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  • Monogenic field
    ''a'' such that the [[ring of integers]] ''O''<sub>''K''</sub> is a polynomial ring '''Z'''[''a'']. The powers of such a element ''a'' constitute a '''po ...lynomial|discriminant]] of the [[Minimal polynomial (field theory)|minimal polynomial]] of α.
    1 KB (208 words) - 16:47, 17 December 2008
  • Discriminant of a polynomial
    ...ant of a polynomial''' is an invariant which determines whether or not a [[polynomial]] has repeated roots. Given a polynomial
    1 KB (163 words) - 18:01, 21 December 2008
  • Minimal polynomial/Definition
    The monic polynomial of least degree which a square matrix or endomorphism satisfies.
    121 bytes (16 words) - 17:52, 11 December 2008
  • Fibonacci polynomials/Definition
    Polynomial sequence which can be considered as a generalisation of the Fibonacci numbe
    126 bytes (16 words) - 07:19, 4 September 2009
  • Separable element/Definition
    An element of a field extension for which the minimal polynomial has distinct roots.
    120 bytes (17 words) - 04:11, 20 December 2008
  • Algebra/Related Articles
    {{r|Cyclotomic polynomial}} {{r|Discriminant of a polynomial}}
    2 KB (247 words) - 06:00, 7 November 2010
  • Normal extension/Definition
    A field extension which contains all the roots of an irreducible polynomial if it contains one such root.
    141 bytes (21 words) - 13:16, 21 December 2008
  • Hall-Littlewood polynomial/External Links
    *{{MathWorld |title=Hall-Littlewood Polynomial |urlname=Hall-LittlewoodPolynomial}}
    97 bytes (7 words) - 04:38, 14 September 2013
  • Cyclotomic polynomial/Definition
    A polynomial whose roots are primitive roots of unity.
    90 bytes (12 words) - 16:50, 8 December 2008
  • Transcendental number
    ...e coefficients are [[integer]]s, or, equivalently, it is not a root of any polynomial whose coefficients are [[rational number|rational]]. ...</math> is irrational. However it is algebraic, since it is a root of the polynomial <math> x^2-2 </math>. It is thus irrational but not transcendental.
    875 bytes (130 words) - 12:27, 8 May 2008
  • Splitting field/Definition
    A field extension generated by the roots of a polynomial.
    93 bytes (13 words) - 13:13, 21 December 2008
  • Littlewood polynomial
    In [[mathematics]], a '''Littlewood polynomial''' is a [[polynomial]] all of whose coefficients are +1 or &minus;1. '''Littlewood's problem''' asks how large the values of such a polynomial must be on the [[unit circle]] in the [[complex plane]]. The answer to thi
    2 KB (230 words) - 16:13, 27 October 2008
  • Polynomial equation/Definition
    An equation in which a polynomial in one or more variables is set equal to zero.
    117 bytes (19 words) - 10:56, 4 September 2009
  • Monogenic field/Definition
    An algebraic number field for which the ring of integers is a polynomial ring.
    114 bytes (17 words) - 17:08, 28 October 2008
  • Characteristic polynomial/Definition
    The polynomial attached to a square matrix or endomorphism det(A-XI)=0.
    107 bytes (14 words) - 17:55, 11 December 2008
  • Cubic equation/Definition
    A polynomial equation with of degree 3 (i.e., ''x''<sup>3</sup>+''px''<sup>2</sup>+''qx'
    132 bytes (19 words) - 17:35, 1 January 2010
  • Fundamental Theorem of Algebra/Definition
    Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a
    144 bytes (20 words) - 02:59, 15 November 2008
  • Characteristic polynomial/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Characteristic polynomial]]. Needs checking by a human. {{r|Minimal polynomial}}
    553 bytes (67 words) - 11:46, 11 January 2010
  • Algebraic number/Definition
    A complex number that is a root of a polynomial with rational coefficients.
    111 bytes (16 words) - 16:34, 13 July 2008
  • Polynomial equation/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Polynomial equation]]. Needs checking by a human. {{r|Polynomial}}
    565 bytes (72 words) - 19:39, 11 January 2010
  • Algebraic independence/Definition
    ...property of elements of an extension field which satisfy only the trivial polynomial relation.
