ACM Communications in Computer Algebra最新文献_第3页

Counting Clean Words According to the Number of Their Clean Neighbors 根据干净邻居的数量来计算干净单词

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ACM Communications in Computer Algebra Pub Date : 2023-03-01 DOI: 10.1145/3610377.3610379

S. B. Ekhad, D. Zeilberger

引用次数: 0

Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces 具有无穷维解空间的序列系数线性差分算子

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ACM Communications in Computer Algebra Pub Date : 2023-03-01 DOI: 10.1145/3610377.3610378

S. Abramov, G. Pogudin

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Marko Petkovšek 1955--2023 Marko Petkovšek 1955-2023

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ACM Communications in Computer Algebra Pub Date : 2023-03-01 DOI: 10.1145/3610377.3610380

Eva U. Petkovšek

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Algorithms for Quadratic Forms over Global Function Fields 全局函数域上二次型的算法

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ACM Communications in Computer Algebra Pub Date : 2022-12-01 DOI: 10.1145/3609983.3609985

Mawunyo Kofi Darkey-Mensah

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引用次数: 0

Symmetric Generation of J2 on 32 Letters J2在32个字母上的对称生成

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ACM Communications in Computer Algebra Pub Date : 2022-12-01 DOI: 10.1145/3609983.3609984

Connie Corona, Zahid Hasan, Bronson Lim

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Adaptive Thiele interpolation 自适应Thiele插值

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ACM Communications in Computer Algebra Pub Date : 2022-09-01 DOI: 10.1145/3594252.3594254

O. S. Celis

引用次数: 1

A Bridge between Euclid and Buchberger: (An Attempt to Enhance Gröbner Basis Algorithm by PRSs and GCDs) Euclid和Buchberger之间的桥梁：（用PRS和GCD增强Gröbner基算法的尝试）

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ACM Communications in Computer Algebra Pub Date : 2022-09-01 DOI: 10.1145/3594252.3594253

Tateaki Sasaki

{"title":"A Bridge between Euclid and Buchberger: (An Attempt to Enhance Gröbner Basis Algorithm by PRSs and GCDs)","authors":"Tateaki Sasaki","doi":"10.1145/3594252.3594253","DOIUrl":"https://doi.org/10.1145/3594252.3594253","url":null,"abstract":"This article surveys a very new method of enhancing Buchberger's Gröbner basis algorithm by the PRSs (polynomial remainder sequences) and the GCDs of multivariate polynomials. Let F = {F1,...,Fm+1} ⊂ K[x, u] be a given system, where (x) = (x1,...,xm) and (u) = (u1,...,un). Currently, we treat only such Fs that are \"healthy\" (see the text). Let [EQUATION], where [EQUATION], be the reduced Gröbner basis of ideal (F) w.r.t. the lexicographic order, to be abbreviated to GB(F). Let [EQUATION], be such that [EQUATION] is a small multiple of G1, and the leading monomial of [EQUATION], is a multiple (hopefully small) of the leading monomial of Gi. Our method computes [EQUATION] first, then computes [EQUATION]. Finally, we will apply Buchberger's method to system [EQUATION]. Four new theorems are given. The first and second ones are to compute the lowest-order element of the ideal generated by relatively prime G, H ∈ K[x, u], without computing any Spolynomial. The third theorem says that if F is healthy then [EQUATION]. We compute resultants in K[u], of F through different routes. Then, by Theorem 3, the resultants will be different multiples of G1. Hence, the GCD of them will be a small multiple of G1. In the elimination of x through different routes, we obtain sets of similar remainders such that the elements of each set have the same leading variable and nearly the same degrees. We call the leading coefficients of mutually similar remainders an \"LCsystem\". We eliminate the leading variables of suitably chosen LCsystems. The fourth theorem constructs a polynomial [EQUATION], such that the leading coefficient of [EQUATION] is the GCD of resultants of elements of an LCsystem chosen.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"97 - 124"},"PeriodicalIF":0.1,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45433243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An SMT solver for non-linear real arithmetic inside maple maple内部非线性实数运算的SMT求解器

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ACM Communications in Computer Algebra Pub Date : 2022-06-01 DOI: 10.1145/3572867.3572880

AmirHosein Sadeghimanesh, M. England

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Jenks prize announcement 詹克斯获奖公告

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ACM Communications in Computer Algebra Pub Date : 2022-06-01 DOI: 10.1145/3572867.3572884

H. Cohen, Bill Allombert, K. Belabas

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Towards signature-based gröbner basis algorithms for computing the nondegenerate locus of a polynomial system 计算多项式系统非退化轨迹的基于签名的gröbner基算法