Journal of Symbolic Computation最新文献_第9页

A computational approach to almost-inner derivations 几乎是内推导的计算方法

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-03-04 DOI: 10.1016/j.jsc.2024.102312

Heiko Dietrich , Willem A. de Graaf

引用次数: 0

Stabilized recovery and model reduction for multivariate exponential polynomials 多变量指数多项式的稳定恢复和模型还原

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-03-01 DOI: 10.1016/j.jsc.2024.102313

Juan Manuel Peña , Tomas Sauer

引用次数: 0

Computing a group action from the class field theory of imaginary hyperelliptic function fields 从类场论计算虚超椭圆函数场的群作用

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-03-01 DOI: 10.1016/j.jsc.2024.102311

Antoine Leudière, Pierre-Jean Spaenlehauer

{"title":"Computing a group action from the class field theory of imaginary hyperelliptic function fields","authors":"Antoine Leudière, Pierre-Jean Spaenlehauer","doi":"10.1016/j.jsc.2024.102311","DOIUrl":"https://doi.org/10.1016/j.jsc.2024.102311","url":null,"abstract":"<div>We explore algorithmic aspects of a simply transitive commutative group action coming from the class field theory of imaginary hyperelliptic function fields. Namely, the Jacobian of an imaginary hyperelliptic curve defined over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math> acts on a subset of isomorphism classes of Drinfeld modules. We describe an algorithm to compute the group action efficiently. This is a function field analog of the Couveignes-Rostovtsev-Stolbunov group action. We report on an explicit computation done with our proof-of-concept C++/NTL implementation; it took a fraction of a second on a standard computer. We prove that the problem of inverting the group action reduces to the problem of finding isogenies of fixed τ-degree between Drinfeld <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>X</mi><mo>]</mo></math>-modules, which is solvable in polynomial time thanks to an algorithm by Wesolowski. We give asymptotic complexity bounds for all algorithms presented in this paper.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"125 ","pages":"Article 102311"},"PeriodicalIF":0.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140051678","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

Matrix factorizations of the discriminant of Sn S 判别式的矩阵因式分解

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-02-23 DOI: 10.1016/j.jsc.2024.102310

Eleonore Faber , Colin Ingalls , Simon May , Marco Talarico

{"title":"Matrix factorizations of the discriminant of Sn","authors":"Eleonore Faber , Colin Ingalls , Simon May , Marco Talarico","doi":"10.1016/j.jsc.2024.102310","DOIUrl":"10.1016/j.jsc.2024.102310","url":null,"abstract":"<div>Consider the symmetric group <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> acting as a reflection group on the polynomial ring <math><mi>k</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math> where k is a field, such that Char(k) does not divide n!. We use Higher Specht polynomials to construct matrix factorizations of the discriminant of this group action: these matrix factorizations are indexed by partitions of n and respect the decomposition of the coinvariant algebra into isotypical components. The maximal Cohen–Macaulay modules associated to these matrix factorizations give rise to a noncommutative resolution of the discriminant and they correspond to the nontrivial irreducible representations of <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math>. All our constructions are implemented in Macaulay2 and we provide several examples. We also discuss extensions of these results to Young subgroups of <math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math> and indicate how to generalize them to the reflection groups <math><mi>G</mi><mo>(</mo><mi>m</mi><mo>,</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></math>.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"125 ","pages":"Article 102310"},"PeriodicalIF":0.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000142/pdfft?md5=688baaec9b10f27e6369b86c65d8e101&pid=1-s2.0-S0747717124000142-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947723","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

An improved complexity bound for computing the topology of a real algebraic space curve 计算实代数空间曲线拓扑的改进复杂度约束

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-02-21 DOI: 10.1016/j.jsc.2024.102309

Jin-San Cheng , Kai Jin , Marc Pouget , Junyi Wen , Bingwei Zhang

{"title":"An improved complexity bound for computing the topology of a real algebraic space curve","authors":"Jin-San Cheng , Kai Jin , Marc Pouget , Junyi Wen , Bingwei Zhang","doi":"10.1016/j.jsc.2024.102309","DOIUrl":"10.1016/j.jsc.2024.102309","url":null,"abstract":"<div>We propose a new algorithm to compute the topology of a real algebraic space curve. The novelties of this algorithm are a new technique to achieve the lifting step which recovers points of the space curve in each plane fiber from several projections and a weaker notion of generic position. As distinct to previous work, our sweep generic position does not require that x-critical points have different x-coordinates. The complexity of achieving this sweep generic position property is thus no longer a bottleneck in term of complexity. The bit complexity of our algorithm is <math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>18</mn></mrow></msup><mo>+</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>17</mn></mrow></msup><mi>τ</mi><mo>)</mo></math> where d and τ bound the degree and the bitsize of the integer coefficients, respectively, of the defining polynomials of the curve and polylogarithmic factors are ignored. To the best of our knowledge, this improves upon the best currently known results at least by a factor of <math><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup></math>.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"125 ","pages":"Article 102309"},"PeriodicalIF":0.7,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919633","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

