Journal of Symbolic Computation最新文献

筛选
英文 中文
First-order factors of linear Mahler operators 线性马勒算子的一阶因子
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-01-28 DOI: 10.1016/j.jsc.2025.102424
Frédéric Chyzak , Thomas Dreyfus , Philippe Dumas , Marc Mezzarobba
{"title":"First-order factors of linear Mahler operators","authors":"Frédéric Chyzak ,&nbsp;Thomas Dreyfus ,&nbsp;Philippe Dumas ,&nbsp;Marc Mezzarobba","doi":"10.1016/j.jsc.2025.102424","DOIUrl":"10.1016/j.jsc.2025.102424","url":null,"abstract":"<div><div>We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msub><msup><mrow><mi>M</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>+</mo><mo>…</mo><mo>+</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>M</mi><mo>+</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> where <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> are polynomials in <em>x</em> and <span><math><mi>M</mi><mi>x</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>b</mi></mrow></msup><mi>M</mi></math></span> for some integer <span><math><mi>b</mi><mo>≥</mo><mn>2</mn></math></span>. In other words, we give algorithms for finding all formal infinite product solutions of linear functional equations <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></msup></mrow></msup><mo>)</mo><mo>+</mo><mo>…</mo><mo>+</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mi>f</mi><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>b</mi></mrow></msup><mo>)</mo><mo>+</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></span>.</div><div>The first of our algorithms is adapted from Petkovšek's classical algorithm for the analogous problem in the case of linear recurrences. The second one proceeds by computing a basis of generalized power series solutions of the functional equation and by using Hermite–Padé approximants to detect those linear combinations of the solutions that correspond to first-order factors.</div><div>We present implementations of both algorithms and discuss their use in combination with criteria from the literature to prove the differential transcendence of power series solutions of Mahler equations.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102424"},"PeriodicalIF":0.6,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143288038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The conjugacy problem and canonical representatives in finitely generated nilpotent groups 有限生成幂零群中的共轭问题与正则代表
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-01-27 DOI: 10.1016/j.jsc.2025.102422
Bettina Eick, Óscar Fernández Ayala
{"title":"The conjugacy problem and canonical representatives in finitely generated nilpotent groups","authors":"Bettina Eick,&nbsp;Óscar Fernández Ayala","doi":"10.1016/j.jsc.2025.102422","DOIUrl":"10.1016/j.jsc.2025.102422","url":null,"abstract":"<div><div>We introduce a variation on the conjugacy problem for elements and subgroups in a finitely generated nilpotent group <em>G</em> given by a nilpotent presentation and we describe effective algorithms for its solution. While the classical conjugacy problem takes elements or subgroups <em>a</em> and <em>b</em> of <em>G</em> and asks to construct <span><math><mi>g</mi><mo>∈</mo><mi>G</mi></math></span> with <span><math><msup><mrow><mi>a</mi></mrow><mrow><mi>g</mi></mrow></msup><mo>=</mo><mi>b</mi></math></span>, our variation defines and determines a <em>canonical representative</em> <span><math><mi>C</mi><mi>a</mi><mi>n</mi><msub><mrow><mi>o</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>)</mo></math></span> in <span><math><msup><mrow><mi>a</mi></mrow><mrow><mi>G</mi></mrow></msup></math></span>. This allows to solve the conjugacy problem via an equality test <span><math><mi>C</mi><mi>a</mi><mi>n</mi><msub><mrow><mi>o</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>a</mi><mo>)</mo><mo>=</mo><mi>C</mi><mi>a</mi><mi>n</mi><msub><mrow><mi>o</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span>. Additionally, our algorithms compute the associated centralizers or normalizers, respectively. We exhibit a variety of examples to demonstrate that our new methods are highly effective and often outperform the existing methods to solve the conjugacy problems for elements and subgroups in finitely generated nilpotent groups.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102422"},"PeriodicalIF":0.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the existence of telescopers for P-recursive sequences 关于p -递归序列的望远镜的存在性
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-01-27 DOI: 10.1016/j.jsc.2025.102423
Lixin Du
{"title":"On the existence of telescopers for P-recursive sequences","authors":"Lixin Du","doi":"10.1016/j.jsc.2025.102423","DOIUrl":"10.1016/j.jsc.2025.102423","url":null,"abstract":"<div><div>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-Petkovšek reduction for P-recursive sequences.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102423"},"PeriodicalIF":0.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143177145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fast evaluation of generalized Todd polynomials: Applications to MacMahon's partition analysis and integer programming 广义Todd多项式的快速求值:在MacMahon划分分析和整数规划中的应用
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-01-27 DOI: 10.1016/j.jsc.2025.102420
Guoce Xin , Yingrui Zhang , ZiHao Zhang
