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- ...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
- ...s method). Only after all this would we introduce a formal definition of a polynomial as an infinite sequence with finite support over a ring. (Zuh? they would r ..., as well as the word ''ring'' and the discrepancy between polynomials and polynomial functions to the advanced page.9 KB (1,496 words) - 16:44, 24 December 2008
- ...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
- ...nomial|degree]] which that object satisfies. Examples include the minimal polynomial of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[a ...ver a field ''F''. We give ''A'' the structure of a [[module]] over the [[polynomial ring]] ''F''[''X''] by defining the action of <math>f(x) = \sum_{n=0}^d f_i4 KB (613 words) - 02:34, 4 January 2013
- 34 bytes (3 words) - 13:06, 27 May 2008
- ...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]]s2 KB (264 words) - 22:53, 19 February 2010
- 12 bytes (1 word) - 14:57, 22 December 2008
- 12 bytes (1 word) - 22:35, 17 February 2009
- 275 bytes (37 words) - 13:47, 8 March 2009
- ...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
- 12 bytes (1 word) - 13:04, 8 March 2009
- 153 bytes (21 words) - 13:19, 20 December 2008
- In [[mathematics]], a '''Littlewood polynomial''' is a [[polynomial]] all of whose coefficients are +1 or −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 thi2 KB (230 words) - 16:13, 27 October 2008
- ...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
- *<i>See [[Hermite polynomial/Addendum|Addendum]] for a table of Hermite polynomials through</i> ''n'' = ...://mathworld.wolfram.com/HermitePolynomial.html Eric W. Weisstein, Hermite Polynomial]4 KB (580 words) - 06:31, 31 May 2009
- ...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
- 92 bytes (9 words) - 16:15, 27 October 2008
- 12 bytes (1 word) - 04:00, 30 January 2009
- 34 bytes (3 words) - 05:56, 22 August 2007
- 12 bytes (1 word) - 14:57, 11 December 2008
- | pagename = Polynomial | abc = Polynomial733 bytes (69 words) - 06:08, 15 March 2024
- 12 bytes (1 word) - 10:44, 13 November 2007
- #REDIRECT [[Polynomial#Degree]]31 bytes (3 words) - 02:18, 22 December 2008
- 12 bytes (1 word) - 16:56, 7 February 2009
- ...algebra]] the '''characteristic polynomial''' of a [[square matrix]] is a polynomial which has the [[eigenvalue]]s of the matrix as roots. Let ''A'' be an ''n''×''n'' matrix. The characteristic polynomial of ''A'' is the determinant911 bytes (131 words) - 22:35, 17 February 2009
- 33 bytes (3 words) - 09:44, 27 May 2008
- | pagename = minimal polynomial | abc = minimal polynomial2 KB (226 words) - 09:29, 15 March 2024
- | pagename = polynomial equation | abc = polynomial equation2 KB (229 words) - 15:44, 22 December 2008
- 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 form2 KB (295 words) - 15:43, 7 December 2008
- | pagename = Characteristic polynomial | abc = polynomial, Characteristic2 KB (227 words) - 07:20, 15 March 2024
- The monic polynomial of least degree which a square matrix or endomorphism satisfies.121 bytes (16 words) - 17:52, 11 December 2008
- The polynomial attached to a square matrix or endomorphism det(A-XI)=0.107 bytes (14 words) - 17:55, 11 December 2008
- 12 bytes (1 word) - 16:02, 5 December 2008
- | pagename = Polynomial ring | abc = polynomial ring733 bytes (62 words) - 13:05, 8 March 2009
- | pagename = Littlewood polynomial | abc = Littlewood polynomial2 KB (229 words) - 16:14, 27 October 2008
- | pagename = Hall polynomial | abc = Hall polynomial735 bytes (62 words) - 13:46, 8 March 2009
- 77 bytes (9 words) - 08:29, 4 September 2009
- | pagename = Hermite polynomial | abc = Hermite polynomial2 KB (227 words) - 09:06, 30 January 2009
- A polynomial whose roots are primitive roots of unity.90 bytes (12 words) - 16:50, 8 December 2008
- A polynomial all of whose coefficients are plus or minus 1.95 bytes (13 words) - 16:16, 27 October 2008
- | pagename = Cyclotomic polynomial | abc = Cyclotomic polynomial2 KB (229 words) - 14:57, 11 December 2008
- 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
- * [[Littlewood polynomial]]675 bytes (84 words) - 04:37, 14 September 2013
- The following is a list of [[Hermite polynomial]]s ''H''<sub>''n''</sub>(''x'') through ''n'' = 12. The polynomials are sta891 bytes (128 words) - 08:50, 30 January 2009
- Auto-populated based on [[Special:WhatLinksHere/Polynomial]]. Needs checking by a human. {{r|Cyclotomic polynomial}}2 KB (206 words) - 19:38, 11 January 2010
