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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
Legendre polynomial

34 bytes (3 words) - 05:56, 22 August 2007
Cyclotomic polynomial
...et of primitive [[root of unity|roots of unity]]. The ''n''-th cyclotomic polynomial, denoted by Φ''n'' has [[integer]] cofficients.

1 KB (206 words) - 14:55, 11 December 2008
Monic polynomial
#REDIRECT [[Polynomial#Degree]]

31 bytes (3 words) - 02:18, 22 December 2008
Polynomial/Approval

12 bytes (1 word) - 10:44, 13 November 2007
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
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
Legendre Polynomial

34 bytes (3 words) - 13:06, 27 May 2008
Characteristic polynomial
...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 determinant

911 bytes (131 words) - 22:35, 17 February 2009
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
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
Minimal polynomial
...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_i

4 KB (613 words) - 02:34, 4 January 2013
Hermite polynomial
*See [[Hermite polynomial/Addendum|Addendum]] for a table of Hermite polynomials through ''n'' = ...://mathworld.wolfram.com/HermitePolynomial.html Eric W. Weisstein, Hermite Polynomial]

4 KB (580 words) - 06:31, 31 May 2009
Littlewood polynomial
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 thi

2 KB (230 words) - 16:13, 27 October 2008
Polynomial/Definition

153 bytes (21 words) - 13:19, 20 December 2008
Minimal polynomial/Bibliography

151 bytes (17 words) - 02:37, 4 January 2013
Cyclotomic polynomial/Definition
A polynomial whose roots are primitive roots of unity.

90 bytes (12 words) - 16:50, 8 December 2008
Polynomial of Legendre

33 bytes (3 words) - 09:44, 27 May 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
Hermite polynomial/Addendum
The following is a list of [[Hermite polynomial]]s ''H''''n''(''x'') through ''n'' = 12. The polynomials are sta

891 bytes (128 words) - 08:50, 30 January 2009
Littlewood polynomial/Definition
A polynomial all of whose coefficients are plus or minus 1.

95 bytes (13 words) - 16:16, 27 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
Hermite polynomial/Definition

241 bytes (43 words) - 09:11, 30 January 2009
Hall-Littlewood polynomial
* [[Littlewood polynomial]]

675 bytes (84 words) - 04:37, 14 September 2013
Hall polynomial/Definition

77 bytes (9 words) - 08:29, 4 September 2009
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
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
Polynomial/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Polynomial]]. Needs checking by a human. {{r|Cyclotomic polynomial}}

2 KB (206 words) - 19:38, 11 January 2010
Polynomial ring/Definition

136 bytes (20 words) - 10:57, 4 September 2009
Littlewood polynomial/Related Articles
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
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
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
Cyclotomic polynomial/Related Articles
{{r|polynomial}}

864 bytes (139 words) - 14:58, 11 December 2008
Hall polynomial/Related Articles
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
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
Polynomial ring/Related Articles
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
Hall-Littlewood polynomial/Definition

103 bytes (13 words) - 08:30, 4 September 2009
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/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Minimal polynomial]]. Needs checking by a human.

544 bytes (70 words) - 18:34, 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
Degree of a polynomial
#REDIRECT [[Polynomial#Degree]]

31 bytes (3 words) - 02:17, 22 December 2008
Hall-Littlewood polynomial/External Links
*{{MathWorld |title=Hall-Littlewood Polynomial |urlname=Hall-LittlewoodPolynomial}}

97 bytes (7 words) - 04:38, 14 September 2013
Hall-Littlewood polynomial/Related Articles
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
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
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
Discriminant of a polynomial/Related Articles
{{r|Polynomial}}

870 bytes (138 words) - 17:57, 21 December 2008

Page text matches

Characteristic polynomial
...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 determinant

911 bytes (131 words) - 22:35, 17 February 2009
Completing the square/Definition
Rewriting a quadratic polynomial as a constant multiple of a linear polynomial plus a constant.

