Journal of Symbolic Computation最新文献_第5页

Chebyshev subdivision and reduction methods for solving multivariable systems of equations 求解多元方程组的切比雪夫细分和还原法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-03 DOI: 10.1016/j.jsc.2024.102392

Erik Parkinson , Kate Wall , Jane Slagle , Daniel Treuhaft , Xander de la Bruere , Samuel Goldrup , Timothy Keith , Peter Call , Tyler J. Jarvis

{"title":"Chebyshev subdivision and reduction methods for solving multivariable systems of equations","authors":"Erik Parkinson , Kate Wall , Jane Slagle , Daniel Treuhaft , Xander de la Bruere , Samuel Goldrup , Timothy Keith , Peter Call , Tyler J. Jarvis","doi":"10.1016/j.jsc.2024.102392","DOIUrl":"10.1016/j.jsc.2024.102392","url":null,"abstract":"<div><div>We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and elimination checks that leverage special properties of Chebyshev polynomials. We prove the method has quadratic convergence locally near simple zeros of the system. It also finds all nonsimple zeros, but convergence to those zeros is not guaranteed to be quadratic. We also analyze the arithmetic complexity and the numerical stability of the algorithm and provide numerical evidence in dimensions up to five that the method is both fast and accurate on a wide range of problems. Our tests show that the algorithm outperforms other standard methods on the problem of finding all real zeros in a bounded domain. Our Python implementation of the algorithm is publicly available at <span><span>https://github.com/tylerjarvis/RootFinding</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102392"},"PeriodicalIF":0.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142422636","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

Self-intersections of surfaces that contain two circles through each point 每点包含两个圆的曲面的自交点

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-27 DOI: 10.1016/j.jsc.2024.102390

Niels Lubbes

引用次数: 0

Asymptotics of solutions of special second-order linear recurrencies with polynomial coefficients and boundary effects of polynomial filters 具有多项式系数的特殊二阶线性回归方程解的渐近性和多项式滤波器的边界效应

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI: 10.1016/j.jsc.2024.102386

Alexey A. Kytmanov , Sergey P. Tsarev

引用次数: 0

An m-adic algorithm for bivariate Gröbner bases 二元格氏基的 m-adic 算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI: 10.1016/j.jsc.2024.102389

Éric Schost , Catherine St-Pierre

{"title":"An m-adic algorithm for bivariate Gröbner bases","authors":"Éric Schost , Catherine St-Pierre","doi":"10.1016/j.jsc.2024.102389","DOIUrl":"10.1016/j.jsc.2024.102389","url":null,"abstract":"<div><div>Let <span><math><mi>A</mi></math></span> be a domain, with <span><math><mi>m</mi><mo>⊆</mo><mi>A</mi></math></span> a maximal ideal, and let <span><math><mi>F</mi><mo>⊆</mo><mi>A</mi><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>]</mo></math></span> be any finite generating set of an ideal with finitely many roots (in an algebraic closure of the fraction field <span><math><mi>K</mi></math></span> of <span><math><mi>A</mi></math></span>). We present a randomized <span><math><mi>m</mi></math></span>-adic algorithm to recover the lexicographic Gröbner basis <span><math><mi>G</mi></math></span> of <span><math><mo>〈</mo><mi>F</mi><mo>〉</mo><mo>⊆</mo><mi>K</mi><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>]</mo></math></span>, or of its primary component at the origin. We observe that previous results of Lazard's that use Hermite normal forms to compute Gröbner bases for ideals with two generators can be generalized to a generating set <span><math><mi>F</mi></math></span> of cardinality greater than two. We use this result to bound the size of the coefficients of <span><math><mi>G</mi></math></span>, and to control the probability of choosing a <em>good</em> maximal ideal <span><math><mi>m</mi><mo>⊆</mo><mi>A</mi></math></span>. We give a complete cost analysis over number fields (<span><math><mi>K</mi><mo>=</mo><mi>Q</mi><mo>(</mo><mi>α</mi><mo>)</mo></math></span>) and function fields (<figure><img></figure>), and we obtain a complexity that is less than cubic in terms of the dimension of <span><math><mi>K</mi><mo>/</mo><mo>〈</mo><mi>G</mi><mo>〉</mo></math></span> and softly linear in the size of its coefficients.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102389"},"PeriodicalIF":0.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421940","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