- 136 bytes (20 words) - 10:57, 4 September 2009
- 241 bytes (43 words) - 09:11, 30 January 2009
- 151 bytes (17 words) - 02:37, 4 January 2013
- 92 bytes (9 words) - 17:24, 27 October 2008
- Auto-populated based on [[Special:WhatLinksHere/Hermite polynomial]]. Needs checking by a human.512 bytes (63 words) - 17:10, 11 January 2010
- A type of polynomial whose roots generate extensions of degree ''p'' in characteristic ''p''.129 bytes (17 words) - 02:24, 5 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Hall polynomial]]. Needs checking by a human. {{r|Hall-Littlewood polynomial}}464 bytes (58 words) - 17:04, 11 January 2010
- | pagename = Artin-Schreier polynomial | abc = Artin-Schreier polynomial2 KB (229 words) - 16:01, 5 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Polynomial equation]]. Needs checking by a human. {{r|Polynomial}}565 bytes (72 words) - 19:39, 11 January 2010
- ...ant of a polynomial''' is an invariant which determines whether or not a [[polynomial]] has repeated roots. Given a polynomial1 KB (163 words) - 18:01, 21 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Polynomial ring]]. Needs checking by a human. {{r|Minimal polynomial}}770 bytes (96 words) - 19:39, 11 January 2010
- 12 bytes (1 word) - 17:56, 21 December 2008
- 103 bytes (13 words) - 08:30, 4 September 2009
- Auto-populated based on [[Special:WhatLinksHere/Minimal polynomial]]. Needs checking by a human.544 bytes (70 words) - 18:34, 11 January 2010
- #REDIRECT [[Polynomial#Degree]]31 bytes (3 words) - 02:17, 22 December 2008
- | pagename = Hall-Littlewood polynomial | abc = Hall-Littlewood polynomial2 KB (229 words) - 17:24, 27 October 2008
- {{r|polynomial}}864 bytes (139 words) - 14:58, 11 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Littlewood polynomial]]. Needs checking by a human. {{r|Hall-Littlewood polynomial}}470 bytes (58 words) - 18:08, 11 January 2010
- 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
- *{{MathWorld |title=Hall-Littlewood Polynomial |urlname=Hall-LittlewoodPolynomial}}97 bytes (7 words) - 04:38, 14 September 2013
- An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences be156 bytes (24 words) - 16:29, 3 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Hall-Littlewood polynomial]]. Needs checking by a human. {{r|Hall polynomial}}475 bytes (59 words) - 17:03, 11 January 2010
- | pagename = Discriminant of a polynomial | abc = Discriminant of a polynomial838 bytes (69 words) - 12:12, 16 October 2010
- Auto-populated based on [[Special:WhatLinksHere/Artin-Schreier polynomial]]. Needs checking by a human.449 bytes (56 words) - 11:04, 11 January 2010
- {{r|Polynomial}}870 bytes (138 words) - 17:57, 21 December 2008
Page text matches
- ...algebra]] the '''characteristic polynomial''' of a [[square matrix]] is a polynomial which has the [[eigenvalue]]s of the matrix as roots. Let ''A'' be an ''n''×''n'' matrix. The characteristic polynomial of ''A'' is the determinant911 bytes (131 words) - 22:35, 17 February 2009
- Rewriting a quadratic polynomial as a constant multiple of a linear polynomial plus a constant.131 bytes (18 words) - 08:44, 6 August 2008
- ...ed in nondeterministic polynomial time or, equivalently, can be checked in polynomial time.171 bytes (23 words) - 09:22, 13 August 2010
- == "A quasi-polynomial algorithm for discrete logarithm ..." ==369 bytes (54 words) - 22:39, 23 March 2014
- ...istic algorithm in polynomial time can also be solved deterministically in polynomial time.245 bytes (34 words) - 16:08, 27 July 2023
- Auto-populated based on [[Special:WhatLinksHere/Polynomial]]. Needs checking by a human. {{r|Cyclotomic polynomial}}2 KB (206 words) - 19:38, 11 January 2010
- ...nomial|degree]] which that object satisfies. Examples include the minimal polynomial of a [[square matrix]], an [[endomorphism]] of a [[vector space]] or an [[a ...ver a field ''F''. We give ''A'' the structure of a [[module]] over the [[polynomial ring]] ''F''[''X''] by defining the action of <math>f(x) = \sum_{n=0}^d f_i4 KB (613 words) - 02:34, 4 January 2013
- Auto-populated based on [[Special:WhatLinksHere/Littlewood polynomial]]. Needs checking by a human. {{r|Hall-Littlewood polynomial}}470 bytes (58 words) - 18:08, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Hall polynomial]]. Needs checking by a human. {{r|Hall-Littlewood polynomial}}464 bytes (58 words) - 17:04, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Hall-Littlewood polynomial]]. Needs checking by a human. {{r|Hall polynomial}}475 bytes (59 words) - 17:03, 11 January 2010