    134 bytes (18 words) - 15:49, 23 December 2008
  • Galois theory/Definition
    Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions.
    158 bytes (20 words) - 08:08, 4 September 2009
  • Artin-Schreier polynomial/Definition
    A type of polynomial whose roots generate extensions of degree ''p'' in characteristic ''p''.
    129 bytes (17 words) - 02:24, 5 December 2008
  • Transcendental number/Definition
    A number which is not algebraic: that is, does not satisfy any polynomial with integer or rational coefficients.
    148 bytes (21 words) - 15:21, 31 October 2008
  • Content (algebra)/Definition
    The highest common factor of the coefficients of a polynomial.
    98 bytes (13 words) - 15:03, 29 October 2008
  • Polynomial equation
    ...and where one is interested in finding [[solution (equation)|solution]]s. Polynomial equations occur frequently in applications -- typically [[linear equation|l ...[[polynonial equation/Advanced|"Advanced"]] subpage for information about polynomial equations with other types of coefficients.
    4 KB (647 words) - 16:35, 22 December 2008
  • Artin-Schreier polynomial
    In [[field theory]], an '''Artin-Schreier polynomial''' is a polynomial whose roots are used to generate [[field extension]]s of [[prime number|pri An Artin-Schreier polynomial over a field ''F'' is of the form
    2 KB (295 words) - 15:43, 7 December 2008
  • Rational function
    ...om ''irrational function'' which cannot be written as a [[ratio]] of two [[polynomial]]s. ...and ''t'' are [[polynomial function]] in ''x'' and ''t'' is not the [[zero polynomial]]. The [[domain (mathematics)|domain]] of ''f'' is the set of all points '
    1 KB (234 words) - 05:28, 9 December 2008
  • Cyclotomic polynomial
    ...et of primitive [[root of unity|roots of unity]]. The ''n''-th cyclotomic polynomial, denoted by Φ<sub>''n''</sub> has [[integer]] cofficients.
    1 KB (206 words) - 14:55, 11 December 2008
  • Fibonacci polynomials
    ...acci polynomials''' are a generalization of [[Fibonacci number]]s. These [[polynomial]]s are defined by: *[[Polynomial sequence]]s
    694 bytes (111 words) - 17:51, 21 January 2008
  • Algebraic geometry
    ...is a [[polynomial]] equation, whereas the second cannot be represented by polynomial equations. The first approximation of the adjective ''algebraic'' could be ..., a set of points in <math>\scriptstyle \mathbb{K}^n </math> that satisfy polynomial equations with coefficients in the field <math>\scriptstyle \mathbb{K}.</ma
    2 KB (287 words) - 10:43, 11 June 2009
  • Discriminant of a polynomial/Definition
    An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences be
    156 bytes (24 words) - 16:29, 3 December 2008
  • Eigenvalue/Related Articles
    {{r|Characteristic polynomial}} {{r|Minimal polynomial}}
    949 bytes (118 words) - 16:12, 11 January 2010
  • Field extension/Related Articles
    {{r|Artin-Schreier polynomial}} {{r|Minimal polynomial}}
    857 bytes (112 words) - 16:32, 11 January 2010
  • Characteristic (mathematics)
    {{r|Characteristic polynomial}}
    191 bytes (21 words) - 12:52, 31 May 2009
  • Algebraic number/Related Articles
    {{r|Minimal polynomial}} {{r|Polynomial}}
    887 bytes (126 words) - 02:29, 22 December 2008
  • Resultant (algebra)/Related Articles
    {{r|Polynomial}} {{r|Discriminant of a polynomial}}
    879 bytes (140 words) - 17:59, 21 December 2008
  • Integral closure/Definition
    The ring of elements of an extension of a ring which satisfy a monic polynomial over the base ring.
