Journal of Symbolic Computation最新文献

{"title":"Bifurcations in a population model on N patches with strong Allee effect and spatial dispersal through Jacobian matrices","authors":"Ya-Lun Tsai","doi":"10.1016/j.jsc.2025.102544","DOIUrl":"10.1016/j.jsc.2025.102544","url":null,"abstract":"<div><div>In a single species population model on <em>n</em> identical patches with strong Allee effect and spatial dispersal, we study the steady states of the system with respect to the same Allee threshold <em>β</em> for all patches and the same dispersal rate <em>α</em> if they are connected. In the cases of connected patches with complete digraphs, we find the bifurcation polynomials for all <span><math><mi>n</mi><mo>&gt;</mo><mn>1</mn></math></span> through Jacobian matrices, and classify the numbers of steady states completely for <em>n</em> up to 14. For any fixed <em>n</em>, if <span><math><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></mfrac></math></span>, there are only three steady states, two stables and one unstable that generalizes the case of <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span>. All the bifurcation polynomials are obtained efficiently by computing Gröbner bases with elimination orderings for systems containing Jacobian determinants.</div><div>On the other hand, for <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, we count the numbers of steady states for all possible connectivities through considering all non-isomorphic digraphs with three nodes. For most connectivities, the numbers of steady states do not always decrease monotonously when <em>β</em> is fixed and <em>α</em> increases as the previous known cases. Interestingly, there are some connectivities where the number of steady states does not eventually reduce to the minimal. Here, if the Gröbner basis computation is not feasible with Jacobian determinants to obtain the bifurcation polynomials, we present a method to compute them by simply resultants for two polynomials to eliminate variables without using Jacobian determinants of order greater than one.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"135 ","pages":"Article 102544"},"PeriodicalIF":1.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145883878","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}

{"title":"Efficient detection of redundancies in systems of linear inequalities","authors":"Rui-Juan Jing ,&nbsp;Marc Moreno Maza ,&nbsp;Chirantan Mukherjee ,&nbsp;Yan-Feng Xie ,&nbsp;Chun-Ming Yuan","doi":"10.1016/j.jsc.2025.102527","DOIUrl":"10.1016/j.jsc.2025.102527","url":null,"abstract":"<div><div>Fourier-Motzkin elimination is a fundamental operation in polyhedral geometry. It can be performed by several equivalent procedures, and can be regarded as an adaptation of Gaussian elimination to systems of linear inequalities. These procedures tend to generate large numbers of redundant inequalities. Efficiently detecting these redundancies is essential for obtaining software implementation of practical interest. In this paper, we propose a novel detection technique. We demonstrate its benefits over alternative approaches. A detailed experimentation is reported.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"135 ","pages":"Article 102527"},"PeriodicalIF":1.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737433","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}

{"title":"Strongly and transitive chordal graphs and their applications in complexity analysis of triangular decomposition","authors":"Zhaoxing Qi ,&nbsp;Chenqi Mou","doi":"10.1016/j.jsc.2025.102549","DOIUrl":"10.1016/j.jsc.2025.102549","url":null,"abstract":"<div><div>Triangular decomposition is a versatile computational tool for studying polynomial ideals, but the complexity is not well understood due to its intricate behaviors. Inspired by the recent interplay between polynomial system solving and chordal graphs, in this paper we analyze the complexity of triangular decomposition by using chordal graphs.</div><div>We first introduce a new vertex ordering of graphs called the substrong elimination one which characterizes strongly chordal graphs. Using this ordering, we propose a polynomial selection strategy for triangular decomposition over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and show that for polynomial sets with strongly chordal associated graphs, the variables of any polynomial occurring in the decomposition with this strategy are contained in certain maximal clique. For <em>ℓ</em> polynomials in <em>n</em> variables with such an associated graph of treewidth <em>m</em>, under certain worst-case assumptions, the complexity of triangular decomposition over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> using this strategy is proved to be <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>m</mi></mrow></msup><mi>ℓ</mi><mi>n</mi><msup><mrow><mo>(</mo><mfrac><mrow><mi>m</mi><mi>ℓ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span>, smaller than the original <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> when <span><math><mi>m</mi><mo>≪</mo><mi>n</mi></math></span>.</div><div>To extend these results to other algorithms for triangular decomposition over any field, we introduce the concept of transitive chordal graph based on the transitive vertex ordering. Then when the transitive perfect elimination ordering is used for a collection of algorithms, the similar inclusion of the variables in the maximal cliques is proved without requiring additional selection strategies. As a direct consequence, these algorithms are chordality-preserving when combined with transitive chordal graphs. At the end, we provide complexity analyses for two algorithms using transitive chordal graphs of bounded treewidths.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"135 ","pages":"Article 102549"},"PeriodicalIF":1.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924764","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}

