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Moment varieties of the inverse Gaussian and gamma distributions are nondefective 反高斯分布和伽马分布的矩变化是无缺陷的
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-05-19 DOI: 10.1016/j.jsc.2025.102460
Oskar Henriksson , Kristian Ranestad , Lisa Seccia , Teresa Yu
{"title":"Moment varieties of the inverse Gaussian and gamma distributions are nondefective","authors":"Oskar Henriksson ,&nbsp;Kristian Ranestad ,&nbsp;Lisa Seccia ,&nbsp;Teresa Yu","doi":"10.1016/j.jsc.2025.102460","DOIUrl":"10.1016/j.jsc.2025.102460","url":null,"abstract":"<div><div>We show that the parameters of a <em>k</em>-mixture of inverse Gaussian or gamma distributions are algebraically identifiable from the first <span><math><mn>3</mn><mi>k</mi><mo>−</mo><mn>1</mn></math></span> moments, and rationally identifiable from the first <span><math><mn>3</mn><mi>k</mi><mo>+</mo><mn>2</mn></math></span> moments. Our proofs are based on Terracini's classification of defective surfaces, careful analysis of the intersection theory of moment varieties, and a recent result on sufficient conditions for rational identifiability of secant varieties by Massarenti–Mella.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"132 ","pages":"Article 102460"},"PeriodicalIF":0.6,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125175","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
Quantifier elimination for normal cone computations 用于正常锥体计算的量词消除
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-05-13 DOI: 10.1016/j.jsc.2025.102456
Michael Mandlmayr , Ali K. Uncu
{"title":"Quantifier elimination for normal cone computations","authors":"Michael Mandlmayr ,&nbsp;Ali K. Uncu","doi":"10.1016/j.jsc.2025.102456","DOIUrl":"10.1016/j.jsc.2025.102456","url":null,"abstract":"<div><div>We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where the constraint qualifications fail and extra work for other methods becomes inevitable. This method also serves as a tool to calculate the regular co-derivative for semismooth* Newton methods. We list algorithms and their demonstrations of different use cases for this approach.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102456"},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090472","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
A syzygial method for equidimensional decomposition 等维分解的协同方法
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-29 DOI: 10.1016/j.jsc.2025.102455
Rafael Mohr
{"title":"A syzygial method for equidimensional decomposition","authors":"Rafael Mohr","doi":"10.1016/j.jsc.2025.102455","DOIUrl":"10.1016/j.jsc.2025.102455","url":null,"abstract":"<div><div>Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gröbner bases. This algorithm avoids the use of elimination, homological algebra and processing the input equations one-by-one present in previous algorithms. We experimentally demonstrate the practical interest of our algorithm compared to the state of the art.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102455"},"PeriodicalIF":0.6,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903629","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
Computing finite and infinite free resolutions with Pommaret-like bases 用类波马雷基底计算有限和无限自由分辨率
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-28 DOI: 10.1016/j.jsc.2025.102454
Amir Hashemi , Matthias Orth , Werner M. Seiler
{"title":"Computing finite and infinite free resolutions with Pommaret-like bases","authors":"Amir Hashemi ,&nbsp;Matthias Orth ,&nbsp;Werner M. Seiler","doi":"10.1016/j.jsc.2025.102454","DOIUrl":"10.1016/j.jsc.2025.102454","url":null,"abstract":"<div><div>Free resolutions are an important tool in algebraic geometry for the structural analysis of modules over polynomial rings and their quotient rings. Minimal free resolutions are unique up to isomorphism and induce homological invariants in the form of Betti numbers. It is known that Pommaret bases of ideals in the polynomial ring induce finite free resolutions and that the Castelnuovo-Mumford regularity and projective dimension can be read off directly from the Pommaret basis. In this article, we generalize this construction to Pommaret-like bases, which are generally smaller. We apply Pommaret-like bases also to infinite resolutions over quotient rings. Over Clements–Lindström rings, we derive bases for the free modules in the resolution using only the Pommaret-like basis. Finally, restricting to monomial ideals in a non-quotient polynomial ring, we derive an explicit formula for the differential of the induced resolution.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102454"},"PeriodicalIF":0.6,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903628","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
Semantics of division for polynomial solvers 多项式解的除法语义
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-22 DOI: 10.1016/j.jsc.2025.102453
Christopher W. Brown
{"title":"Semantics of division for polynomial solvers","authors":"Christopher W. Brown","doi":"10.1016/j.jsc.2025.102453","DOIUrl":"10.1016/j.jsc.2025.102453","url":null,"abstract":"<div><div>How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both the computer algebra and computational logic communities are unsatisfactory for systems that consider the satisfiability of formulas with quantifiers or that perform quantifier elimination. To address this, we propose the notion of the <em>fair-satisfiability</em> of a formula, use it to characterize formulas with divisions that are <em>well-defined</em>, meaning that they adequately guard divisions against division by zero, and provide a <em>translation algorithm</em> that converts a formula with divisions into a purely polynomial formula that is satisfiable if and only if the original formula is fair-satisfiable. This provides a semantics for division with some nice properties, which we describe and prove in the paper.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102453"},"PeriodicalIF":0.6,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900392","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