    135 bytes (22 words) - 13:39, 1 January 2009
  • Generic point
    ...ety]] is a point for which the coordinates have the property that the only polynomial relations that hold among them are the defining equations of the variety it ...nction field]] '''R'''(''t'') is generic, as it is on the circle but every polynomial relation between the coordinates is deducible from the relation ''X''<sup>2
    1 KB (240 words) - 20:00, 7 February 2009
  • Algebraic independence
    ...he ''s''<sub>''i''</sub> are distinct elements of ''S'', must be zero as a polynomial. If there is a non-zero polynomial ''f'' such that ''f''(''s''<sub>1</sub>,...,''s''<sub>''n''</sub>)=0, then
    2 KB (253 words) - 17:52, 6 January 2009
  • Discriminant
    {{r|Discriminant of a polynomial}}
    136 bytes (19 words) - 11:05, 31 May 2009
  • Rational number/Related Articles
    {{r|Minimal polynomial}} {{r|Polynomial}}
    1 KB (169 words) - 19:54, 11 January 2010
  • Tutte matrix
    ...perfect matching exists. (It should be noted that this is not the [[Tutte polynomial]] of ''G''.)
    2 KB (259 words) - 17:10, 28 October 2008
  • Ring (mathematics)/Related Articles
    {{r|Polynomial ring}} {{r|Polynomial}}
    1 KB (174 words) - 20:03, 11 January 2010
  • Galois theory
    ...r why there are no simple formulas for extracting the roots of the general polynomial of fifth (or higher) degree. The core idea behind Galois theory is that given a polynomial ''f'' with coefficients in a field ''K'' (typically the rational numbers),
    4 KB (683 words) - 22:17, 7 February 2010
  • Null set
    * The set of points where given [[polynomial]]s or other [[function (mathematics)|function]]s take the value zero.
    276 bytes (39 words) - 12:55, 31 May 2009
  • Cubic equation
    ...ly [[algebra]], a '''cubic equation''' is an [[equation]] involving only [[polynomial]]s of the third degree. Although cubic equations occur less frequently in ...moves to the right or left on the [[real line]], so does the value of the polynomial on the left of the above equation.
    3 KB (483 words) - 23:24, 17 December 2008
  • Splitting field
    In [[algebra]], a '''splitting field''' for a polynomial ''f'' over a field ''F'' is a [[field extension]] ''E''/''F'' with the prop A splitting field for a given polynomial always exists, and is unique up to [[field isomorphism]].
    1 KB (147 words) - 09:16, 4 July 2009
  • Degree (disambiguation)
    {{rpl|Degree of a polynomial}}
    175 bytes (27 words) - 04:17, 24 September 2013
  • Polynomial
    ...alled a polynomial ''in one variable''), whereas <math>x^2+y^2</math> is a polynomial in two variables, <math>x</math> and <math>y</math>. ...on]]s of the [[reactant]]s change. This variation is often specified by a polynomial whose variables are the concentrations.
    8 KB (1,242 words) - 02:01, 10 November 2009
  • Generating function/Definition
    ...,…, where a Taylor series expansion of g(x,y) in powers of y will have the polynomial ƒn (x) as the coefficient for the term yn.
    250 bytes (42 words) - 08:09, 4 September 2009
  • Algebraic number
    ...], an '''algebraic number''' is a [[complex number]] that is a root of a [[polynomial]] with [[rational number|rational]] coefficients. ...nts. If an algebraic number ''x'' can be written as the root of a [[monic polynomial]] with integer coefficients, that is, one whose [[leading coefficient]] is
    7 KB (1,145 words) - 00:49, 20 October 2013
  • Algebraic surface/Definition
    ...plex n-space which consists of the set of complex solutions of a system of polynomial equations in n variables such that S is a complex two-manifold in the neigh
    247 bytes (42 words) - 05:59, 4 September 2009
  • Serge Lang/Related Articles
    {{r|Discriminant of a polynomial}} {{r|Polynomial ring}}
    1 KB (187 words) - 20:18, 11 January 2010
  • Quadratic equation/Related Articles
    {{r|polynomial equation}}
    199 bytes (24 words) - 11:54, 4 December 2008
  • Linear equation/Advanced
    ...real number]] [[coefficient]]s. However, one can algebraically manipulate polynomial equations in the usual way as long as the coefficients can be added and mu ...s)|ring]] theory. One can define polynomials, and in particular quadratic polynomial equations, as long as the coefficients are in a ring. The real numbers is
    3 KB (418 words) - 14:53, 4 March 2009
  • Quadratic equation
    ...[algebra]], a '''quadratic equation''' is an [[equation]] involving only [[polynomial]]s of the second degree. Quadratic equations are a common part of mathemati Every polynomial equation can be put into the form:
    8 KB (1,360 words) - 16:44, 17 December 2008
  • Binomial theorem/Related Articles
    {{r|Polynomial}}
    263 bytes (35 words) - 06:59, 15 July 2008
  • Polynomial ring
    ...ng (mathematics)|ring]] is a construction of a ring which formalises the [[polynomial]]s of [[elementary algebra]]. ==Construction of the polynomial ring==
    4 KB (604 words) - 23:54, 20 February 2010
  • Root of unity
    ...1; the primitive ''n''-th roots of unity are the roots of the [[cyclotomic polynomial]] Φ<sub>''n''</sub>(''X'').
