List of polynomial topics

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

Basics

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

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

*Binomial theorem
*Blossom (functional)
*Root (mathematics)
*Radical (mathematics)
**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
*Quadratic equation
**Completing the square
*Cubic function
*Quartic function
*Quintic equation
**Abel-Ruffini theorem
**Quintic function
**Bring radical
*Fundamental theorem of algebra
*Hurwitz polynomial
*Tschirnhaus transformation
*Galois theory
*Discriminant of a polynomial
**Resultant
*Elimination theory
**Gröbner basis
*Sturm's theorem
*Descartes' rule of signs

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

*Additive polynomials
*Appell sequence
*Askey–Wilson polynomials
*Bell polynomials
*Bernoulli polynomials
*Binomial type
*Caloric polynomial
*Charlier polynomials
*Chebyshev polynomials
*Ehrhart polynomial
*Fibonacci polynomials
*Hahn polynomials
*Heat polynomial — see caloric polynomial
*Hermite polynomials
*Kravchuk polynomials
*Laguerre polynomials
*Legendre polynomials
**Spherical harmonic
*Meixner polynomials
*Newton polynomial
*Orthogonal polynomials
*Racah polynomials
*Rook polynomial
*Schur polynomials
*Sheffer sequence
*Touchard polynomials
*Wilkinson's polynomial
*Wilson polynomials

Knot polynomials

*Alexander polynomial
*HOMFLY polynomial
*Jones polynomial

Algorithms

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