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Practical polynomial factoring in polynomial time [PDF]
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011 State of the art factoring in Q[x] is dominated in theory by a combinatorial reconstruction problem while, excluding some rare polynomials, performance tends to be dominated by Hensel lifting. We present an algorithm which gives a practical improvement (less Hensel lifting) for these more common polynomials.
William Hart +2 more
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An explicit Wiener–Hopf factorization algorithm for matrix polynomials and its exact realizations within ExactMPF package [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022 VÍCTOR Adukov +2 more
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A heuristic technique for decomposing multisets of non-negative integers according to the Minkowski sum [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We study the following problem. Given a multiset $M$ of non-negative integers, decide whether there exist and, in the positive case, compute two non-trivial multisets whose Minkowski sum is equal to $M$.
Luciano Margara
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Some Families of Differential Equations Associated with Multivariate Hermite Polynomials
Fractal and Fractional, 2023 In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial differential ...
Badr Saad T. Alkahtani +2 more
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Fractal and Fractional, 2021 This article has a motive to derive a new class of differential equations and associated integral equations for some hybrid families of Laguerre–Gould–Hopper-based Sheffer polynomials.
Naeem Ahmad +4 more
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Factorization of motion polynomials [PDF]
Journal of Symbolic Computation, 2019 In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial factor and factorizations.
Zijia Li +2 more
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The Numerical Factorization of Polynomials [PDF]
Foundations of Computational Mathematics, 2015 Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the ...
Wenyuan Wu, Zhonggang Zeng
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Bilinear character correlators in superintegrable theory
European Physical Journal C: Particles and Fields, 2023 We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the Schur functions.
A. Mironov, A. Morozov
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Random polynomials and polynomial factorization [PDF]
, 1996 We give a precise average-case analysis of a complete polynomial factorization chain over finite fields by methods based on generating functions and singularity analysis.
Philippe Flajolet +2 more
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Factoring octonion polynomials [PDF]
International Journal of Algebra and Computation, 2020 We provide an analogue of Wedderburn’s factorization method for central polynomials with coefficients in an octonion division algebra, and present an algorithm for fully factoring polynomials of degree [Formula: see text] with [Formula: see text] conjugacy classes of roots, counting multiplicities.
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