Journal of Computational Algebra最新文献

Computing quadratic subfields of number fields 计算数字域的二次子域

Journal of Computational Algebra Pub Date : 2025-07-23 DOI: 10.1016/j.jaca.2025.100039

Andreas-Stephan Elsenhans , Jürgen Klüners

引用次数: 0

A 3-skeleton for a classifying space for the symmetric group 对称群分类空间的3-骨架

Journal of Computational Algebra Pub Date : 2025-06-23 DOI: 10.1016/j.jaca.2025.100038

Matthew B. Day , Trevor Nakamura

{"title":"A 3-skeleton for a classifying space for the symmetric group","authors":"Matthew B. Day , Trevor Nakamura","doi":"10.1016/j.jaca.2025.100038","DOIUrl":"10.1016/j.jaca.2025.100038","url":null,"abstract":"<div><div>We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg–MacLane classifying space for the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Our complex starts with the presentation for <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span> adjacent transpositions with squaring, commuting, and braid relations, and adds seven classes of 3-cells that fill in certain 2-spheres bounded by these relations. We use a rewriting system and a combinatorial method of K. Brown to prove the correctness of our construction. Our main application is a computation of the second cohomology of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> in certain twisted coefficient modules; we use this computation in a companion paper to study splitting of extensions related to braid groups. As another application, we give a concrete description of the third homology of <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with untwisted coefficients in <span><math><mi>Z</mi></math></span>.</div></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"15 ","pages":"Article 100038"},"PeriodicalIF":0.0,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517258","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 algorithm to compute the Hausdorff dimension of regular branch groups 正则分支群的Hausdorff维数计算算法

Journal of Computational Algebra Pub Date : 2025-06-19 DOI: 10.1016/j.jaca.2025.100037

Jorge Fariña-Asategui

引用次数: 0

Nested fifth root radical identities from elliptic curves 椭圆曲线的嵌套五根根恒等式

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100032

Joseph Tonien

引用次数: 0

Ideals of generic forms 一般形式的理想

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100033

Ralf Fröberg

引用次数: 0

Listing words in free groups 在自由组中列出单词

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100034

Colin Ramsay

引用次数: 0

Computational and theoretical aspects of rational parametrization of generalized tubular surfaces 广义管状曲面合理参数化的计算与理论研究

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100030

J. William Hoffman , Haohao Wang

{"title":"Computational and theoretical aspects of rational parametrization of generalized tubular surfaces","authors":"J. William Hoffman , Haohao Wang","doi":"10.1016/j.jaca.2025.100030","DOIUrl":"10.1016/j.jaca.2025.100030","url":null,"abstract":"<div><div>This paper consists of two components - a computational part and a theoretical part. The former targets the computer-aided geometric design of tubular surfaces. The latter focuses on the algebraic geometry of a family of conic curves. At the application level, we provide a straightforward and easy to implement computational algorithm to rationally parametrize generalized real tubular surfaces via moving lines. We discover that syzygies, i.e., moving lines, can be calculated directly from a given implicit equation of a projective conic. Specifically, we describe two linear polynomial vectors in 3-space whose entries are formulated in terms of the coefficients of the given implicit equation of the conic. We then prove that these two vectors are, in fact, a <em>μ</em>-basis, the generators for the syzygy module of the given conic, and furnish the rational parametrization of the given conic. At the theoretical level, we first briefly review the classical projection method for a rational parametrization of a generic non-degenerate conic. This is compared to the syzygy method, i.e., moving lines. We conclude the paper with an illustrative figure that depicts and compares the classical projection method and our moving line method.</div></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"13 ","pages":"Article 100030"},"PeriodicalIF":0.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Differential uniformity properties of some classes of permutation polynomials 几类置换多项式的微分均匀性

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100035

Kirpa Garg , Sartaj Ul Hasan , Pantelimon Stănică

{"title":"Differential uniformity properties of some classes of permutation polynomials","authors":"Kirpa Garg , Sartaj Ul Hasan , Pantelimon Stănică","doi":"10.1016/j.jaca.2025.100035","DOIUrl":"10.1016/j.jaca.2025.100035","url":null,"abstract":"<div><div>The notion of <em>c</em>-differential uniformity has received a lot of attention since its proposal <span><span>[5]</span></span>, and recently a characterization of perfect <em>c</em>-nonlinear functions in terms of difference sets in some quasigroups was obtained in <span><span>[1]</span></span>. Moreover, in a very recent manuscript by Pal and Stănică <span><span>[19]</span></span>, an intriguing connection was discovered showing that in fact, the boomerang uniformity for an odd APN function (odd characteristic) equals its <em>c</em>-differential uniformity when <span><math><mi>c</mi><mo>=</mo><mo>−</mo><mn>1</mn></math></span>, if the function is a permutation, otherwise it is the maximum of the <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-DDT entries disregarding the first row/column. The construction of functions, especially permutations, with low <em>c</em>-differential uniformity is an interesting and difficult mathematical problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low <em>c</em>-differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest, from a mathematical perspective.</div></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"13 ","pages":"Article 100035"},"PeriodicalIF":0.0,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144240750","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

Zeros of S-characters 0个s字符

Journal of Computational Algebra Pub Date : 2025-03-01 DOI: 10.1016/j.jaca.2025.100031

Thomas Breuer , Michael Joswig , Gunter Malle

引用次数: 0

Symmetric perfect 2-colorings of J(10,3) J(10,3) 的对称完全 2 色

Journal of Computational Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jaca.2024.100028

Paul Tricot

引用次数: 0