131 bytes (18 words) - 08:44, 6 August 2008
NP complexity class/Definition
...ed in nondeterministic polynomial time or, equivalently, can be checked in polynomial time.

171 bytes (23 words) - 09:22, 13 August 2010
P-versus-NP problem/Definition
...istic algorithm in polynomial time can also be solved deterministically in polynomial time.

245 bytes (34 words) - 16:08, 27 July 2023
Polynomial/Related Articles
Auto-populated based on [[Special:WhatLinksHere/Polynomial]]. Needs checking by a human. {{r|Cyclotomic polynomial}}

2 KB (206 words) - 19:38, 11 January 2010
Minimal polynomial
...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_i

4 KB (613 words) - 02:34, 4 January 2013
Littlewood polynomial/Related Articles
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
Hall polynomial/Related Articles
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
Hall-Littlewood polynomial/Related Articles
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
Polynomials
#REDIRECT [[polynomial]]

24 bytes (2 words) - 12:02, 1 April 2007
Degree of a polynomial
#REDIRECT [[Polynomial#Degree]]

31 bytes (3 words) - 02:17, 22 December 2008
Monic polynomial
#REDIRECT [[Polynomial#Degree]]

31 bytes (3 words) - 02:18, 22 December 2008
Leading coefficient
#REDIRECT [[Polynomial#Degree]]

31 bytes (3 words) - 02:21, 22 December 2008
Completing the square/Related Articles
{{r|Polynomial}} {{r|Quadratic polynomial}}

259 bytes (33 words) - 08:47, 6 August 2008
Polynomial ring/Related Articles
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
Cayley-Hamilton theorem
#REDIRECT [[Characteristic polynomial#Cayley-Hamilton theorem]]

63 bytes (5 words) - 17:05, 11 December 2008
Morphism of finite type/Definition
A set of polynomial equations with finitely many variables.

96 bytes (12 words) - 21:18, 4 September 2009
Littlewood polynomial/Definition
A polynomial all of whose coefficients are plus or minus 1.

95 bytes (13 words) - 16:16, 27 October 2008
Content (algebra)
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
Associated Legendre function/External Links
Weisstein, Eric W. "Legendre Polynomial." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Leg

149 bytes (17 words) - 19:13, 1 September 2009
Monogenic field
''a'' such that the [[ring of integers]] ''O''''K'' 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
Cyclotomic polynomial/Definition
A polynomial whose roots are primitive roots of unity.

90 bytes (12 words) - 16:50, 8 December 2008
Hall-Littlewood polynomial/External Links
*{{MathWorld |title=Hall-Littlewood Polynomial |urlname=Hall-LittlewoodPolynomial}}

97 bytes (7 words) - 04:38, 14 September 2013
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 −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''3+''px''2+''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''n'' 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''2

1 KB (240 words) - 20:00, 7 February 2009
Algebraic independence
...he ''s''''i'' are distinct elements of ''S'', must be zero as a polynomial. If there is a non-zero polynomial ''f'' such that ''f''(''s''1,...,''s''''n'')=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''n''(''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.

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Distributivity/Related Articles
{{r|Polynomial ring}}

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E (mathematics)/Related Articles
{{r|Polynomial}}

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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]].

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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

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Hall-Littlewood polynomial
* [[Littlewood polynomial]]

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Elementary function/Related Articles
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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

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Exponential function/Related Articles
{{r|Polynomial}}

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Associated Legendre function
...ction''' ''P''''ℓ''''m'' is related to a [[Legendre polynomial]] ''P''''ℓ'' by the following equation ...s the factor (1−''x'' ² )½ and hence is not a polynomial.

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Identity matrix/Related Articles
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Multiplication/Related Articles
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Taylor series
...derivative of the function being approximated when it is approximated by a polynomial of degree <math>n</math>. the Taylor series can be used to make the [[polynomial approximation]] of [[holomorphic function]]s, just truncating the series.

