Results 1 to 10 of about 219 (119)
A novel linear algebra-based method for complex interval linear systems in circuit analysis [PDF]
HeliyonIn this paper, systems of multivariate interval linear equations with complex interval coefficients are examined, and a novel linear algebra-based approach for locating all of their solutions is proposed.
Maryam Farahmand Nejad +2 more
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The Extension of the GVW Algorithm to Valuation Domains
Complexity, 2021 The GVW algorithm is an effective algorithm to compute Gröbner bases for polynomial ideals over a field. Combined with properties of valuation domains and the idea of the GVW algorithm, we propose a new algorithm to compute Gröbner bases for polynomial ...
Dongmei Li, Licui Zheng
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Gröbner Bases with Reduction Machines [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 In this paper, we make a contribution to the computation of Gröbner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we investigate what ...
Georgiana Şurlea, Adrian Crăciun
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Gröbner–Shirshov Bases Theory for Trialgebras
Mathematics, 2021 We establish a method of Gröbner–Shirshov bases for trialgebras and show that there is a unique reduced Gröbner–Shirshov basis for every ideal of a free trialgebra.
Juwei Huang, Yuqun Chen
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Rationalizing Denominators Using Gröbner Bases
Complexity, 2022 The problem of rationalizing denominators for two types of fractions is discussed in the paper. By using the theory and algorithms of Gröbner bases, we first introduce a method to rationalize the denominators of fractions with square root and cube root ...
Dongmei Li +3 more
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International Journal of Advanced Robotic Systems, 2021 This article presents an analysis of computational efficiency to solve the inverse kinematics problem of anthropomorphic robots. Two approaches are investigated: the first approach uses Paul’s method applied to the matrix obtained by the Denavit ...
Sérgio Ricardo Xavier da Silva +2 more
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Feynman integral reduction using Gröbner bases
Journal of High Energy Physics, 2023 We investigate the reduction of Feynman integrals to master integrals using Gröbner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal.
Mohamed Barakat +4 more
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New Operated Polynomial Identities and Gröbner-Shirshov Bases
Mathematics, 2022 Twenty years ago, Rota posed the problem of finding all possible algebraic identities that can be satisfied by a linear operator on an algebra, named Rota’s Classification Problem later. Rota’s Classification Problem has proceeded two steps to understand
Jinwei Wang, Zhicheng Zhu, Xing Gao
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s-Sequences and Monomial Modules
Mathematics, 2021 In this paper we study a monomial module M generated by an s-sequence and the main algebraic and homological invariants of the symmetric algebra of M. We show that the first syzygy module of a finitely generated module M, over any commutative Noetherian ...
Gioia Failla, Paola Lea Staglianó
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A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
Open Mathematics, 2015 Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable ...
Zhao Xiangui, Zhang Yang
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