Journal of Symbolic Computation最新文献

{"title":"Extraspecial pairs in the multiply laced root systems and calculating structure constants","authors":"Rafael Stekolshchik","doi":"10.1016/j.jsc.2025.102519","DOIUrl":"10.1016/j.jsc.2025.102519","url":null,"abstract":"<div><div>The concept of <em>special</em> and <em>extraspecial pairs</em> of roots was introduced by <span><span>Carter (1989)</span></span> to calculate structure constants of simple Lie algebras. Let <span><math><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>}</mo></math></span> be a special pair of roots for which the structure constant <span><math><mi>N</mi><mo>(</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>)</mo></math></span> is sought, and let <span><math><mo>{</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>}</mo></math></span> be the extraspecial pair of roots corresponding to <span><math><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>}</mo></math></span>. In this paper, we introduce the notion of a <em>quartet</em>, the ordered set <span><math><mo>{</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>}</mo></math></span> consisting of the special and corresponding extraspecial pairs. The classification of quartets makes it possible to simplify the formulas for calculations of the structure constants. Quartet <span><math><mi>q</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>}</mo></math></span> is said to be a <em>mono-quartet</em> if vectors <span><math><mi>s</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mi>r</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> are not roots at the same time. Quartet <em>q</em> is said to be <em>simple</em> if it satisfies the following properties: if <span><math><mi>s</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> (resp. <span><math><mi>r</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>) is a root, then <span><math><mo>|</mo><mi>s</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>=</mo><mo>|</mo><mi>s</mi><mo>|</mo></math></span> (resp. <span><math><mo>|</mo><mi>r</mi><mo>−</mo><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>=</mo><mo>|</mo><mi>r</mi><mo>|</mo></math></span>). It is shown that for the simple Lie algebra of type <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> (resp. type <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>) all quartets are mono- and simple (resp. simple). These facts allows to simplify the well-known recurrent formulas for calculations of structure constants derived from the fundamental Carter formula (<span><span>1989</span></span>, p. 59). As a consequence, the algorithm for calculating the structural constants can be signifi","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102519"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321092","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":"Early termination for sparse interpolation of polynomials in Chebyshev bases","authors":"Erich L. Kaltofen ,&nbsp;Zhi-Hong Yang","doi":"10.1016/j.jsc.2025.102507","DOIUrl":"10.1016/j.jsc.2025.102507","url":null,"abstract":"<div><div>We show that the early termination algorithm in [Kaltofen and Lee, JSC, vol. 36, nr. 3–4, 2003] for interpolating a polynomial that is a linear combination of <em>t</em> Chebyshev polynomials of the first kind can be modified to use <span><math><mn>2</mn><mi>t</mi><mo>+</mo><mn>1</mn></math></span> randomized evaluation points; Kaltofen and Lee required <span><math><mn>2</mn><mi>t</mi><mo>+</mo><mn>2</mn></math></span> randomized evaluation points. Our variants work for scalar fields of any characteristic. The number <span><math><mn>2</mn><mi>t</mi><mo>+</mo><mn>1</mn></math></span> of evaluations matches that of the early termination version of the Prony sparse interpolation algorithm for the standard basis of powers of the variable [Kaltofen, Lee and Lobo, Proc. ISSAC 2000].</div><div>Our interpolation algorithm can compute the term locator polynomial in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> field arithmetic operations while storing <span><math><mi>O</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> intermediate field elements by Heinig's Toeplitz solver with singular sections [Heinig and Rost, “Algebraic Methods for Toeplitz-like Matrices and Operators,” Birkhäuser, 1984]. We describe a slight modification for the Levinson-Durbin-Heinig algorithm that mirrors the Berlekamp-Massey algorithm for Hankel matrices.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102507"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097421","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":"Towards automated generation of fast and accurate algorithms for recursive matrix multiplication","authors":"Jean-Guillaume Dumas ,&nbsp;Clément Pernet ,&nbsp;Alexandre Sedoglavic","doi":"10.1016/j.jsc.2025.102524","DOIUrl":"10.1016/j.jsc.2025.102524","url":null,"abstract":"<div><div>We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and accuracy of numerical matrix multiplication. We start by a unification on known max-norm bounds on matrix multiplication stability and then extend them to further norms and more generally to recursive bilinear algorithms and the alternative basis matrix multiplication algorithms. Then our strategy has three phases. First, we reduce those bounds by minimizing a growth factor along the orbits of the associated matrix multiplication tensor decomposition. Second, we develop heuristics that minimize the number of operations required to realize a bilinear formula, while further improving its accuracy. Third, we perform an alternative basis sparsification that improves on the time