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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
  • 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
  • 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
  • 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
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