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Journal of Symbolic Computation, 1998 Let \(R\) be either \(Z\) or \(F_q [y]\), \(F_q\) the finite field containing \(q\) elements, and let \(r \in R\) be a non-zero non-unit. The aim of the work is to describe all possible factorizations into irreducibles of polynomials in \(R[x]\) over the ring \(R/(r)\) where \((r)\) is the ideal generated by \(r\).
Joachim von zur Gathen, Silke Hartlieb
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An Algorithm for the Factorization of Split Quaternion Polynomials [PDF]
, 2021 We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists.
Schröcker, Hans-Peter +1 more
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The Numerical Factorization of a Polynomial [PDF]
SIAM Review, 1971 A number of methods can be found in the literature for the numerical factorization of a polynomial, and references to some are given in the bibliography below. Well-known examples are those of Lin and of Bairstow. Many are quadratically convergent, but most require a sufficiently close initial factorization to start with.
Householder, A. S., Stewart, G. W.
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Parallel Factorization of Boolean Polynomials [PDF]
, 2019 Polynomial factorization is a classical algorithmic problem in algebra, which has a wide range of applications. Of special interest is factorization over finite fields, among which the field of order two is probably the most important one due to the ...
Ponomaryov, D +11 more
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A generalization of the Bernoulli polynomials
Journal of Applied Mathematics, 2003 A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the ...
Pierpaolo Natalini, Angela Bernardini
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Bernoulli F-polynomials and Fibo–Bernoulli matrices
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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On (r; t; s)-nuclear polynomials
Moroccan Journal of Pure and Applied Analysis, 2022 In this work we extend the concept of (r; t; s)-nuclear operators presented by Lapresté in (Studia math., T. LVII. 1976, 47 – 83) to n-homogeneous polynomials. Factorization and inclusion properties are described.
Bougoutaia Amar +2 more
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On the Existence of Hurwitz Polynomials with no Hadamard Factorization [PDF]
, 2020 A Hurwitz stable polynomial of degree $n\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e., element-wise multiplication) of two Hurwitz stable polynomials of degree $n$.
Góra, Michał, Białas, Stanisław
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On generalized Heun equation with some mathematical properties
Acta Polytechnica, 2022 We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters.
Nasser Saad
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Factoring with cyclotomic polynomials [PDF]
26th Annual Symposium on Foundations of Computer Science (sfcs 1985), 1985 This paper discusses some new integer factoring methods involving cyclotomic polynomials. There are several polynomials f ( X
Eric Bach 0001, Jeffrey O. Shallit
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