Results 291 to 300 of about 912,120 (337)

On Multiplication of Polynomials Modulo a Polynomial

SIAM Journal on Computing, 1980
The multiplicative complexity of the direct product of algebras $A_p $ of polynomials modulo a polynomial P is studied. In particular, we show that if P and Q are irreducible polynomials then the multiplicative complexity of $A_{\text{P}} \times A_{\text{Q}} $ is $2\deg ({\text{P}})\deg ({\text{Q}}) - {\text{k}}$, where k is the number of factors of P ...
openaire   +3 more sources

A Polynomial Shared by Certain Differential Polynomials

Bulletin of the Iranian Mathematical Society, 2023
Let \(f\) and \(g\) be two nonconstant meromorphic functions in the complex plane \(\mathbb{C}\). If \(a\in\mathbb{C}\cup\infty\), then we denote by \(\overline{E}(a;f)\) the set of zeros of \(f-a\), and by \(E(a;f)\) we denote the set of pairs \(z,\nu\) such that \(z\) is a zero of \(f-a\) with multiplicity \(\nu\) (here the poles of \(f\) are ...
Indrajit Lahiri, Kalyan Sinha
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Polynomial Decompositions in Polynomial Time

2014
Fix a prime p. Given a positive integer k, a vector of positive integers Δ = (Δ1, Δ2, …, Δ k ) and a function \(\Gamma: \mathbb{F}_p^k \to \mathbb{F}_p\), we say that a function \(P: \mathbb{F}_p^n \to \mathbb{F}_p\) is (k,Δ,Γ)-structured if there exist polynomials \(P_1, P_2, \dots, P_k:\mathbb{F}_p^n \to \mathbb{F}_p\) with each deg(P i ) ≤ Δ i such ...
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Polynomials and Complex Polynomials

1997
If F is a field and n is a nonnegative integer, then a polynomial of degree n over F is a formal sum of the form $$P(x) = {a_0} + {a_1}x + \cdots + {a_n}{x^n}$$ With a i ∈ F for i = 0, .., n, a n ≠ 0 and x an indeterminate. A polynomial P(χ) over F is either a polynomial of some degree or the expression P(χ) = 0, which is called the zero ...
Benjamin Fine, Gerhard Rosenberger
openaire   +1 more source

The Permanental Polynomial

Journal of Chemical Information and Computer Sciences, 2000
This study identifies properties and uses of the permanental polynomial of adjacency matrixes of unweighted chemical graphs. Coefficients and zeroes of the polynomial for several representative structures are provided, and their properties are discussed.
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Polynomials and Trigonometric Polynomials

1976
Setting cos ϑ = x, the expressions $$ T_n \left( x \right) = \cos n\vartheta {\text{ }}U_n \left( x \right) = \frac{1} {{n + 1}}T'_{n + 1} \left( x \right) = \frac{{\sin \left( {n + 1} \right)\vartheta }} {{\sin \vartheta }}'{\text{ }}n = 0,1,2,...
George Pólya, Gabor Szegö
openaire   +1 more source

On Polynomials in a Polynomial

Bulletin of the London Mathematical Society, 1972
Evyatar, A., Scott, D. B.
openaire   +2 more sources

Interior-point polynomial algorithms in convex programming

Siam studies in applied mathematics, 1994
Y. Nesterov, A. Nemirovskii
semanticscholar   +1 more source

Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree

Advances in Computational Mathematics, 1995
H. Wendland
semanticscholar   +1 more source

Local polynomial modelling and its applications

, 1994
Jianqing Fan, I. Gijbels
semanticscholar   +1 more source