In algebra, an alternating polynomial is a polynomial f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} such that if one switches any two of the...
7 KB (1,171 words) - 23:31, 5 August 2024
it is an alternating polynomial, not a symmetric polynomial. The defining property of the Vandermonde polynomial is that it is alternating in the entries...
4 KB (575 words) - 16:07, 6 August 2023
property of this invariant states that the Jones polynomial of an alternating link is an alternating polynomial. This property was proved by Morwen Thistlethwaite...
17 KB (2,339 words) - 23:46, 13 August 2024
symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally...
21 KB (3,833 words) - 01:08, 26 January 2024
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that...
16 KB (2,690 words) - 13:46, 29 July 2024
_{n}}\end{matrix}}\right]} are alternating polynomials by properties of the determinant. A polynomial is alternating if it changes sign under any transposition...
20 KB (3,749 words) - 13:05, 23 May 2024
symmetric functions are polynomial functions, which are given by the symmetric polynomials. A related notion is alternating polynomials, which change sign...
5 KB (873 words) - 01:02, 18 December 2023
of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...
51 KB (8,173 words) - 20:35, 14 June 2024
Taylor series (redirect from Taylor polynomial)
of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...
48 KB (8,253 words) - 02:02, 23 August 2024
In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct...
6 KB (783 words) - 21:16, 19 May 2024