Classification of primitive quandles of small order 小阶原始角堆的分类
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-22 DOI: 10.1016/j.jsc.2025.102452
Dilpreet Kaur, Pushpendra Singh
{"title":"Classification of primitive quandles of small order","authors":"Dilpreet Kaur,&nbsp;Pushpendra Singh","doi":"10.1016/j.jsc.2025.102452","DOIUrl":"10.1016/j.jsc.2025.102452","url":null,"abstract":"<div><div>In this article, we describe primitive quandles with the help of primitive permutation groups. As a consequence, we enumerate finite non-affine primitive quandles up to order 4096.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102452"},"PeriodicalIF":0.6,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869616","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
Decomposition loci of tensors 张量的分解轨迹
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-22 DOI: 10.1016/j.jsc.2025.102451
Alessandra Bernardi , Alessandro Oneto , Pierpaola Santarsiero
{"title":"Decomposition loci of tensors","authors":"Alessandra Bernardi ,&nbsp;Alessandro Oneto ,&nbsp;Pierpaola Santarsiero","doi":"10.1016/j.jsc.2025.102451","DOIUrl":"10.1016/j.jsc.2025.102451","url":null,"abstract":"<div><div>The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that the decomposition locus consists of all rank-one tensors except the tangency point only. We also explicitly compute decomposition loci of all tensors belonging to tensor spaces with finitely many orbits with respect to the action of product of general linear groups.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102451"},"PeriodicalIF":0.6,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878859","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
Linear preservers of secant varieties and other varieties of tensors 割线变体和其他变体张量的线性保持器
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-17 DOI: 10.1016/j.jsc.2025.102449
Fulvio Gesmundo , Young In Han , Benjamin Lovitz
{"title":"Linear preservers of secant varieties and other varieties of tensors","authors":"Fulvio Gesmundo ,&nbsp;Young In Han ,&nbsp;Benjamin Lovitz","doi":"10.1016/j.jsc.2025.102449","DOIUrl":"10.1016/j.jsc.2025.102449","url":null,"abstract":"<div><div>We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduce a number of techniques built on different geometric properties of the varieties of interest. Our main result is a simple characterization of the linear preservers of secant varieties of Segre varieties in many cases, including <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msup><mrow><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>×</mo><mi>k</mi></mrow></msup><mo>)</mo></math></span> for all <span><math><mi>r</mi><mo>≤</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>⌊</mo><mi>k</mi><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></msup></math></span>. We also characterize the linear preservers of several other sets of tensors, including subspace varieties, the variety of slice rank one tensors, symmetric tensors of bounded Waring rank, the variety of biseparable tensors, and hyperdeterminantal surfaces. Computational techniques and applications in quantum information theory are discussed. We provide geometric proofs for several previously known results on linear preservers.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102449"},"PeriodicalIF":0.6,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895673","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 Chow-Lam form 周林式
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-15 DOI: 10.1016/j.jsc.2025.102450
Elizabeth Pratt , Bernd Sturmfels
{"title":"The Chow-Lam form","authors":"Elizabeth Pratt ,&nbsp;Bernd Sturmfels","doi":"10.1016/j.jsc.2025.102450","DOIUrl":"10.1016/j.jsc.2025.102450","url":null,"abstract":"<div><div>The classical Chow form encodes any projective variety by one equation. We here introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates, we obtain universal projection formulas. These were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra, and we develop his approach further. Universal formulas for branch loci are obtained from Hurwitz-Lam forms. Our focus is on computations and applications in geometry.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102450"},"PeriodicalIF":0.6,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869618","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
Partial semiorthogonal decompositions for quiver moduli 颤模的偏半正交分解
IF 0.6 4区 数学
Journal of Symbolic Computation Pub Date : 2025-04-14 DOI: 10.1016/j.jsc.2025.102448
Gianni Petrella
{"title":"Partial semiorthogonal decompositions for quiver moduli","authors":"Gianni Petrella","doi":"10.1016/j.jsc.2025.102448","DOIUrl":"10.1016/j.jsc.2025.102448","url":null,"abstract":"<div><div>We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the semiorthogonal decompositions of moduli of vector bundles on curves. Our results are obtained with <span>QuiverTools</span>, an open-source package of tools for quiver representations, their moduli spaces and their geometrical properties.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102448"},"PeriodicalIF":0.6,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839767","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
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