5 KB (898 words) - 12:58, 11 June 2009
Quadratic equation/Advanced
...ecifically [[algebra]], a '''quadratic equation''' is one involving only [[polynomial]]s of the second degree. Quadratic equations are a common part of mathemati However, one can algebraically manipulate polynomial equations in the usual way as long as the coefficients can be added and mu

10 KB (1,580 words) - 08:52, 4 March 2009
Legendre-Gauss Quadrature formula
...ath>w_i</math>, characterised in that, if the function <math>f</math> is [[polynomial]] of degree smaller than <math>2N</math>, then the exact equality takes pla The nodes <math>x_i</math> in equation (1) are zeros of the [[Legendre polynomial]] <math>P_N</math>:

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Calculus/Related Articles
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Content (algebra)/Related Articles
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Multiple (mathematics)
...ultiple of another can also appear in other contexts. For instance, one [[polynomial]] can be a multiple of another. Please see the [[divisor (ring theory)|abs

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Splitting field/Related Articles
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Galois theory/Related Articles
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Differential ring
* The [[formal derivative]] makes the polynomial ring ''R''[''X''] over ''R'' a differential ring with

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Hermite polynomial/Addendum
The following is a list of [[Hermite polynomial]]s ''H''''n''(''x'') through ''n'' = 12. The polynomials are sta

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Algebraic number/Advanced
...have dropped this requirement. An algebraic number must be a root of a [[polynomial]] with [[rational number|rational]] coefficients.

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Advanced Encryption Standard
...[[Galois field]] '''GF'''(''28''); multiply it by one constant polynomial modulo another

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Elementary function
...ction|functions]] arising in the study of [[calculus]]. They include the [[polynomial|polynomials]], which are the object of study of [[elementary algebra]]. Mor ...th> times and then multiplied by the [[constant]] <math>a</math>. The '''[[polynomial|polynomials]]''' then are [[finite]] [[linear combination|linear combinatio

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Special function/Catalogs/List
{{r|Polynomial}}

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NP complexity class
The '''NP complexity class''' (Non-deterministic [[Polynomial time]]) consists of all types of yes/no questions where whenever the polynomial in the length of the input. See technicalities section for formal definitio

15 KB (2,548 words) - 21:03, 20 August 2010
Integral closure
...S'' integral over ''R'': that is, all elements of ''S'' satisfying a monic polynomial with coefficients in ''R''. The integral closure is a [[subring]] of ''S''

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Diagonal matrix
* The [[minimal polynomial]] of ''A'' has no repeated roots;

2 KB (230 words) - 02:39, 7 January 2009
Graph coloring
==Chromatic polynomial== The '''chromatic polynomial''' counts the number of ways a graph can be coloured using no more than a g

14 KB (2,315 words) - 00:35, 9 February 2010
Characteristic function
* The [[characteristic polynomial]] in [[linear algebra]].

2 KB (242 words) - 02:01, 2 February 2009
Hermite polynomial
*See [[Hermite polynomial/Addendum|Addendum]] for a table of Hermite polynomials through ''n'' = ...://mathworld.wolfram.com/HermitePolynomial.html Eric W. Weisstein, Hermite Polynomial]

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Scheme (mathematics)
...atics)|ring]] of functions, which is the [[quotient ring|quotient]] of a [[polynomial ring]]. These algebraic properties can be defined in the context of arbitr

4 KB (743 words) - 03:55, 14 February 2010
Ring (mathematics)
...ize the [[integer]]s. Other common examples of rings include the ring of [[polynomial]]s of one variable with real coefficients, or a ring of square [[matrix|mat *The set of [[polynomial|polynomials]] forms a commutative ring.

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Pi (mathematical constant)/Proofs/Student level proof that 22 over 7 exceeds π
where −4 is the remainder of the polynomial division.

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Complexity of algorithms
* Polynomial time algorithms, * Super-polynomial time algorithms (grow faster than polynomial time algorithms).

