Search results

{{r|Minimal polynomial}}

** 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]

...eld extension]] ''E''/''F'' which contains all the roots of an irreducible polynomial if it contains one such root.

{{r|Polynomial ring}}

{{r|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>. ...e usual addition and multiplication operations for polynomials, called a [[polynomial ring]].

...<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

* [[Littlewood polynomial]]

{{r|Polynomial}}

{{r|Cyclotomic polynomial}}

{{r|Hermite polynomial}}

{{r|Minimal polynomial}}

{{r|Polynomial ring}}

{{r|Polynomial}}

{{r|Hermite polynomial}}

{{r|Artin-Schreier polynomial}}

{{r|Polynomial}}

{{r|Polynomial ring}}

...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

{{r|Polynomial}}

...ction''' ''P''_''ℓ''^''m'' is related to a [[Legendre polynomial]] ''P''_''ℓ'' by the following equation ...s the factor (1&minus;''x'' &sup2; )^&frac12; and hence is not a polynomial.

{{r|Characteristic polynomial}}

{{r|Polynomial equation}}

{{r|Polynomial}}

{{r|Polynomial}}

...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.

...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

...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>:

{{r|Polynomial}}

{{r|Polynomial}}

{{r|Polynomial}}

{{r|polynomial}}

...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

{{r|Polynomial}}

{{r|Polynomial}}

{{r|Polynomial}}

* The [[formal derivative]] makes the polynomial ring ''R''[''X''] over ''R'' a differential ring with

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

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

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

...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

{{r|Polynomial}}

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

...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''

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

==Chromatic polynomial== The '''chromatic polynomial''' counts the number of ways a graph can be coloured using no more than a g

* The [[characteristic polynomial]] in [[linear algebra]].

*<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]

...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

...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.