Výsledky vyhledávání - "Polynomial greatest common divisor"

Lang–Vojta conjecture over function fields for surfaces dominating $${{\mathbb {G}}}_m^2$$

Autor: Laura Capuano, Amos Turchet

Publikováno v: European Journal of Mathematics. 8:573-610

We prove the nonsplit case of the Lang–Vojta conjecture over function fields for surfaces of log general type that are ramified covers of $${{\mathbb {G}}}_m^2$$ G m 2 . This extends the results of Corvaja and Zannier (J Differ Geom 93(3):355–377

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ca45826b455eee733fd7de0c31424342
https://doi.org/10.1007/s40879-021-00502-8

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Approximate GCD by bernstein basis, and its applications

Autor: Kosaku Nagasaka

Publikováno v: ISSAC

For the given pair of univariate polynomials generated by empirical data hence with a priori error on their coefficients, computing their greatest common divisor can be done by several known approximate GCD algorithms that are usually for polynomials

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0e00f051f3daf43b88d7de3ade0f9276
https://doi.org/10.1145/3373207.3403991

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High performance SIMD modular arithmetic for polynomial evaluation

Autor: Pierre Fortin, Ambroise Fleury, Michael Monagan, François Lemaire

Publikováno v: Concurrency and Computation: Practice and Experience
Concurrency and Computation: Practice and Experience, Wiley, 2021, 33 (16), pp.e6270. ⟨10.1002/cpe.6270⟩
Concurrency and Computation: Practice and Experience, 2021, 33 (16), pp.e6270. ⟨10.1002/cpe.6270⟩

International audience; Two essential problems in Computer Algebra, namely polynomial factorization and polynomial greatest common divisor computation, can be efficiently solved thanks to multiple polynomial evaluations in two variables using modular

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f78b5b399005de0eb59802b6125c1d3
http://arxiv.org/abs/2004.11571

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Algebraic certificates for the structural properties of parametric linear systems

Autor: Antonio Tornambè, Laura Menini, Corrado Possieri

Publikováno v: IFAC World Congress, pp. 4676–4681, 11-17/07/2021
info:cnr-pdr/source/autori:Menini, Laura; Possieri, Corrado; Tornambè, Antonio/congresso_nome:IFAC World Congress/congresso_luogo:/congresso_data:11-17%2F07%2F2021/anno:2020/pagina_da:4676/pagina_a:4681/intervallo_pagine:4676–4681

In this paper, by exploiting the concept of polynomial greatest common divisor, some algebraic tests are proposed to certify the structural properties of both discrete-time and continuous-time linear systems. Furthermore, by exploiting the concept of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8aaaf9119a7430c59aa93722af16d11e
http://hdl.handle.net/2108/294413

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Polynomial Greatest Common Divisor as a Solution of System of Linear Equations

Autor: D. Dolgov

Publikováno v: Lobachevskii Journal of Mathematics. 39:985-991

In this article we present a new algebraic approach to the greatest common divisor (GCD) computation of two polynomials based on Bezout’s identity. This approach is based on the solution of system of linear equations. Also we introduce the dmod ope

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8fa7c9a1e1e9c587606fdcdae890804f
https://doi.org/10.1134/s1995080218070090

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Blind image deconvolution via Hankel based method for computing the GCD of polynomials

Autor: Marwa Dridi, Maher Moakher, Skander Belhaj, Haithem Ben Kahla

Publikováno v: Mathematics and Computers in Simulation. 144:138-152

In this paper we present an algorithm, that is based on computing approximate greatest common divisors (GCD) of polynomials, for solving the problem of blind image deconvolution. Specifically, we design a specialized algorithm for computing the GCD o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::670127d988f9a7d1056ec7eb47c6d73d
https://doi.org/10.1016/j.matcom.2017.07.008

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Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials

Autor: Marilena Mitrouli, Dimitrios Christou, Dimitrios Triantafyllou

Publikováno v: Special Matrices, Vol 5, Iss 1, Pp 202-224 (2017)

This paper revisits the Bézout, Sylvester, and power-basis matrix representations of the greatest common divisor (GCD) of sets of several polynomials. Furthermore, the present work introduces the application of the QR decomposition with column pivot

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e747cd964153b178100722114bc1ff78
https://doaj.org/article/6fa06bdda3b942ffa196d203ce82e56f

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Shortest division chains in unique factorization domains

Autor: Maksim Vaskouski, Nikita Kondratyonok

Publikováno v: Journal of Symbolic Computation. 77:175-188

We investigate the problem on the validity of the Lazard theorem analogue (or the Kronecker-Vahlen theorem), which states that the least remainder Euclidean Algorithm (EA) has the shortest length over any other versions of EA, in unique factorization

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f11f91e400e8db967447ea31ab3b9087
https://doi.org/10.1016/j.jsc.2016.02.003

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The factorization of the linear differential operator

Autor: Klara Janglajew, Ewa Schmeidel

Publikováno v: Tatra Mountains Mathematical Publications. 63:139-151

In this paper, necessary and sufficient conditions for factorization of a linear differential operator are presented. As a consequence of the factorization result some criterion of polynomial factorization is obtained. As a special case of the main r

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f84cfc5c25aa23f58e2534aeb726bd96
https://doi.org/10.1515/tmmp-2015-0026

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The Greatest Common Divisors of Euclidean Domain Matrices

Autor: Nur Erawaty, Mawardi Bahri, Loecky Haryanto, Amir Kamal Amir

One of the Euclidean Domain is the ring of polynomials over reals . Since the notion of greatest common divisor of two matrices with polynomial entries is well-defined, in this paper the same notion is generalized to two matrices with entries from an

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d03f4402c2f9cf5a075ba4045255b63
http://repository.unhas.ac.id/handle/123456789/24276

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