7 KB (1,080 words) - 07:53, 10 August 2008
Adrien-Marie Legendre
...as an important French mathematician whose name lives on in the [[Legendre polynomial]]s and [[associated Legendre functions]]. ...t to distance he obtained an expansion of the force in ordinary [[Legendre polynomial]]s and taking derivatives with respect to latitude angle he obtained [[ass

6 KB (854 words) - 09:52, 24 July 2011
Algebra/Timelines
* Circa 1050: Chinese mathematician [[Jia Xian]] finds numerical solutions of polynomial equations. ...ations with more than one unknown, various cubic, quartic and higher-order polynomial equations, [[Pell's equation]], the general indeterminate quadratic equatio

8 KB (1,117 words) - 08:22, 5 December 2011
Linear equation
...uation. To see this, we simplify the right side until it becomes a linear polynomial: ...to the form <math>p(x,y) = 0</math> where <math>p(x,y)</math> is a linear polynomial in the variables ''x'' and ''y''. As with equations in one variable, it is

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Computational complexity theory
...be solved by a [[Deterministic Turing machine|deterministic machine]] in [[polynomial time]]. This class corresponds to an intuitive idea of the problems which ...by a [[Non-deterministic Turing machine|''non''-deterministic machine]] in polynomial time. This class contains many problems that people would like to be able

17 KB (2,637 words) - 13:14, 6 November 2010
Pi (mathematical constant)/Proofs/Proof that π is irrational
Then ''f'' is a polynomial function each of whose coefficients is 1/n<nowiki>!</nowiki> times an integ

2 KB (325 words) - 06:31, 15 September 2009
Justesen code
...f ''F'' = GF(2m) and the codewords are obtained by taking every polynomial ''f'' over ''F'' of degree less than ''K'' and listing the values of ''f''

2 KB (272 words) - 15:36, 29 October 2008
Group theory
...c equations, as part of what is now called [[Galois theory]]. Consider the polynomial <math>x^2 + 1</math>, it is [[irreducible]] over the real numbers, meaning ...f the extension <math>\mathbb{C}/\mathbb{R}</math> or, more simply, of the polynomial <math>x^2 + 1</math>. This is but one example of how groups can arise in ma

15 KB (2,535 words) - 20:29, 14 February 2010
Elliptic curve
If <math>f(x,y,z)</math> is a [[homogenous]] degree 3 (also called "cubic") polynomial in three variables, such that at no point <math>(x:y:z)\in \mathbb{P}^2</ma ...<math>(0:1:0)</math>: we may thus assume that the only terms in the cubic polynomial <math>f</math> which include <math>y</math>, are <math>y^2z,xyz,yz^2</math>

10 KB (1,637 words) - 16:03, 17 December 2008
Rational number
...t correctly, means a polynomial with rational coefficients, also called a "polynomial over the rationals". However, [[rational function]] does '''not''' mean the

9 KB (1,446 words) - 08:52, 30 May 2009
Derivation (mathematics)
* The [[formal derivative]] is a derivation on the [[polynomial ring]] ''R''[''X''] with constants ''R''.

2 KB (361 words) - 16:44, 4 January 2013
Convolution (mathematics)
...zero) with addition as the operation. The corresponding convolution is [[polynomial ring]] multiplication.

2 KB (338 words) - 17:41, 23 December 2008
Different ideal
...which also generates a [[power integral basis]]. If ''f'' is the minimal polynomial for α then the different is generated by ''f'''(α).

2 KB (382 words) - 09:40, 12 June 2009
Small angle approximation
...times differentiable in some proximity of the point zero. The ''Maclaurin polynomial'' order ''n'' is defined as:

2 KB (368 words) - 20:13, 29 January 2022
Finite field
...over since the non 0 elements of F form a group, they are all roots of the polynomial

2 KB (406 words) - 20:45, 8 February 2010
Associated Legendre function/Proofs
...nomials. Namely, a Legendre polynomial of order ''l'' is orthogonal to any polynomial Π''p'' of order ''p'' lower than ''l''. In bra-ket notation The bra is a polynomial of order ''k'', because