Symbolic-numeric algorithm for parameter estimation in discrete-time models with exp 离散时间模型参数估计的符号-数字算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-26 DOI: 10.1016/j.jsc.2024.102387

Yosef Berman , Joshua Forrest , Matthew Grote , Alexey Ovchinnikov , Sonia L. Rueda

{"title":"Symbolic-numeric algorithm for parameter estimation in discrete-time models with exp","authors":"Yosef Berman , Joshua Forrest , Matthew Grote , Alexey Ovchinnikov , Sonia L. Rueda","doi":"10.1016/j.jsc.2024.102387","DOIUrl":"10.1016/j.jsc.2024.102387","url":null,"abstract":"<div><div>Dynamic models describe phenomena across scientific disciplines, yet to make these models useful in application the unknown parameter values of the models must be determined. Discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. In this paper, we propose a symbolic-numeric approach for parameter estimation in discrete-time models that involve univariate non-algebraic (locally) analytic functions such as exp. We illustrate the performance (precision) of our approach by applying our approach to two archetypal discrete-time models in biology (the flour beetle ‘LPA’ model and discrete Lotka-Volterra competition model). Unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values up to a specified precision given time-series data for the measured variables provided that there are finitely many parameter values that fit the data and that the used polynomial system solver can find all roots of the associated polynomial system with interval coefficients.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102387"},"PeriodicalIF":0.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142422637","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

Algorithm for globally identifiable reparametrizations of ODEs 全局可识别的 ODEs 重参数化算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-09-10 DOI: 10.1016/j.jsc.2024.102385

Sebastian Falkensteiner , Alexey Ovchinnikov , J. Rafael Sendra

引用次数: 0

Subresultants of several univariate polynomials in Newton basis 几个单变量多项式在牛顿基上的子结果

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-30 DOI: 10.1016/j.jsc.2024.102378

Weidong Wang, Jing Yang

引用次数: 0

D-algebraic functions D 代函数

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102377

Rida Ait El Manssour , Anna-Laura Sattelberger , Bertrand Teguia Tabuguia

引用次数: 0

Invariant neural architecture for learning term synthesis in instantiation proving 在实例化证明中学习术语合成的不变神经架构

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-28 DOI: 10.1016/j.jsc.2024.102375

Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota

{"title":"Invariant neural architecture for learning term synthesis in instantiation proving","authors":"Jelle Piepenbrock , Josef Urban , Konstantin Korovin , Miroslav Olšák , Tom Heskes , Mikoláš Janota","doi":"10.1016/j.jsc.2024.102375","DOIUrl":"10.1016/j.jsc.2024.102375","url":null,"abstract":"<div><p>The development of strong CDCL-based propositional (SAT) solvers has greatly advanced several areas of automated reasoning (AR). One of the directions in AR is therefore to make use of SAT solvers in expressive formalisms such as first-order logic, for which large corpora of general mathematical problems exist today. This is possible due to Herbrand's theorem, which allows reduction of first-order problems to propositional problems by instantiation. The core challenge is synthesizing the appropriate instances from the typically infinite Herbrand universe.</p><p>In this work, we develop a machine learning system targeting this task, addressing its combinatorial and invariance properties. In particular, we develop a GNN2RNN architecture based on a graph neural network (GNN) that learns from problems and their solutions independently of many symmetries and symbol names (addressing the abundance of Skolems), combined with a recurrent neural network (RNN) that proposes for each clause its instantiations. The architecture is then combined with an efficient ground solver and, starting with zero knowledge, iteratively trained on a large corpus of mathematical problems. We show that the system is capable of solving many problems by such educated guessing, finding proofs for 32.12% of the training set. The final trained system solves 19.74% of the unseen test data on its own. We also observe that the trained system finds solutions that the iProver and CVC5 systems did not find.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102375"},"PeriodicalIF":0.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000798/pdfft?md5=03f2c9a993930436ebd44dced50d3406&pid=1-s2.0-S0747717124000798-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150873","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

Graph sequence learning for premise selection 用于前提选择的图序列学习

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-08-27 DOI: 10.1016/j.jsc.2024.102376

Edvard K. Holden, Konstantin Korovin

引用次数: 0