- #REDIRECT [[polynomial]]24 bytes (2 words) - 12:02, 1 April 2007
- #REDIRECT [[Polynomial#Degree]]31 bytes (3 words) - 02:17, 22 December 2008
- #REDIRECT [[Polynomial#Degree]]31 bytes (3 words) - 02:18, 22 December 2008
- #REDIRECT [[Polynomial#Degree]]31 bytes (3 words) - 02:21, 22 December 2008
- {{r|Polynomial}} {{r|Quadratic polynomial}}259 bytes (33 words) - 08:47, 6 August 2008
- Auto-populated based on [[Special:WhatLinksHere/Polynomial ring]]. Needs checking by a human. {{r|Minimal polynomial}}770 bytes (96 words) - 19:39, 11 January 2010
- | pagename = Polynomial ring | abc = polynomial ring733 bytes (62 words) - 13:05, 8 March 2009
- | pagename = Hall polynomial | abc = Hall polynomial735 bytes (62 words) - 13:46, 8 March 2009
- #REDIRECT [[Characteristic polynomial#Cayley-Hamilton theorem]]63 bytes (5 words) - 17:05, 11 December 2008
- A set of polynomial equations with finitely many variables.96 bytes (12 words) - 21:18, 4 September 2009
- | pagename = Polynomial | abc = Polynomial733 bytes (69 words) - 06:08, 15 March 2024
- A polynomial all of whose coefficients are plus or minus 1.95 bytes (13 words) - 16:16, 27 October 2008
- In [[algebra]], the '''content''' of a [[polynomial]] is the [[highest common factor]] of its coefficients. A polynomial is ''[[Primitive polynomial|primitive]]'' if it has content unity.971 bytes (132 words) - 15:00, 29 October 2008
- Weisstein, Eric W. "Legendre Polynomial." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Leg149 bytes (17 words) - 19:13, 1 September 2009
- ''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
- ...ant of a polynomial''' is an invariant which determines whether or not a [[polynomial]] has repeated roots. Given a polynomial1 KB (163 words) - 18:01, 21 December 2008
- The monic polynomial of least degree which a square matrix or endomorphism satisfies.121 bytes (16 words) - 17:52, 11 December 2008
- | pagename = Discriminant of a polynomial | abc = Discriminant of a polynomial838 bytes (69 words) - 12:12, 16 October 2010
- Polynomial sequence which can be considered as a generalisation of the Fibonacci numbe126 bytes (16 words) - 07:19, 4 September 2009
- An element of a field extension for which the minimal polynomial has distinct roots.120 bytes (17 words) - 04:11, 20 December 2008
- {{r|Cyclotomic polynomial}} {{r|Discriminant of a polynomial}}2 KB (247 words) - 06:00, 7 November 2010
- 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
- A polynomial whose roots are primitive roots of unity.90 bytes (12 words) - 16:50, 8 December 2008
- *{{MathWorld |title=Hall-Littlewood Polynomial |urlname=Hall-LittlewoodPolynomial}}97 bytes (7 words) - 04:38, 14 September 2013
- ...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
- A field extension generated by the roots of a polynomial.93 bytes (13 words) - 13:13, 21 December 2008
- In [[mathematics]], a '''Littlewood polynomial''' is a [[polynomial]] all of whose coefficients are +1 or −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 thi2 KB (230 words) - 16:13, 27 October 2008
- An algebraic number field for which the ring of integers is a polynomial ring.114 bytes (17 words) - 17:08, 28 October 2008
- 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
- The polynomial attached to a square matrix or endomorphism det(A-XI)=0.107 bytes (14 words) - 17:55, 11 December 2008
- 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
- Any nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a144 bytes (20 words) - 02:59, 15 November 2008
- 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
- A complex number that is a root of a polynomial with rational coefficients.111 bytes (16 words) - 16:34, 13 July 2008
- Auto-populated based on [[Special:WhatLinksHere/Polynomial equation]]. Needs checking by a human. {{r|Polynomial}}565 bytes (72 words) - 19:39, 11 January 2010
- ...property of elements of an extension field which satisfy only the trivial polynomial relation.134 bytes (18 words) - 15:49, 23 December 2008
- A type of polynomial whose roots generate extensions of degree ''p'' in characteristic ''p''.129 bytes (17 words) - 02:24, 5 December 2008
- 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
- 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
- The highest common factor of the coefficients of a polynomial.98 bytes (13 words) - 15:03, 29 October 2008