16 KB (2,776 words) - 12:52, 22 March 2012
Harmonic oscillator (quantum)
The functions ''H''''n''(x) are [[Hermite polynomial]]s; the first few are: The differential equation of Hermite with [[Hermite polynomial|polynomial]] solutions ''H''''n''(''y'') is

10 KB (1,632 words) - 21:28, 11 September 2021
Resultant (algebra)
...1 and ''n''-1 respectively, and ''R'' a scalar. If ''f'' and ''g'' have a polynomial common factor this must divide ''R'' and so ''R'' must be zero. Conversely

2 KB (388 words) - 17:58, 21 December 2008
Nonlinear programming
...ogramming problems can be solved in a number of steps that is bounded by a polynomial in the input size (see [[computational complexity]]).

3 KB (405 words) - 18:02, 1 January 2008
Legendre polynomials
...{1, ''x'', ''x''², x³, …} the ''n''th degree polynomial ''P''''n'' can be constructed recursively. The Gram-Schmidt proc Weisstein, Eric W. "Legendre Polynomial." From MathWorld--A Wolfram Web Resource. [http://mathworld.wolfram.com/Leg

7 KB (1,091 words) - 06:21, 10 September 2009
Complex number
...is that it is [[algebraically closed]]. This means that any non-constant [[polynomial]] with complex coefficients has a complex root. This result is known as the ...roduced a new number, <math>i</math>, which is defined to be a root of the polynomial. Suddenly, all non-constant polynomials have a root in this new setting whe

18 KB (3,028 words) - 17:12, 25 August 2013
Number
...re discovered while searching solutions to some [[polynomial]]s (e.g., the polynomial <math> \scriptstyle x^2 + 1 = 0 </math> has two solutions, one being <math> # A complex number that is solution to a [[polynomial]] in integer coefficients is an [[algebraic number]]. This set includes all

11 KB (1,701 words) - 20:07, 1 July 2021
Fourier operator
...math> can be used as a an origin to construct a self–Fourier function as a polynomial where <math>\mathrm{HermiteH}</math> are the [[Hermit polynomial]]s

11 KB (1,589 words) - 08:58, 9 September 2020
Eigenvalue
The origin of this equation, the [[characteristic polynomial]] of ''A'', is the [[eigenvalue problem]], which is to find the eigenvalues

4 KB (731 words) - 17:16, 11 December 2008
Complex number/Citable Version
...is that it is [[algebraically closed]]. This means that any non-constant [[polynomial]] with complex coefficients has a complex root. This result is known as the ...roduced a new number, <math>i</math>, which is defined to be a root of the polynomial. Suddenly, all non-constant polynomials have a root in this new setting whe

20 KB (3,304 words) - 17:11, 25 August 2013
E (mathematics)
...scendental number]]<ref name="maor_37"/>, i.e. it is not solution of any [[polynomial]] having a finite number of [[rational number|rational]] coefficients.

3 KB (527 words) - 12:19, 16 March 2008
Cauchy-Schwarz inequality
...inite quadratic function of ''t'', it follows that the [[discriminant of a polynomial|discriminant]] of ''f'' is non-positive definite. That is,

4 KB (629 words) - 16:46, 17 December 2008
Solid harmonics
where <math> P_\ell(\cos\theta)</math> is a [[Legendre polynomial]] of order ''l''. Upon writing ''u'' = cos θ the ''m''th derivative of the Legendre polynomial can be written as the following expansion in ''u''

16 KB (2,612 words) - 09:02, 9 February 2010
Newton's method
...ple. The [[golden ratio]] (φ ≈ 1.618) is the largest root of the polynomial <math>f(x) = x^2 - x - 1</math>; to calculate this root, we can use the New ...n's method never leave the real line. When Newton's method is applied to a polynomial with complex roots, the region of convergence around each root has a compli

17 KB (2,889 words) - 12:40, 11 June 2009
Derivative at a point
...n \mapsto n.X^{n-1}</math> and this extends to a linear map ''D'' on the [[polynomial ring]] <math>R[X]</math> over any [[ring theory|ring]] ''R''. Similarly we

5 KB (861 words) - 14:04, 23 February 2011
Greatest common divisor
An important example is the ring of [[polynomial]]s:

5 KB (797 words) - 04:57, 21 April 2010
Real number
...be deduced. For instance, we can prove from these properties that every [[polynomial]] of odd degree with real numbers as coefficients has a root in the real nu ...al numbers. For example ''real [[matrix (mathematics)|matrix]]'', ''real [[polynomial]]'' and ''real [[Lie algebra]]''.