{"title":"Fast evaluation of generalized Todd polynomials: Applications to MacMahon's partition analysis and integer programming","authors":"Guoce Xin ,&nbsp;Yingrui Zhang ,&nbsp;ZiHao Zhang","doi":"10.1016/j.jsc.2025.102420","DOIUrl":"10.1016/j.jsc.2025.102420","url":null,"abstract":"<div><div>The Todd polynomials, denoted as <span><math><msub><mrow><mtext>td</mtext></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math></span>, are characterized by their generating function:<span><span><span><math><munder><mo>∑</mo><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></munder><msub><mrow><mtext>td</mtext></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mi>s</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>=</mo><munderover><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><mfrac><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>s</mi></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>s</mi></mrow></msup><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo></math></span></span></span> These polynomials serve as fundamental components in the Todd class of toric varieties – a concept of significant relevance in the study of lattice polytopes and number theory. We identify that generalized Todd polynomials emerge naturally within the realm of MacMahon's partition analysis, particularly in the context of computing the Ehrhart series. We introduce an efficient method for the evaluation of generalized Todd polynomials for numerical values of <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. This is achieved through the development of expedited operations in the quotient ring <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>[</mo><mo>[</mo><mi>s</mi><mo>]</mo><mo>]</mo></math></span> modulo <span><math><msup><mrow><mi>s</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, where <em>p</em> is a large prime. The practical implications of our work are demonstrated through two applications: firstly, we facilitate a recalculated resolution of the Ehrhart series for magic squares of order 6, a problem initially addressed by the first author, reducing computation time from 70 days to approximately 1 day; secondly, we present a polynomial-time algorithm for Integer Linear Programming in the scenario where the dimension is fixed, exhibiting a notable enhancement in computational efficiency.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102420"},"PeriodicalIF":0.6,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving order 3 difference equations 解3阶差分方程
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-01-13 DOI: 10.1016/j.jsc.2025.102419
Heba Bou KaedBey, Mark van Hoeij, Man Cheung Tsui
{"title":"Solving order 3 difference equations","authors":"Heba Bou KaedBey,&nbsp;Mark van Hoeij,&nbsp;Man Cheung Tsui","doi":"10.1016/j.jsc.2025.102419","DOIUrl":"10.1016/j.jsc.2025.102419","url":null,"abstract":"<div><div>We classify order 3 linear difference operators over <span><math><mi>C</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion of absolute irreducibility for difference modules, and classify modules of arbitrary dimension that are irreducible but not absolutely irreducible.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102419"},"PeriodicalIF":0.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computational Algebra and Geometry: A special issue in memory and honor of Agnes Szanto 计算代数与几何:纪念和纪念阿格尼斯·桑托的特刊
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2024-12-17 DOI: 10.1016/j.jsc.2024.102418
Carlos D'Andrea, Hoon Hong, Evelyne Hubert, Teresa Krick
{"title":"Computational Algebra and Geometry: A special issue in memory and honor of Agnes Szanto","authors":"Carlos D'Andrea,&nbsp;Hoon Hong,&nbsp;Evelyne Hubert,&nbsp;Teresa Krick","doi":"10.1016/j.jsc.2024.102418","DOIUrl":"10.1016/j.jsc.2024.102418","url":null,"abstract":"","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102418"},"PeriodicalIF":0.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143160245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quadratic equations in the lamplighter group 点灯组的二次方程
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2024-12-09 DOI: 10.1016/j.jsc.2024.102417
Alexander Ushakov, Chloe Weiers
{"title":"Quadratic equations in the lamplighter group","authors":"Alexander Ushakov,&nbsp;Chloe Weiers","doi":"10.1016/j.jsc.2024.102417","DOIUrl":"10.1016/j.jsc.2024.102417","url":null,"abstract":"<div><div>In this paper we study the complexity of solving quadratic equations in the lamplighter group. We give a complete classification of cases (depending on genus and other characteristics of a given equation) when the problem is <strong>NP</strong>-complete or polynomial-time decidable. We notice that the conjugacy problem can be solved in linear time. Finally, we prove that the problem belongs to the class <strong>XP</strong>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102417"},"PeriodicalIF":0.6,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topological closure of formal powers series ideals and application to topological rewriting theory 形式幂级数理想的拓扑闭包及其在拓扑改写理论中的应用
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2024-12-04 DOI: 10.1016/j.jsc.2024.102416
Cyrille Chenavier, Thomas Cluzeau, Adya Musson-Leymarie