- ...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
- 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 form2 KB (295 words) - 15:43, 7 December 2008
- ...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
- ...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
- ...acci polynomials''' are a generalization of [[Fibonacci number]]s. These [[polynomial]]s are defined by: *[[Polynomial sequence]]s694 bytes (111 words) - 17:51, 21 January 2008
- ...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}.</ma2 KB (287 words) - 10:43, 11 June 2009
- An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences be156 bytes (24 words) - 16:29, 3 December 2008
- {{r|Characteristic polynomial}} {{r|Minimal polynomial}}949 bytes (118 words) - 16:12, 11 January 2010
- {{r|Artin-Schreier polynomial}} {{r|Minimal polynomial}}857 bytes (112 words) - 16:32, 11 January 2010
- {{r|Characteristic polynomial}}191 bytes (21 words) - 12:52, 31 May 2009
- {{r|Minimal polynomial}} {{r|Polynomial}}887 bytes (126 words) - 02:29, 22 December 2008
- {{r|Polynomial}} {{r|Discriminant of a polynomial}}879 bytes (140 words) - 17:59, 21 December 2008
- 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
- ...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>21 KB (240 words) - 20:00, 7 February 2009
- ...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, then2 KB (253 words) - 17:52, 6 January 2009
- {{r|Discriminant of a polynomial}}136 bytes (19 words) - 11:05, 31 May 2009
- {{r|Minimal polynomial}} {{r|Polynomial}}1 KB (169 words) - 19:54, 11 January 2010
- ...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
- {{r|Polynomial ring}} {{r|Polynomial}}1 KB (174 words) - 20:03, 11 January 2010
- ...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
- * 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
- ...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
- 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
- {{rpl|Degree of a polynomial}}175 bytes (27 words) - 04:17, 24 September 2013
- ...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
- ...,…, 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
- ...], 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]] is7 KB (1,145 words) - 00:49, 20 October 2013
- ...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 neigh247 bytes (42 words) - 05:59, 4 September 2009
- {{r|Discriminant of a polynomial}} {{r|Polynomial ring}}1 KB (187 words) - 20:18, 11 January 2010
- {{r|polynomial equation}}199 bytes (24 words) - 11:54, 4 December 2008
- ...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 is3 KB (418 words) - 14:53, 4 March 2009
- ...[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
- {{r|Polynomial}}263 bytes (35 words) - 06:59, 15 July 2008
- ...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
- ...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
- {{r|polynomial equation}}317 bytes (40 words) - 00:19, 11 December 2008
- ...''. 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 [[Ga2 KB (342 words) - 12:52, 21 January 2009
- ...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
- | pagename = minimal polynomial | abc = minimal polynomial2 KB (226 words) - 09:29, 15 March 2024
- | pagename = Characteristic polynomial | abc = polynomial, Characteristic2 KB (227 words) - 07:20, 15 March 2024
- {{r|Cyclotomic polynomial}} {{r|Polynomial}}2 KB (247 words) - 17:28, 11 January 2010
- {{r|polynomial equation}}267 bytes (32 words) - 12:09, 19 December 2008
- | pagename = Hermite polynomial | abc = Hermite polynomial2 KB (227 words) - 09:06, 30 January 2009
- | pagename = Littlewood polynomial | abc = Littlewood polynomial2 KB (229 words) - 16:14, 27 October 2008
- | pagename = Cyclotomic polynomial | abc = Cyclotomic polynomial2 KB (229 words) - 14:57, 11 December 2008
- | pagename = polynomial equation | abc = polynomial equation2 KB (229 words) - 15:44, 22 December 2008
- | pagename = Artin-Schreier polynomial | abc = Artin-Schreier polynomial2 KB (229 words) - 16:01, 5 December 2008
- | pagename = Hall-Littlewood polynomial | abc = Hall-Littlewood polynomial2 KB (229 words) - 17:24, 27 October 2008
- ...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</math5 KB (924 words) - 16:35, 11 December 2008
- ...the origins of Galois theory should be expanded to include permutations of polynomial roots studied by Lagrange and/or Abel's work contemporary to Galois's? I b ===The Galois group of a polynomial - a basic example===9 KB (1,510 words) - 21:04, 15 January 2009