19 KB (2,948 words) - 10:07, 28 February 2024
Atmospheric reentry/Bibliography
...k. The partition functions listed in NASA SP-3096 are inaccurate (use the polynomial fits from the Gordon and McBride code, CEA). NASA SP-3096 can sometimes be

4 KB (630 words) - 15:38, 20 July 2008
Matrix
...t is [[diagonalizable matrix|diagonalisable]] since its minimal polynomial polynomial ''X''2-''X'' has no repeated roots. The kernel and image of ''P

15 KB (2,209 words) - 02:10, 14 February 2010
Algebra
...n|multiply]]ing [[number]]s, the concept of [[variables]], definition of [[polynomial]]s, along with [[factorization]] and determining their [[root (mathematics) ...o-by-two [[Matrix (mathematics)|matrices]], the set of all second-degree [[polynomial]]s (''ax''2 + ''bx'' + ''c''), the set of all two dimensional [[

18 KB (2,669 words) - 08:38, 17 April 2024
Entire function
Examples of entire functions are [[polynomial]] and [[exponential]] functions.

6 KB (827 words) - 14:44, 19 December 2008
Special function/Catalogs/Catalog
* [[Polynomial]]s

8 KB (1,184 words) - 14:58, 8 December 2009
Power function
...e [[power function]] could be used for short writing of expressions with [[polynomial]]s with [[number]]s.

8 KB (1,339 words) - 13:11, 8 August 2021
Gaussian type orbitals
...ized) Cartesian GTOs are defined by an angular part which is a homogeneous polynomial in the components ''x'', ''y'', and ''z'' of the position vector '''''r'''' ...ered to be the radial part of an AO. It can be multiplied by a homogeneous polynomial in ''x'', ''y'', and ''z'' to become a Cartesian GTO, or χ(''r'') can b

15 KB (2,490 words) - 12:23, 19 April 2009
Exponential growth
...value is largest until ''x'' gets around 7. The blue line represents the polynomial ''x''3. Polynomials grow subexponentially, since the exponent ( ...of any kind (the basis of the [[Malthusian catastrophe]]) as well as any [[polynomial]] growth, i.e., for all α:

14 KB (2,099 words) - 13:37, 10 April 2024
Algebraic number field
...y)|primitive element]] for ''K''/'''Q''', and letting ''f'' be the minimal polynomial of α. Then the embeddings correspond to the ''n'' roots of ''f'' in '''C'

7 KB (1,077 words) - 17:18, 10 January 2009
Holomorphic function
All [[polynomial]] functions in ''z'' with complex [[coefficient]]s are holomorphic on '''C'

9 KB (1,434 words) - 15:35, 7 February 2009
Tetration
==Polynomial approximation== ...onPolynomial25power.jpg|right|600px|Fig.N. Approximation of tetration with polynomial of 25th power}}

65 KB (10,203 words) - 04:16, 8 September 2014
RSA algorithm
The problem with that is that no really efficient (polynomial in the number of bits in N) solution for factoring is known, despite consid

7 KB (1,171 words) - 05:48, 8 April 2024
Hyperelliptic curve
...rm <math>y^2-f(x)</math> in the affine plane, where <math>f(x)</math> is a polynomial in <math>x</math>, and the degree of <math>f(x)</math> is either twice the

9 KB (1,597 words) - 15:29, 4 December 2007
Hydrogen-like atom
...equation has well-behaved (regular at the origin, vanishing for infinity) polynomial solutions written as ...rand, 2nd edition (1956), p. 130. Note that the convention of the Laguerre polynomial in this book differs from the present one. If we indicate the Laguerre in t