{"title":"Computing the character table of a 2-local maximal subgroup of the Monster","authors":"Anthony Pisani","doi":"10.1016/j.jsc.2025.102540","DOIUrl":"10.1016/j.jsc.2025.102540","url":null,"abstract":"<div><div>We employ the recently developed hybrid and <span>mmgroup</span> computational models for groups to calculate the character table of <figure><img></figure>, a maximal subgroup of the Monster sporadic simple group. This completes the list of the character tables of maximal subgroups of the Monster. Our approach illustrates how the aforementioned computational models can be used to calculate relatively straightforwardly in the Monster.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"135 ","pages":"Article 102540"},"PeriodicalIF":1.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737432","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}

{"title":"Invariants recovering the reduction type of a hyperelliptic curve","authors":"Lilybelle Cowland Kellock,&nbsp;Elisa Lorenzo García","doi":"10.1016/j.jsc.2025.102533","DOIUrl":"10.1016/j.jsc.2025.102533","url":null,"abstract":"<div><div>Tate's algorithm tells us that for an elliptic curve <em>E</em> over a local field <em>K</em> of residue characteristic ≥5, <span><math><mi>E</mi><mo>/</mo><mi>K</mi></math></span> has potentially good reduction if and only if <span><math><mtext>ord</mtext><mo>(</mo><msub><mrow><mi>j</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo><mo>≥</mo><mn>0</mn></math></span>. It also tells us that when <span><math><mi>E</mi><mo>/</mo><mi>K</mi></math></span> is semistable the dual graph of the special fibre of the minimal regular model of <span><math><mi>E</mi><mo>/</mo><msup><mrow><mi>K</mi></mrow><mrow><mtext>unr</mtext></mrow></msup></math></span> can be recovered from <span><math><mtext>ord</mtext><mo>(</mo><msub><mrow><mi>j</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo></math></span>. We generalise these results to hyperelliptic curves of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span> over local fields of odd residue characteristic <em>K</em> by defining a list of absolute invariants that determine the potential stable model of a genus <em>g</em> hyperelliptic curve <em>C</em>. They also determine the dual graph of the special fibre of the minimal regular model of <span><math><mi>C</mi><mo>/</mo><msup><mrow><mi>K</mi></mrow><mrow><mtext>unr</mtext></mrow></msup></math></span> if <span><math><mi>C</mi><mo>/</mo><mi>K</mi></math></span> is semistable. This list depends only on the genus of <em>C</em>, and the absolute invariants can be written in terms of the coefficients of a Weierstrass equation for <em>C</em>. We explicitly describe the method by which the valuations of the invariants recover the dual graphs. Additionally, we show by way of a counterexample that if <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>, there is no list of invariants whose valuations determine the dual graph of the special fibre of the minimal regular model of a genus <em>g</em> hyperelliptic curve <em>C</em> over a local field <em>K</em> of odd residue characteristic when <em>C</em> is not assumed to be semistable.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"135 ","pages":"Article 102533"},"PeriodicalIF":1.1,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625258","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}

{"title":"New dimension polynomials of inversive difference field extensions and inversive difference modules","authors":"Alexander Levin","doi":"10.1016/j.jsc.2025.102521","DOIUrl":"10.1016/j.jsc.2025.102521","url":null,"abstract":"<div><div>In this paper we introduce new types of characteristic sets in rings of inversive difference polynomials over an inversive difference field <em>K</em> and in inversive difference <em>K</em>-modules. These characteristic sets are defined via reductions associated with partitions of the basic set of automorphisms <em>σ</em> and with a generalization of the concept of the effective order of an ordinary difference polynomial. Using these characteristic sets, we provide an effective construction of multivariate difference dimension polynomials of a new type. They describe the transcendence degrees of intermediate fields of inversive difference field extensions and dimensions of submodules of inversive difference modules that are obtained by adjoining transforms of the generators whose orders with respect to the components of the partition of <em>σ</em> are bounded by two sequences of natural numbers. We show that such dimension polynomials carry substantially more invariants (that is, characteristics that do not depend on the set of generators) than standard (univariate) difference dimension polynomials. We also show how the obtained results can be applied to the equivalence problem for systems of algebraic difference equations and to the isomorphism problem for inversive difference modules.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102521"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321163","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}