{"title":"Topological closure of formal powers series ideals and application to topological rewriting theory","authors":"Cyrille Chenavier,&nbsp;Thomas Cluzeau,&nbsp;Adya Musson-Leymarie","doi":"10.1016/j.jsc.2024.102416","DOIUrl":"10.1016/j.jsc.2024.102416","url":null,"abstract":"<div><div>We investigate formal power series ideals and their relationship to topological rewriting theory. Since commutative formal power series algebras are Zariski rings, their ideals are closed for the adic topology defined by the maximal ideal generated by the indeterminates. We provide a constructive proof of this result which, given a formal power series in the topological closure of an ideal, consists in computing a cofactor representation of the series with respect to a standard basis of the ideal. We apply this result in the context of topological rewriting theory, where two natural notions of confluence arise: topological confluence and infinitary confluence. We give explicit examples illustrating that in general, infinitary confluence is a strictly stronger notion than topological confluence. Using topological closure of ideals, we finally show that in the context of rewriting theory on commutative formal power series, infinitary and topological confluences are equivalent when the monomial order considered is compatible with the degree.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102416"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal generating sets for matrix monoids 矩阵模群的最小生成集
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2024-12-03 DOI: 10.1016/j.jsc.2024.102415
F. Hivert, J.D. Mitchell, F.L. Smith , W.A. Wilson
{"title":"Minimal generating sets for matrix monoids","authors":"F. Hivert,&nbsp;J.D. Mitchell,&nbsp;F.L. Smith ,&nbsp;W.A. Wilson","doi":"10.1016/j.jsc.2024.102415","DOIUrl":"10.1016/j.jsc.2024.102415","url":null,"abstract":"<div><div>In this paper, we determine minimal generating sets for several well-known monoids of matrices over certain semirings. In particular, we find minimal generating sets for the monoids consisting of: all <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> boolean matrices when <span><math><mi>n</mi><mo>≤</mo><mn>8</mn></math></span>; the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> boolean matrices containing the identity matrix (the <em>reflexive</em> boolean matrices) when <span><math><mi>n</mi><mo>≤</mo><mn>7</mn></math></span>; the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> boolean matrices containing a permutation (the <em>Hall</em> matrices) when <span><math><mi>n</mi><mo>≤</mo><mn>8</mn></math></span>; the upper, and lower, triangular boolean matrices of every dimension; the <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrices over the semiring <span><math><mi>N</mi><mo>∪</mo><mo>{</mo><mo>−</mo><mo>∞</mo><mo>}</mo></math></span> with addition ⊕ defined by <span><math><mi>x</mi><mo>⊕</mo><mi>y</mi><mo>=</mo><mi>max</mi><mo>⁡</mo><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> and multiplication ⊗ given by <span><math><mi>x</mi><mo>⊗</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>y</mi></math></span> (the <em>max-plus</em> semiring); the <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrices over any quotient of the max-plus semiring by the congruence generated by <span><math><mi>t</mi><mo>=</mo><mi>t</mi><mo>+</mo><mn>1</mn></math></span> where <span><math><mi>t</mi><mo>∈</mo><mi>N</mi></math></span>; the <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrices over the min-plus semiring and its finite quotients by the congruences generated by <span><math><mi>t</mi><mo>=</mo><mi>t</mi><mo>+</mo><mn>1</mn></math></span> for all <span><math><mi>t</mi><mo>∈</mo><mi>N</mi></math></span>; and the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> matrices over <span><math><mi>Z</mi><mo>/</mo><mi>n</mi><mi>Z</mi></math></span> relative to their group of units.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102415"},"PeriodicalIF":0.6,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fast algorithm for denumerants with three variables 具有三个变量的常数的快速算法
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2024-12-02 DOI: 10.1016/j.jsc.2024.102414
Feihu Liu, Guoce Xin
{"title":"A fast algorithm for denumerants with three variables","authors":"Feihu Liu,&nbsp;Guoce Xin","doi":"10.1016/j.jsc.2024.102414","DOIUrl":"10.1016/j.jsc.2024.102414","url":null,"abstract":"<div><div>Let <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></math></span> be distinct positive integers such that <span><math><mi>a</mi><mo>&lt;</mo><mi>b</mi><mo>&lt;</mo><mi>c</mi></math></span> and <span><math><mi>gcd</mi><mo>⁡</mo><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span>. For any non-negative integer <em>n</em>, the denumerant function <span><math><mi>d</mi><mo>(</mo><mi>n</mi><mo>;</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span> denotes the number of solutions of the equation <span><math><mi>a</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mi>b</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><mi>c</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mi>n</mi></math></span> in non-negative integers <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>. We present an algorithm that computes <span><math><mi>d</mi><mo>(</mo><mi>n</mi><mo>;</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></span> with a time complexity of <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>b</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"129 ","pages":"Article 102414"},"PeriodicalIF":0.6,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143159655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信