{"results":[{"id":"arxiv_2510.05103","title":"A note on a paper by Hashemi and Kapur","authors":[{"name":"Anna Nymann Heisel"},{"name":"Niels Lauritzen"}],"abstract":"Recently Hashemi and Kapur published an algorithm [1] for Groebner basis conversion by truncating polynomials according to a source and a target monomial order. Here we present a counterexample to this algorithm.","source":"arXiv","year":2025,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/2510.05103","pdf_url":"https://arxiv.org/pdf/2510.05103","is_open_access":true,"published_at":"2025-08-18T14:21:09Z","score":69},{"id":"arxiv_2311.06065","title":"On the Existence of Telescopers for P-recursive Sequences","authors":[{"name":"Lixin Du"}],"abstract":"We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive sequences.","source":"arXiv","year":2023,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/2311.06065","pdf_url":"https://arxiv.org/pdf/2311.06065","is_open_access":true,"published_at":"2023-11-10T14:00:50Z","score":67},{"id":"arxiv_1903.12427","title":"Computing huge Groebner basis like cyclic10 over $\\Q$ with Giac","authors":[{"name":"Bernard Parisse"}],"abstract":"We present a short description on how to fine-tune the modular algorithm implemented in the Giac computer algebra system to reconstruct huge Groebner basis over $\\Q$.The classical cyclic10 benchmark will serve as example.","source":"arXiv","year":2019,"language":"en","subjects":["cs.SC","cs.MS"],"url":"https://arxiv.org/abs/1903.12427","pdf_url":"https://arxiv.org/pdf/1903.12427","is_open_access":true,"published_at":"2019-03-29T10:00:47Z","score":63},{"id":"arxiv_1702.07248","title":"Generalized Bruhat decomposition in commutative domains","authors":[{"name":"Gennadi Malaschonok"}],"abstract":"Deterministic recursive algorithms for the computation of generalized Bruhat decomposition of the matrix in commutative domain are presented. This method has the same complexity as the algorithm of matrix multiplication.","source":"arXiv","year":2017,"language":"en","subjects":["cs.SC"],"doi":"10.1007/978-3-319-02297-0_20","url":"https://arxiv.org/abs/1702.07248","pdf_url":"https://arxiv.org/pdf/1702.07248","is_open_access":true,"published_at":"2017-02-23T14:59:12Z","score":61},{"id":"arxiv_1712.07935","title":"A non-commutative algorithm for multiplying (7 $\\times$ 7) matrices using 250 multiplications","authors":[{"name":"Alexandre Sedoglavic"}],"abstract":"We present a non-commutative algorithm for multiplying (7x7) matrices using 250 multiplications and a non-commutative algorithm for multiplying (9x9) matrices using 520 multiplications. These algorithms are obtained using the same divide-and-conquer technique.","source":"arXiv","year":2017,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1712.07935","pdf_url":"https://arxiv.org/pdf/1712.07935","is_open_access":true,"published_at":"2017-12-21T13:49:28Z","score":61},{"id":"arxiv_1703.06120","title":"Roots multiplicity without companion matrices","authors":[{"name":"Przemysław Koprowski"}],"abstract":"We show a method for constructing a polynomial interpolating roots' multiplicities of another polynomial, that does not use companion matrices. This leads to a modification to Guersenzvaig--Szechtman square-free decomposition algorithm that is more efficient both in theory and in practice.","source":"arXiv","year":2017,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1703.06120","pdf_url":"https://arxiv.org/pdf/1703.06120","is_open_access":true,"published_at":"2017-03-17T17:28:23Z","score":61},{"id":"arxiv_1611.02569","title":"Sparse multivariate factorization by mean of a few bivariate factorizations","authors":[{"name":"Bernard Parisse"}],"abstract":"We describe an algorithm to factor sparse multivariate polynomials using O(d) bivariate factorizations where d is the number of variables. This algorithm is implemented in the Giac/Xcas computer algebra system.","source":"arXiv","year":2016,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1611.02569","pdf_url":"https://arxiv.org/pdf/1611.02569","is_open_access":true,"published_at":"2016-11-08T15:53:13Z","score":60},{"id":"arxiv_1601.02756","title":"Factorization of C-finite Sequences","authors":[{"name":"Manuel Kauers"},{"name":"Doron Zeilberger"}],"abstract":"We discuss how to decide whether a given C-finite sequence can be written nontrivially as a product of two other C-finite sequences.","source":"arXiv","year":2016,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1601.02756","pdf_url":"https://arxiv.org/pdf/1601.02756","is_open_access":true,"published_at":"2016-01-12T07:45:00Z","score":60},{"id":"arxiv_1606.02845","title":"Inverse Mellin Transform of Holonomic Sequences","authors":[{"name":"Jakob Ablinger"}],"abstract":"We describe a method to compute the inverse Mellin transform of holonomic sequences, that is based on a method to compute the Mellin transform of holonomic functions. Both methods are implemented in the computer algebra package HarmonicSums.","source":"arXiv","year":2016,"language":"en","subjects":["cs.SC","math-ph","math.CO"],"url":"https://arxiv.org/abs/1606.02845","pdf_url":"https://arxiv.org/pdf/1606.02845","is_open_access":true,"published_at":"2016-06-09T07:24:05Z","score":60},{"id":"arxiv_1503.02239","title":"On the Computation of the Galois Group of Linear Difference