Journal of Computational Algebra最新文献

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

Improved computation of polynomial roots over number fields when using complex embeddings 使用复嵌入时改进数域上多项式根的计算

Journal of Computational Algebra Pub Date : 2024-10-21 DOI: 10.1016/j.jaca.2024.100026

Andrea Lesavourey , Thomas Plantard , Willy Susilo

引用次数: 0

Signature-based algorithm under non-compatible term orders and its application to change of ordering 非相容词序下基于签名的算法及其在更改词序中的应用

Journal of Computational Algebra Pub Date : 2024-10-21 DOI: 10.1016/j.jaca.2024.100027

Masayuki Noro

引用次数: 0

Rational Askey–Wilson Bernstein bases and a multirational Askey–Wilson blossom 有理阿斯基-威尔逊伯恩斯坦基和多有理阿斯基-威尔逊花

Journal of Computational Algebra Pub Date : 2024-10-21 DOI: 10.1016/j.jaca.2024.100025

Plamen Simeonov , Ron Goldman

引用次数: 0

Factoring perfect reconstruction filter banks into causal lifting matrices: A Diophantine approach 将完美重构滤波器组分解为因果提升矩阵：一种二阶方法

Journal of Computational Algebra Pub Date : 2024-10-09 DOI: 10.1016/j.jaca.2024.100024

Christopher M. Brislawn

{"title":"Factoring perfect reconstruction filter banks into causal lifting matrices: A Diophantine approach","authors":"Christopher M. Brislawn","doi":"10.1016/j.jaca.2024.100024","DOIUrl":"10.1016/j.jaca.2024.100024","url":null,"abstract":"<div><div>The elementary theory of bivariate linear Diophantine equations over polynomial rings is used to construct causal lifting factorizations (elementary matrix decompositions) for causal two-channel FIR perfect reconstruction transfer matrices and wavelet transforms. The Diophantine approach generates causal factorizations satisfying certain polynomial degree-reducing inequalities, enabling a new factorization strategy called the <em>Causal Complementation Algorithm</em>. This provides a causal (i.e., polynomial, hence <em>realizable</em>) alternative to the noncausal lifting scheme developed by Daubechies and Sweldens using the Extended Euclidean Algorithm for Laurent polynomials. The new approach replaces the Euclidean Algorithm with Gaussian elimination employing a slight generalization of polynomial division that ensures existence and uniqueness of quotients whose remainders satisfy user-specified divisibility constraints. The Causal Complementation Algorithm is shown to be more general than the causal version of the Euclidean Algorithm approach by generating additional causal lifting factorizations beyond those obtainable using the polynomial Euclidean Algorithm.</div></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"12 ","pages":"Article 100024"},"PeriodicalIF":0.0,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530144","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

New condensation methods with applications to the computation of Brauer character tables 应用于计算布劳尔字符表的新凝聚方法

Journal of Computational Algebra Pub Date : 2024-10-02 DOI: 10.1016/j.jaca.2024.100023

Klaus Lux , A.J.E. Ryba

引用次数: 0

Monomial-agnostic computation of vanishing ideals 消失理想的一元对立计算

Journal of Computational Algebra Pub Date : 2024-09-01 DOI: 10.1016/j.jaca.2024.100022

Hiroshi Kera , Yoshihiko Hasegawa

{"title":"Monomial-agnostic computation of vanishing ideals","authors":"Hiroshi Kera , Yoshihiko Hasegawa","doi":"10.1016/j.jaca.2024.100022","DOIUrl":"10.1016/j.jaca.2024.100022","url":null,"abstract":"<div><p>Approximate basis computation of vanishing ideals has recently been studied extensively in computational algebra and data-driven applications such as machine learning. However, symbolic computation and the dependency on term order remain essential gaps between the two fields. In this study, we present the first <em>monomial-agnostic</em> basis computation, which works fully numerically with proper normalization and without term order. This is realized by gradient normalization, a newly proposed data-dependent normalization that normalizes a polynomial with the magnitude of gradients at given points. Its data-dependent nature brings various advantages: i) efficient resolution of the spurious vanishing problem, the scale-variance issue of approximately vanishing polynomials, without accessing coefficients of terms, ii) scaling-consistent basis computation, ensuring that input scaling does not lead to an essential change in the output, and iii) robustness against input perturbations, where the upper bound of error is determined only by the magnitude of the perturbations. Existing studies did not achieve any of these. As further applications of gradient information, we propose a monomial-agnostic basis reduction method and a regularization method to manage positive-dimensional ideals.</p></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"11 ","pages":"Article 100022"},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772827724000123/pdfft?md5=06e4502098d7758928fc1fb98de7de21&pid=1-s2.0-S2772827724000123-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137138","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

Conjugacy class fusion from four maximal subgroups of the Monster 怪物的四个最大子群的共轭类融合

Journal of Computational Algebra Pub Date : 2024-07-25 DOI: 10.1016/j.jaca.2024.100021

Anthony Pisani, Tomasz Popiel

引用次数: 0

Explicit construction of a plane sextic model for genus-five Howe curves, II 五属豪曲线平面六分模型的显式构建，II

Journal of Computational Algebra Pub Date : 2024-07-17 DOI: 10.1016/j.jaca.2024.100019

Momonari Kudo

{"title":"Explicit construction of a plane sextic model for genus-five Howe curves, II","authors":"Momonari Kudo","doi":"10.1016/j.jaca.2024.100019","DOIUrl":"10.1016/j.jaca.2024.100019","url":null,"abstract":"<div><p>A <em>Howe curve</em> is defined as the normalization of the fiber product over a projective line of two hyperelliptic curves. Howe curves are very useful to produce important classes of curves over fields of positive characteristic, e.g., maximal, superspecial, or supersingular ones. Determining their feasible equations explicitly is a basic problem, and it has been solved in the hyperelliptic case and in the non-hyperelliptic case with genus not greater than 4. In this paper, we construct an explicit plane sextic model for non-hyperelliptic Howe curves of genus 5. We also determine the number and type of singularities on our sextic model, and prove that the singularities are generically 4 double points. Our results together with Moriya-Kudo's recent ones imply that for each <span><math><mi>s</mi><mo>∈</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></span>, there exists a non-hyperelliptic curve <em>H</em> of genus 5 with <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>H</mi><mo>)</mo><mo>⊃</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> such that its associated plane sextic has <em>s</em> double points.</p></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"11 ","pages":"Article 100019"},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2772827724000093/pdfft?md5=3625c91a9b897ff1d916dbfe0aef7474&pid=1-s2.0-S2772827724000093-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141962691","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

Computing superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group 计算属 4 的超特殊超椭圆曲线，其自形群适当包含克莱因 4 群

Journal of Computational Algebra Pub Date : 2024-07-15 DOI: 10.1016/j.jaca.2024.100020

Ryo Ohashi , Momonari Kudo

引用次数: 0