0 are called roots (or zeroes) of the polynomial p.
 * Graphing
 * End behaviour –
 * Concavity –
 * Orientation –
 * Tangency point –
 * Inflection point – Point where concavity changes.

Basics

 * Polynomial
 * Coefficient
 * Monomial
 * Polynomial long division
 * Synthetic division
 * Polynomial factorization
 * Rational function
 * Partial fraction
 * Partial fraction decomposition over R
 * Vieta's formulas
 * Integer-valued polynomial
 * Algebraic equation
 * Factor theorem
 * Polynomial remainder theorem

Elementary abstract algebra

 * See also Theory of equations below.


 * Polynomial ring
 * Greatest common divisior of two polynomials
 * Symmetric function
 * Homogeneous polynomial
 * Polynomial SOS (sum of squares)

Theory of equations

 * Polynomial family
 * Quadratic function
 * Cubic function
 * Quartic function
 * Quintic function
 * Sextic function
 * Septic function
 * Octic function
 * Completing the square
 * Abel–Ruffini theorem
 * Bring radical
 * Binomial theorem
 * Blossom (functional)
 * Root of a function
 * nth root (radical)
 * Surd
 * Square root
 * Methods of computing square roots
 * Cube root
 * Root of unity
 * Constructible number
 * Complex conjugate root theorem
 * Algebraic element
 * Horner scheme
 * Rational root theorem
 * Gauss's lemma (polynomial)
 * Irreducible polynomial
 * Eisenstein's criterion
 * Primitive polynomial
 * Fundamental theorem of algebra
 * Hurwitz polynomial
 * Polynomial transformation
 * Tschirnhaus transformation
 * Galois theory
 * Discriminant of a polynomial
 * Resultant
 * Elimination theory
 * Gröbner basis
 * Regular chain
 * Triangular decomposition
 * Sturm's theorem
 * Descartes' rule of signs
 * Carlitz–Wan conjecture
 * Polynomial decomposition, factorization under functional composition

Calculus with polynomials

 * Delta operator
 * Bernstein–Sato polynomial

Polynomial interpolation

 * Lagrange polynomial
 * Runge's phenomenon
 * Spline (mathematics)

Weierstrass approximation theorem

 * Bernstein polynomial

Linear algebra

 * Characteristic polynomial
 * Minimal polynomial
 * Invariant polynomial

Named polynomials and polynomial sequences

 * Abel polynomials
 * Actuarial polynomials
 * Additive polynomials
 * All one polynomials
 * Appell sequence
 * Askey–Wilson polynomials
 * Bell polynomials
 * Bernoulli polynomials
 * Bernstein polynomial
 * Bessel polynomials
 * Binomial type
 * Brahmagupta polynomials
 * Caloric polynomial
 * Charlier polynomials
 * Chebyshev polynomials
 * Chihara–Ismail polynomials
 * Cyclotomic polynomials
 * Dickson polynomial
 * Ehrhart polynomial
 * Exponential polynomials
 * Favard's theorem
 * Fibonacci polynomials
 * Gegenbauer polynomials
 * Hahn polynomials
 * Hall–Littlewood polynomials
 * Heat polynomial &mdash; see caloric polynomial
 * Heckman–Opdam polynomials
 * Hermite polynomials
 * Hurwitz polynomial
 * Jack function
 * Jacobi polynomials
 * Koornwinder polynomials
 * Kostka polynomial
 * Kravchuk polynomials
 * Laguerre polynomials
 * Laurent polynomial
 * Linearised polynomial
 * Littlewood polynomial
 * Legendre polynomials
 * Associated Legendre polynomials
 * Spherical harmonic
 * Lucas polynomials
 * Macdonald polynomials
 * Meixner polynomials
 * Necklace polynomial
 * Newton polynomial
 * Orthogonal polynomials
 * Orthogonal polynomials on the unit circle
 * Permutation polynomial
 * Racah polynomials
 * Rogers polynomials
 * Rogers–Szegő polynomials
 * Rook polynomial
 * Schur polynomials
 * Shapiro polynomials
 * Sheffer sequence
 * Spread polynomials
 * Tricomi–Carlitz polynomials
 * Touchard polynomials
 * Wilkinson's polynomial
 * Wilson polynomials
 * Zernike polynomials
 * Pseudo-Zernike polynomials

Knot polynomials

 * Alexander polynomial
 * HOMFLY polynomial
 * Jones polynomial

Algorithms

 * Karatsuba multiplication
 * Lenstra–Lenstra–Lovász lattice basis reduction algorithm (for polynomial factorization)
 * Lindsey–Fox algorithm
 * Schönhage–Strassen algorithm

Other
Polynomial mapping