complexity constant and mostly preserves the overall accuracy. Let <span><math><mo>〈</mo><mi>m</mi><mo>×</mo><mi>k</mi><mo>×</mo><mi>n</mi><mo>:</mo><mi>r</mi><mo>〉</mo></math></span> denote a non-commutative algorithm multiplying an <span><math><mi>m</mi><mo>×</mo><mi>k</mi></math></span> matrix with an <span><math><mi>k</mi><mo>×</mo><mi>n</mi></math></span> matrix, using <em>r</em> coefficient products. Our strategy allows us to propose a <span><math><mo>〈</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>:</mo><mn>7</mn><mo>〉</mo></math></span> algorithm that reaches simultaneously a better accuracy in practice, compared to previously known such fast <span><math><mo>〈</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>:</mo><mn>7</mn><mo>〉</mo></math></span> Strassen-like algorithms, and a time complexity bound with the best currently known leading term (obtained via alternative basis sparsification). We also present detailed results of our technique on Smirnov's <span><math><mo>〈</mo><mn>3</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>6</mn><mo>:</mo><mn>40</mn><mo>〉</mo></math></span> family of algorithms.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102524"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362884","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":"Tropical combinatorics of max-linear Bayesian networks","authors":"Carlos Améndola,&nbsp;Kamillo Ferry","doi":"10.1016/j.jsc.2025.102518","DOIUrl":"10.1016/j.jsc.2025.102518","url":null,"abstract":"<div><div>A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs). This family of polytropes arises in algebraic statistics when describing the model class of max-linear Bayesian networks. We show how the edge weights of a network directly relate to the facet structure of the corresponding polytrope. We also give a classification of polytropes from weighted DAGs at different levels of equivalence. These results give insight on the statistical problem of identifiability for a max-linear Bayesian network.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102518"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321164","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":"Symbolic integration on planar differential foliations","authors":"Thierry Combot","doi":"10.1016/j.jsc.2025.102506","DOIUrl":"10.1016/j.jsc.2025.102506","url":null,"abstract":"<div><div>We consider the problem of symbolic integration of <span><math><mo>∫</mo><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mi>d</mi><mi>x</mi></math></span> where <em>G</em> is rational and <span><math><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a non algebraic solution of a differential equation <span><math><msup><mrow><mi>y</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></span> with <em>F</em> rational. Substituting in the integral <span><math><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> by <span><math><mi>y</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>, the general solution of <span><math><msup><mrow><mi>y</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>F</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></span>, we have a parametrized integral <span><math><mi>I</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>. We prove that <span><math><mi>I</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span> is, as a two variable function in <span><math><mi>x</mi><mo>,</mo><mi>h</mi></math></span>, either differentially transcendental, or, with a good parametrization in <em>h</em>, there exists a linear differential operator <em>L</em> in <em>h</em> with constant coefficients, called a telescoper, such that <span><math><mi>L</mi><mi>I</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span> is rational in <span><math><mi>x</mi><mo>,</mo><mi>y</mi></math></span> and the <em>h</em> derivatives of <em>y</em>. This notion generalizes elementary integration. We present an algorithm to compute such telescoper given a priori bound on the order ord of <em>L</em> and degree <em>N</em> of <span><math><mi>L</mi><mi>I</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>, with complexity <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>ω</mi><mo>+</mo><mn>1</mn></mrow></msup><msup><mrow><mtext>ord</mtext></mrow><mrow><mi>ω</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>N</mi><msup><mrow><mtext>ord</mtext></mrow><mrow><mi>ω</mi><mo>+</mo><mn>3</mn></mrow></msup><mo>)</mo></math></span>. For the specific foliation <span><math><mi>y</mi><mo>=</mo><mi>ln</mi><mo>⁡</mo><mi>x</mi></math></span>, a more complete algorithm without a priori bound is presented. Oppositely, non existence of telescoper is proven for a classical planar Hamiltonian system. As an application, we present an algorithm which always finds, if they exist, the Liouvillian solutions of a planar rational vector field, given a bound large enough for some notion of complexity height.