    1 KB (197 words) - 22:01, 7 February 2009
  • Cubic equation/Related Articles
    {{r|polynomial equation}}
    317 bytes (40 words) - 00:19, 11 December 2008
  • Cyclotomic field
    ...''. Otherwise, the splitting of ''p'' depends on the factorisation of the polynomial <math>X^n-1</math> modulo ''p'', which in turn depends on the [[highest com ...of <math>X^n-1</math>. Since the powers of ζ are the roots of the latter polynomial, ''F'' is a [[splitting field]] for <math>\Phi_n(X)</math> and hence a [[Ga
    2 KB (342 words) - 12:52, 21 January 2009
  • Legendre-Gauss Quadrature formula/Definition
    ...ation of the integral with the sum of N terms, which becomes exact for the polynomial integrand of order < 2N.
    574 bytes (85 words) - 19:43, 30 January 2009
  • Integer/Related Articles
    {{r|Cyclotomic polynomial}} {{r|Polynomial}}
    2 KB (247 words) - 17:28, 11 January 2010
  • Linear equation/Related Articles
    {{r|polynomial equation}}
    267 bytes (32 words) - 12:09, 19 December 2008
  • Fundamental Theorem of Algebra
    ...ers]] has at least one complex number as a root. In other words, given any polynomial ...must have at least one complex root. Since it is not true that every such polynomial has to have at least one real root (as the example <math>p(x) = x^2+1</math
    5 KB (924 words) - 16:35, 11 December 2008
  • Hall polynomial
    ...N'' has type <math>\mu</math>. Hall showed that the functions ''g'' are [[polynomial]] functions of ''p'' with integer coefficients: these are the ''Hall polyno interpreted as the [[Hall-Littlewood polynomial]] functions. The theory of [[Schur function]]s
    2 KB (264 words) - 22:53, 19 February 2010
  • Field extension
    ...xtension field ''E''/''F'' is ''algebraic'' over ''F'' if it satisfies a [[polynomial]] with coefficients in ''F'', and ''transcendental'' over ''F'' if it is no ...ion field is ''separable'' over ''F'' if it is algebraic and its [[minimal polynomial]] over ''F'' has distinct roots. Every algebraic element is separable over
    3 KB (435 words) - 22:38, 22 February 2009
  • Basis (linear algebra)
    ...quely as a combination of only finitely many powers: indeed, this is how a polynomial is defined.
    3 KB (464 words) - 19:45, 1 December 2008
  • Legendre-Gauss Quadrature formula/Related Articles
    {{r|Polynomial}}
    449 bytes (56 words) - 18:02, 11 January 2010
  • Artin-Schreier polynomial/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Artin-Schreier polynomial]]. Needs checking by a human.
    449 bytes (56 words) - 11:04, 11 January 2010
  • Hermite polynomial/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Hermite polynomial]]. Needs checking by a human.
    512 bytes (63 words) - 17:10, 11 January 2010
  • Frobenius map/Related Articles
    {{r|Artin-Schreier polynomial}}
    483 bytes (61 words) - 16:42, 11 January 2010
  • Gram-Schmidt orthogonalization/Related Articles
    {{r|Hermite polynomial}}
    512 bytes (63 words) - 16:57, 11 January 2010
  • Möbius function/Related Articles
    {{r|Cyclotomic polynomial}}
    532 bytes (69 words) - 18:44, 11 January 2010
  • Minimal polynomial/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Minimal polynomial]]. Needs checking by a human.