Equations","authors":[{"name":"Ruyong Feng"}],"abstract":"We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.","source":"arXiv","year":2015,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1503.02239","pdf_url":"https://arxiv.org/pdf/1503.02239","is_open_access":true,"published_at":"2015-03-08T02:20:14Z","score":59},{"id":"arxiv_1503.06126","title":"Polynomial complexity recognizing a tropical linear variety","authors":[{"name":"Dima Grigoriev"}],"abstract":"A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.","source":"arXiv","year":2015,"language":"en","subjects":["cs.SC","math.AG"],"url":"https://arxiv.org/abs/1503.06126","pdf_url":"https://arxiv.org/pdf/1503.06126","is_open_access":true,"published_at":"2015-03-20T15:58:25Z","score":59},{"id":"arxiv_1502.07220","title":"Groebner basis in Boolean rings is not polynomial-space","authors":[{"name":"Mark van Hoeij"}],"abstract":"We give an example where the number of elements of a Groebner basis in a Boolean ring is not polynomially bounded in terms of the bitsize and degrees of the input.","source":"arXiv","year":2015,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1502.07220","pdf_url":"https://arxiv.org/pdf/1502.07220","is_open_access":true,"published_at":"2015-02-25T16:09:01Z","score":59},{"id":"ss_71ac7c6ce266708655da0bf205fa09d7c6e0190e","title":"Generalization of Boole-Shannon expansion, consistency of Boolean equations and elimination by orthonormal expansion","authors":[{"name":"V. Sule"}],"abstract":"The well known Boole -Shannon expansion of Boolean functions in several variables (with coefficients in a Boolean algebraB) is also known in more general form in terms of expansion in a setof orthonormal functions. However, unlike the one variable step of this expansion an analogous elimination theorem and consistency is not well known. This article proves such an elimination theorem for a special class of Boolean functions denoted B(�). When the orthonormal setis of polynomial size in number n of variables, the consistency of a Boolean equation f = 0 can be determined in polynomial number of B-operations. A characterization of B(�) is also shown and an elimination based procedure for computing consistency of Boolean equations is proposed. Comments: 15 pages, Revised June 18, 2013 Category: cs.CC, cs.SC, ms.RA ACM class: I.1.2, F.2.2, G.2 MSC class: 03G05, 06E30, 94C10.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Mathematics","Computer Science"],"url":"https://www.semanticscholar.org/paper/71ac7c6ce266708655da0bf205fa09d7c6e0190e","is_open_access":true,"citations":6,"published_at":"","score":57.18},{"id":"arxiv_1201.1177","title":"Computational Tutorial on Gröbner bases embedding Sage in LaTeX with SageTEX","authors":[{"name":"Edinah K. Gnang"}],"abstract":"Elementary tutorial on implementation aspects of Gröbner bases computation.","source":"arXiv","year":2012,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1201.1177","pdf_url":"https://arxiv.org/pdf/1201.1177","is_open_access":true,"published_at":"2012-01-05T14:32:00Z","score":56},{"id":"arxiv_1104.4131","title":"Automated Synthesis of Tableau Calculi","authors":[{"name":"Renate A. Schmidt"},{"name":"Dmitry Tishkovsky"}],"abstract":"This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.","source":"arXiv","year":2011,"language":"en","subjects":["cs.LO","cs.SC"],"doi":"10.2168/LMCS-7(2:6)2011","url":"https://arxiv.org/abs/1104.4131","pdf_url":"https://arxiv.org/pdf/1104.4131","is_open_access":true,"published_at":"2011-04-20T21:22:43Z","score":55},{"id":"arxiv_1011.3721","title":"On the Inverse Of General Cyclic Heptadiagonal and Anti-Heptadiagonal Matrices","authors":[{"name":"A. A. Karawia"}],"abstract":"In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work presented in [A. A. KARAWIA, A New Algorithm for Inverting General Cyclic Heptadiagonal Matrices Recursively, arXiv:1011.2306v1 [cs.SC]]. The symbolic algorithms are suited for implementation using Computer Algebra Systems (CAS) such as MATLAB, MAPLE and MATHEMATICA. An illustrative example is given.","source":"arXiv","year":2010,"language":"en","subjects":["cs.SC","math.NA"],"url":"https://arxiv.org/abs/1011.3721","pdf_url":"https://arxiv.org/pdf/1011.3721","is_open_access":true,"published_at":"2010-11-15T11:42:22Z","score":54},{"id":"arxiv_1012.3442","title":"Théorie de Galois effective : aide mémoire","authors":[{"name":"Annick Valibouze"}],"abstract":"This paper collects many results on galoisian ideals and Galois theory.","source":"arXiv","year":2010,"language":"en","subjects":["cs.SC"],"url":"https://arxiv.org/abs/1012.3442","pdf_url":"https://arxiv.org/pdf/1012.3442","is_open_access":true,"published_at":"2010-12-15T19:49:42Z","score":54},{"id":"crossref_10.1007/bf01168955","title":"Hardening mechanisms in Al-Sc alloys","authors":[{"name":"T. Torma"},{"name":"E. Kov�cs-Cset�nyi"},{"name":"T. Turmezey"},{"name":"T. Ung�r"},{"name":"I. Kov�cs"}],"abstract":"","source":"CrossRef","year":1989,"language":"en","subjects":null,"doi":"10.1007/bf01168955","url":"https://doi.org/10.1007/bf01168955","pdf_url":"http://link.springer.com/content/pdf/10.1007/BF01168955.pdf","is_open_access":true,"citations":35,"published_at":"","score":51.05}],"total":161504,"page":1,"page_size":20,"sources":["arXiv","DOAJ","Semantic Scholar","CrossRef"],"query":"cs.SC"}