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102506"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049629","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":"q-analogues of π-formulas due to Ramanujan and Guillera","authors":"John M. Campbell","doi":"10.1016/j.jsc.2025.102531","DOIUrl":"10.1016/j.jsc.2025.102531","url":null,"abstract":"<div><div>The first known <em>q</em>-analogues for any of the 17 formulas for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></math></span> due to Ramanujan were introduced in 2018 by <span><span>Guo and Liu (2018)</span></span>, via the <em>q</em>-Wilf–Zeilberger method. Through a “normalization” method, which we refer to as <span>EKHAD</span>-normalization, based on the <em>q</em>-polynomial coefficients involved in first-order difference equations obtained from the <em>q</em>-version of Zeilberger's algorithm, we introduce <em>q</em>-WZ pairs that extend WZ pairs introduced by <span><span>Guillera, 2002</span></span>, <span><span>Guillera, 2006</span></span>. We apply our <span>EKHAD</span>-normalization method to prove four new <em>q</em>-analogues for three of Ramanujan's formulas for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></math></span> along with <em>q</em>-analogues of Guillera's first two series for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span>. Our normalization method does not seem to have been previously considered in any equivalent way in relation to <em>q</em>-series, and this is substantiated through our survey on previously known <em>q</em>-analogues of Ramanujan-type series for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></math></span> and of Guillera's series for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span>. We conclude by showing how our method can be adapted to further extend Guillera's WZ pairs by introducing hypergeometric expansions for <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102531"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145568784","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":"Apéry-type series via colored multiple zeta values and Fourier-Legendre series expansions","authors":"Xin Chen,&nbsp;Weiping Wang","doi":"10.1016/j.jsc.2025.102508","DOIUrl":"10.1016/j.jsc.2025.102508","url":null,"abstract":"<div><div>In this paper, by applying the general Fourier-Legendre series expansion, we establish four general series transformations, and obtain a range of relations between the parametric Apéry-type series and the double sums of products of multiple harmonic sums (MHSs) or multiple <em>t</em>-harmonic sums (MtSs) from the Fourier-Legendre series expansions of the complete elliptic integrals of the first and second kind as well as two special expansions provided recently in the literature. By establishing the linearization theorem for the double sums of products above, and using the methods of partial fraction decomposition and transformation of summations, we show that these parametric Apéry-type series are expressible in terms of some elementary series involving MHSs and MtSs, and finally reducible, with an extra factor <span><math><mn>1</mn><mo>/</mo><mi>π</mi></math></span>, to linear combinations of alternating multiple zeta values and colored multiple zeta values of level four. By specifying the parameters, we determine the evaluations of many special Apéry-type series.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"134 ","pages":"Article 102508"},"PeriodicalIF":1.1,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050267","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":"Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant 2","authors":"Hiroyuki Ochiai ,&nbsp;Satoshi Wakatsuki ,&nbsp;Shun'ichi Yokoyama","doi":"10.1016/j.jsc.2025.102485","DOIUrl":"10.1016/j.jsc.2025.102485","url":null,"abstract":"<div><div>In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant 2, and provide a database of such bases. A main application of our database is to obtain congruence relations of algebraic modular forms, which lead non-vanishing theorems for prime twists of modular <em>L</em>-functions.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102485"},"PeriodicalIF":1.1,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886193","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":"Solvable and nilpotent matroids: Realizability and irreducible decomposition of their associated varieties","authors":"Emiliano Liwski,&nbsp;Fatemeh Mohammadi","doi":"10.1016/j.jsc.2025.102484","DOIUrl":"10.1016/j.jsc.2025.102484","url":null,"abstract":"<div><div>We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizability, as well as the irreducible decomposition of their associated matroid and circuit varieties. Additionally, we describe a finite generating set for the corresponding ideals, considered up to radical. We establish sufficient conditions for both the realizability of these matroids and the irreducibility of their associated varieties. Specifically, we establish the realizability and irreducibility of matroid varieties associated with nilpotent matroids and prove the irreducibility of matroid varieties arising from certain classes of solvable paving matroids. Additionally, we analyze the defining polynomial equations of these varieties using Grassmann-Cayley algebra and geometric liftability techniques. Furthermore, we provide a complete generating set for the matroid ideals associated with forest configurations.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102484"},"PeriodicalIF":1.1,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886195","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":"On semi-local decomposition","authors":"Ming-Deh A. Huang","doi":"10.1016/j.jsc.2025.102483","DOIUrl":"10.1016/j.jsc.2025.102483","url":null,"abstract":"<div><div>We consider semi-local polynomial systems and their decomposition. A semi-local polynomial system defines a global polynomial map that is the product of local polynomial maps disguised by global linear isomorphisms. We characterize a subclass of semi-local polynomial systems which can be efficiently decomposed into local systems.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"133 ","pages":"Article 102483"},"PeriodicalIF":1.1,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886196","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}