In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field F {\displaystyle \mathbb {F} } is a linear combination...

the Laurent series is unique. A Laurent polynomial is a Laurent series in which only finitely many coefficients are non-zero. Laurent polynomials differ...

oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t 1 / 2 {\displaystyle t^{1/2}} with integer coefficients...

fractions include the Laurent polynomials, but do not limit denominators to powers of an indeterminate. Laurent polynomials are like polynomials, but allow negative...

Koornwinder polynomials Kostka polynomial Kravchuk polynomials Laguerre polynomials Laurent polynomial Linearised polynomial Littlewood polynomial Legendre...

positive and negative powers of e i x {\displaystyle e^{ix}} , i.e., Laurent polynomials in z {\displaystyle z} under the change of variables x ↦ z := e i...

consider H 1 ( X ) {\displaystyle H_{1}(X)} a module over the ring of Laurent polynomials Z [ t , t − 1 ] {\displaystyle \mathbb {Z} [t,t^{-1}]} . This is...

\;C_{s}+a_{1s}X_{1}+\cdots +a_{ns}X_{n}\}.\end{aligned}}} Given a polynomial f in the Laurent polynomial ring K [ x 1 ± 1 , … , x n ± 1 ] {\displaystyle K[x_{1}^{\pm...

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...

indeterminate or, for historical reasons, a variable. In the context of Laurent polynomials, a Laurent binomial, often simply called a binomial, is similarly defined...

Every Laurent polynomial can be written as a rational function while the converse is not necessarily true, i.e., the ring of Laurent polynomials is a subring...

discovered by Weierstrass in an 1841 paper, but not published at the time. Laurent polynomial Rodriguez, Rubi; Kra, Irwin; Gilman, Jane P. (2012), Complex Analysis:...

{\displaystyle (2-X)^{A}P(X)+X^{A}P(2-X)=2^{A}\qquad (*),} with the Laurent-polynomial X := 1 2 ( 2 − Z − Z − 1 ) {\displaystyle X:={\frac {1}{2}}\left(2-Z-Z^{-1}\right)}...

Amartya Kumar Dutta. The title of her dissertation was "Some results on Laurent polynomial fibrations and Quasi A*-algebras". Professor at Statistical and Mathematics...

states that the number of non-zero complex solutions of a system of Laurent polynomial equations f 1 = ⋯ = f n = 0 {\displaystyle f_{1}=\cdots =f_{n}=0}...

and the coefficient is a complex number). In the context of Laurent polynomials and Laurent series, the exponents of a monomial may be negative, and in...

multidimensional filter banks, but it first need to extend from polynomial matrices to Laurent polynomial matrices. The Gröbner-basis computation can be considered...

up technique to solve problems in arithmetic. In modern algebra a Laurent polynomial is linear combination of some variables, raised to integer powers...

(Freeman Dyson 1962) is a conjecture about the constant term of certain Laurent polynomials, proved independently in 1962 by Wilson and Gunson. Andrews generalized...

polynomial in n variables associated to the partition λ is the unique Laurent polynomial invariant under permutation and inversion of variables, with leading...

contrast, the inclusion of A1 − 0 into A1 is not finite. (Indeed, the Laurent polynomial ring k[y, y−1] is not finitely generated as a module over k[y].) This...

polynomial assigns a Laurent polynomial in the variable t1/2 to the knot or link. Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman...

multidimensional filter banks, but it first need to extend from polynomial matrices to Laurent polynomial matrices. The Grobner basis computation can be considered...

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...

In mathematics, the Faber polynomials Pm of a Laurent series f ( z ) = z − 1 + a 0 + a 1 z + ⋯ {\displaystyle \displaystyle f(z)=z^{-1}+a_{0}+a_{1}z+\cdots...

In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by Joseph Bernstein (1971) and...

algebra corresponding to the multiplicative group Gm = GL(1) is the Laurent polynomial ring k[x, x−1], with comultiplication given by x ↦ x ⊗ x . {\displaystyle...

(\downarrow 2)(c(z))=\sum _{k\in \mathbb {Z} }c_{2k}z^{-k}} . The starred Laurent-polynomial a ∗ ( z ) {\displaystyle a^{*}(z)} denotes the adjoint filter, it...

Polynomial Matrix Spectral Factorization or Matrix Fejer–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices. Polynomial...

{\displaystyle s} is a real sequence with finitely many non-zero elements (a Laurent polynomial) such that s | ( s ↑ 2 ) {\displaystyle s|(s\uparrow 2)} (read: ∃...