{"title":"A note on the multivariate symmetric Hermite interpolant","authors":"Teresa Krick ,&nbsp;Agnes Szanto","doi":"10.1016/j.jsc.2025.102505","DOIUrl":"10.1016/j.jsc.2025.102505","url":null,"abstract":"<div><div>In this note we explicit the notion of Hermite interpolant of a multivariate symmetric polynomial, generalizing the notion of Lagrange interpolant to the case when there are roots coalescence, an extension of the results on the symmetric Hermite interpolation basis by M.-F. Roy and A. Szpirglas included in (<span><span>Roy and Szpirglas, 2020</span></span>).</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102505"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011140","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}

{"title":"Fast in-place accumulation","authors":"Jean-Guillaume Dumas,&nbsp;Bruno Grenet","doi":"10.1016/j.jsc.2025.102523","DOIUrl":"10.1016/j.jsc.2025.102523","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the in-place accumulated multiplication of polynomials or matrices, &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; (that is with only &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; extra space). The difficulty is to combine in-place computations with fast algorithms: those usually come at the expense of (potentially large) extra temporary space, but with accumulation the output variables are not even available to store intermediate values. We first propose a novel automatic design of fast and in-place accumulating algorithms for any bilinear formulae (and thus for polynomial and matrix multiplication) and then extend it to any linear accumulation of a collection of functions. For this, we relax the in-place model to any algorithm allowed to modify its inputs, provided that those are restored to their initial state afterwards. This allows us to ultimately derive unprecedented in-place accumulating algorithms for fast polynomial multiplications and for Strassen-like matrix multiplications.&lt;/div&gt;&lt;div&gt;We then consider the simultaneously fast and in-place computation of the Euclidean polynomial modular remainder &lt;span&gt;&lt;math&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Fast algorithms for this usually also come at the expense of a linear amount of extra temporary space. In particular, they require one to first compute and store the whole quotient &lt;span&gt;&lt;math&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We here propose an &lt;em&gt;in-place&lt;/em&gt; algorithm to compute the remainder only. If &lt;em&gt;A&lt;/em&gt; and &lt;em&gt;B&lt;/em&gt; have respective degree &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;n&lt;/em&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; denotes the complexity of a (not-in-place) algorithm to multiply two degree-&lt;em&gt;k&lt;/em&gt; polynomials, our algorithm uses at most &lt;span&gt;&lt;math&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; arithmetic operations. In this particular case this is a factor &lt;span&gt;&lt;math&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; more than the not-in-place algorithm. But if &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Θ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for some &lt;span&gt;&lt;ma","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102523"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362885","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}

{"title":"Relations among multi-polynomial subresultants","authors":"Hoon Hong ,&nbsp;Jiaqi Meng ,&nbsp;Jing Yang","doi":"10.1016/j.jsc.2025.102520","DOIUrl":"10.1016/j.jsc.2025.102520","url":null,"abstract":"<div><div>Subresultants of two univariate polynomials (bi-polynomial subresultants) are one of the most classic and ubiquitous objects in computational algebra and algebraic geometry. Since their introduction, several interesting relations among them were discovered. Those relations were crucial for both structural understanding and efficient computation of bi-polynomial subresultants.</div><div>Recently, the bi-polynomial subresultants have been generalized to multi-polynomial subresultants, that is, subresultants of several polynomials. They have been already used for tackling some fundamental problems in computational algebra and algebraic geometry. Thus a natural challenge arises: <em>Generalize, if possible, the relations among bi-polynomial subresultants to multi-polynomial subresultants.</em></div><div>In this paper, we tackle this challenge and provide a family of relations among multi-polynomial subresultants, which elegantly generalize some of known relations among bi-polynomial subresultants.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102520"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321162","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}

{"title":"Sasbi-standard bases of modules","authors":"Nazia Jabeen,&nbsp;Junaid Alam Khan","doi":"10.1016/j.jsc.2025.102522","DOIUrl":"10.1016/j.jsc.2025.102522","url":null,"abstract":"<div><div>The theory of Standard bases of modules over the localization of a polynomial ring (with respect to a local ordering &gt;) is well-developed. For a polynomial subalgebra <em>A</em>, the concept of “Subalgebra bases” of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>&gt;</mo></mrow></msub></math></span> (localization of <em>A</em> with respect to &gt;) is well-defined, known as Sasbi bases (subalgebra analogue of Standard bases for ideals). In this paper, we have developed and proposed a theory for Standard bases of modules over <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>&gt;</mo></mrow></msub></math></span> (admitting a finite Sasbi basis), termed as Sasbi-Standard bases. The main goal is to develop a constructive algorithm for the computation of these bases, which we implement in the computer algebra system SINGULAR. We also present an application of these bases to compute singularity invariants: the monoid of values of an algebroid curve and the monomodule of values of the Kähler's differentials.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102522"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362883","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}