19 KB (2,981 words) - 18:31, 3 November 2021
AES competition
...[[Galois field]] '''GF'''(''28''); multiply it by one constant polynomial modulo another

21 KB (3,252 words) - 05:49, 8 April 2024
Trace (mathematics)
The secular determinant is a polynomial in λ:

12 KB (1,903 words) - 10:57, 2 February 2009
Euler's theorem (rotation)
...the complex plane. Moreover, since its secular equation (an ''m''th order polynomial in λ) has real coefficients, it follows that its roots appear in com

12 KB (1,865 words) - 02:49, 19 April 2010
Integral
...an calculate integrals of a large number of functions; for example, of any polynomial.

13 KB (2,303 words) - 16:28, 23 January 2011
Vector space
...<math>\mathbb{C}^n</math>; or [[polynomial]]s of degree ''n''.

15 KB (2,506 words) - 05:16, 11 May 2011
Trigonometric function
...h; they first look up the closest angle in a small table, and then use the polynomial to compute the correction. On simpler devices that lack [[arithmetic and lo

33 KB (5,179 words) - 08:26, 4 June 2010
Number theory
..., an ''algebraic number'' is any complex number that is a solution to some polynomial equation <math>\scriptstyle f(x)=0</math> with rational coefficients; ...solutions to an equation <math>f(x,y)=0</math>, where <math>f</math> is a polynomial in two variables - turns out to depend crucially on the ''genus'' of the cu

27 KB (4,383 words) - 08:05, 11 October 2011
Group (mathematics)
...with the work of [[Évariste Galois]], in 1830, on the problem of when an [[polynomial|algebraic equation]] is soluble by [[radical (mathematics)|radical]]s. Befo

19 KB (3,074 words) - 11:11, 13 February 2009
Van der Waals equation/Citable Version
...unction of pressure ''p''  will require the solution of a third-order polynomial, which yields a complicated expression. Therefore, expressing the [[enthalp

16 KB (2,711 words) - 16:42, 23 September 2013
Fraction (mathematics)
...ented in the form of a fraction, where the numerator and denominator are [[polynomial]]s. They are the [[quotient field]] of the polynomials.

21 KB (3,089 words) - 10:08, 28 February 2024
Tania function
...e approximation is less than 3; in the white spot the approximation by the polynomial of 5th order with respect to <math>t</math> gives at least three significan

19 KB (2,953 words) - 04:47, 11 October 2013
History of number theory
...h>. Thus, nowadays, we speak of ''Diophantine equations'' when we speak of polynomial equations to which rational or integer solutions must be found. and [[Cyclotomic polynomial|cyclotomy]], but truly came into its own with the development of

35 KB (5,526 words) - 11:29, 4 October 2013
Normal distribution
...) = μ''t'' + σ2''t''2/2. Since this is a quadratic polynomial in ''t'', only the first two cumulants are nonzero. ...rm [−1/2, 1/2] deviates. This is equivalent to a twelfth-order polynomial approximation to the normal distribution and is quite usable in many applic

46 KB (6,956 words) - 07:01, 9 June 2009
Spherical harmonics
...tion contains the factor (1−x2) and the ordinary Legendre polynomial ''P''n(1) = 1. So,

34 KB (5,282 words) - 14:21, 1 January 2011
Gamma function
...ions or an evaluation of the sine in the reflection formula. Listings of [[polynomial]]s and [[rational function]]s that approximate the gamma function in a unit

32 KB (5,024 words) - 12:05, 22 December 2008
History of computing
...was a functional machine designed to compile mathematical tables based on polynomial calculation.<ref>{{cite web|url=http://www.csc.liv.ac.uk/~ped/teachadmin/hi

26 KB (3,913 words) - 06:51, 7 April 2014
Mathematics
...aic geometry is the description of geometric objects as solution sets of [[polynomial]] equations, combining the concepts of quantity and space, and also the stu

30 KB (4,289 words) - 16:03, 20 January 2023

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