    544 bytes (70 words) - 18:34, 11 January 2010
  • Completing the square
    ...sum of a constant and a constant multiple of the square of a first-degree polynomial. Thus one has ...riptstyle \Delta </math> stands for the well-known ''discriminant'' of the polynomial, that is <math> \scriptstyle \Delta = b^2 - 4ac </math>.
    3 KB (517 words) - 08:49, 6 August 2008
  • Quantum computing
    ...can solve some problems in polynomial time that would be non deterministic polynomial time complete ([[NP complete]]) on a conventional computer.
    2 KB (307 words) - 17:00, 7 March 2024
  • Ring homomorphism/Related Articles
    {{r|Polynomial ring}}
    522 bytes (67 words) - 20:03, 11 January 2010
  • Pointwise operation/Related Articles
    {{r|Polynomial ring}}
    541 bytes (67 words) - 19:36, 11 January 2010
  • Diagonal matrix/Related Articles
    {{r|Minimal polynomial}}
    550 bytes (71 words) - 15:57, 11 January 2010
  • Noetherian ring
    ** The [[polynomial ring]] over a field #'''Hilbert's Basis Theorem''': The [[polynomial ring]] <math>A[X]</math> is Noetherian (hence so is <math>A[X_1,\ldots,X_n]
    2 KB (326 words) - 09:55, 23 December 2008
  • Normal extension
    ...eld extension]] ''E''/''F'' which contains all the roots of an irreducible polynomial if it contains one such root.
    568 bytes (88 words) - 17:21, 7 February 2009
  • Distributivity/Related Articles
    {{r|Polynomial ring}}
    626 bytes (79 words) - 16:01, 11 January 2010
  • E (mathematics)/Related Articles
    {{r|Polynomial}}
    564 bytes (72 words) - 16:08, 11 January 2010
  • Polynomial/Advanced
    ...alled a polynomial ''in one variable''), whereas <math>x^2+y^2</math> is a polynomial in two variables, <math>x</math> and <math>y</math>. ...e usual addition and multiplication operations for polynomials, called a [[polynomial ring]].
    10 KB (1,741 words) - 10:04, 3 January 2009
  • Commutative algebra
    ...<math>A</math>, the object to consider would be the prime spectrum of a [[polynomial ring]] in sufficiently many variables modulo the ideal generated by the pol
    2 KB (338 words) - 10:01, 23 December 2008
  • Hall-Littlewood polynomial
    * [[Littlewood polynomial]]
    675 bytes (84 words) - 04:37, 14 September 2013
  • Elementary function/Related Articles
    {{r|Polynomial}}
    682 bytes (88 words) - 10:48, 4 October 2013
  • Root of unity/Related Articles
    {{r|Cyclotomic polynomial}}
    592 bytes (76 words) - 20:06, 11 January 2010
  • Kronecker delta/Related Articles
    {{r|Hermite polynomial}}
    721 bytes (92 words) - 17:54, 11 January 2010
  • Cyclotomic field/Related Articles
    {{r|Minimal polynomial}}
    584 bytes (79 words) - 15:48, 11 January 2010
  • Integral domain/Related Articles
    {{r|Polynomial ring}}
    675 bytes (89 words) - 17:28, 11 January 2010
  • Rational function/Related Articles
    {{r|Polynomial}}
    710 bytes (90 words) - 19:54, 11 January 2010
  • Harmonic oscillator (quantum)/Related Articles
    {{r|Hermite polynomial}}
    704 bytes (87 words) - 17:05, 11 January 2010
  • Inverse function/Related Articles
    {{r|Artin-Schreier polynomial}}
    739 bytes (92 words) - 17:31, 11 January 2010
  • Modular arithmetic/Related Articles
    {{r|Polynomial}}
    856 bytes (107 words) - 18:36, 11 January 2010
  • Commutativity/Related Articles
    {{r|Polynomial ring}}
    858 bytes (112 words) - 15:35, 11 January 2010
  • Approximation theory
    ...s as close to the actual function as possible. This is typically done with polynomial or rational approximations. The second is obtaining approximate values of r
    985 bytes (130 words) - 01:40, 14 February 2010
  • Exponential function/Related Articles
    {{r|Polynomial}}
    837 bytes (109 words) - 16:27, 11 January 2010
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