Rational solutions to the first order difference equations in the bivariate difference field 二维差分场中一阶差分方程的有理解

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-02-09 DOI: 10.1016/j.jsc.2024.102308

Qing-Hu Hou , Yarong Wei

{"title":"Rational solutions to the first order difference equations in the bivariate difference field","authors":"Qing-Hu Hou , Yarong Wei","doi":"10.1016/j.jsc.2024.102308","DOIUrl":"https://doi.org/10.1016/j.jsc.2024.102308","url":null,"abstract":"<div>Inspired by Karr's algorithm, we consider the summations involving a sequence satisfying a recurrence of order two. The structure of such summations provides an algebraic framework for solving the difference equations of form <math><mi>a</mi><mi>σ</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>+</mo><mi>b</mi><mi>g</mi><mo>=</mo><mi>f</mi></math> in the bivariate difference field <math><mo>(</mo><mi>F</mi><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>,</mo><mi>σ</mi><mo>)</mo></math>, where <math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>f</mi><mo>∈</mo><mi>F</mi><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math> are known binary functions of α, β, and α, β are two algebraically independent transcendental elements, σ is a transformation that satisfies <math><mi>σ</mi><mo>(</mo><mi>α</mi><mo>)</mo><mo>=</mo><mi>β</mi></math>, <math><mi>σ</mi><mo>(</mo><mi>β</mi><mo>)</mo><mo>=</mo><mi>u</mi><mi>α</mi><mo>+</mo><mi>v</mi><mi>β</mi></math>, where <math><mi>u</mi><mo>,</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>∈</mo><mi>F</mi></math>. Based on it, we then describe algorithms for finding the universal denominator for those equations in the bivariate difference field under certain assumptions. This reduces the general problem of finding the rational solutions of such equations to the problem of finding the polynomial solutions of such equations.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"124 ","pages":"Article 102308"},"PeriodicalIF":0.7,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139901497","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

Tensor decompositions on simplicial complexes with invariance 具有不变性的简单复数上的张量分解

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-19 DOI: 10.1016/j.jsc.2024.102299

Gemma De las Cuevas , Matt Hoogsteder Riera , Tim Netzer

引用次数: 0

Computing the binomial part of a polynomial ideal 计算多项式理想的二项式部分

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-14 DOI: 10.1016/j.jsc.2024.102298

Martin Kreuzer, Florian Walsh

{"title":"Computing the binomial part of a polynomial ideal","authors":"Martin Kreuzer, Florian Walsh","doi":"10.1016/j.jsc.2024.102298","DOIUrl":"10.1016/j.jsc.2024.102298","url":null,"abstract":"<div>Given an ideal I in a polynomial ring <math><mi>K</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math> over a field K, we present a complete algorithm to compute the binomial part of I, i.e., the subideal <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> of I generated by all monomials and binomials in I. This is achieved step-by-step. First we collect and extend several algorithms for computing exponent lattices in different kinds of fields. Then we generalize them to compute exponent lattices of units in 0-dimensional K-algebras, where we have to generalize the computation of the separable part of an algebra to non-perfect fields in characteristic p. Next we examine the computation of unit lattices in finitely generated K-algebras, as well as their associated characters and lattice ideals. This allows us to calculate <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> when I is saturated with respect to the indeterminates by reducing the task to the 0-dimensional case. Finally, we treat the computation of <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> for general ideals by computing their cellular decomposition and dealing with finitely many special ideals called <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-binomial parts. All algorithms have been implemented in SageMath.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"124 ","pages":"Article 102298"},"PeriodicalIF":0.7,"publicationDate":"2024-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000026/pdfft?md5=bc32bb62dcb12f7f2c1d113994ec49bf&pid=1-s2.0-S0747717124000026-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462707","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 post-quantum key exchange protocol from the intersection of conics 来自圆锥交点的后量子密钥交换协议

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-05 DOI: 10.1016/j.jsc.2024.102297

Alberto Alzati, Daniele Di Tullio, Manoj Gyawali, Alfonso Tortora

引用次数: 0

An effective decomposition theorem for Schubert varieties 舒伯特变换的一个有效分解定理

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-01 DOI: 10.1016/j.jsc.2023.102238

Francesca Cioffi, Davide Franco, Carmine Sessa

引用次数: 0