Editing List of polynomial topics

{{Short description|none}}
This is a '''list of [[polynomial]] topics''', by Wikipedia page. See also [[trigonometric polynomial]], [[list of algebraic geometry topics]].

== Terminology ==

*[[Degree of a polynomial|Degree]]: The maximum exponents among the monomials.
*[[Factorization of polynomials|Factor]]: An expression being multiplied.
*[[Linear factor]]: A factor of degree one.
*[[Coefficient]]: An expression multiplying one of the monomials of the polynomial.
*[[Root of a 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&nbsp;''p''.
*[[Graph of a function|Graphing]]
**End behaviour &ndash;
**[[Second derivative#Concavity|Concavity]] &ndash;
**Orientation &ndash;
**[[Tangent|Tangency point]] &ndash;
**[[Inflection point]] &ndash; 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|''n''th root]] (radical)
** [[Surd (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 (disambiguation)|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 (linear algebra)|Minimal polynomial]]
*[[Invariant polynomial]]

==Named polynomials and [[polynomial sequence]]s==

*[[Abel polynomials]]
*[[Actuarial polynomials]]
*[[Additive polynomial]]s
*[[All one polynomial]]s
*[[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 polynomial]]s
*[[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 polynomial]]s
*[[Shapiro polynomials]]
*[[Sheffer sequence]]
*[[Spread polynomials]]
*[[Tricomi–Carlitz polynomials]]
*[[Touchard polynomials]]
*[[Wilkinson's polynomial]]
*[[Wilson polynomials]]
*[[Zernike polynomials]]
**[[Pseudo-Zernike polynomials]]

==[[Knot polynomial]]s==

*[[Alexander polynomial]]
*[[HOMFLY polynomial]]
*[[Jones polynomial]]

==[[Algorithm]]s==
*[[Karatsuba multiplication]]
*[[Lenstra–Lenstra–Lovász lattice basis reduction algorithm]] (for polynomial factorization)
*[[Lindsey–Fox algorithm]]
*[[Schönhage–Strassen algorithm]]

== Other ==
[[Polynomial mapping]]

{{DEFAULTSORT:Polynomial Topics}}
[[Category:Mathematics-related lists]]
[[Category:Polynomials|*List]]