Journal of Symbolic Computation最新文献_第4页

A geometric algorithm for the factorization of rational motions in conformal three space 共形三空间有理运动因式分解的几何算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-05 DOI: 10.1016/j.jsc.2024.102388

Zijia Li , Hans-Peter Schröcker , Johannes Siegele

引用次数: 0

A new algorithm for Gröbner bases conversion 格氏碱基转换的新算法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-04 DOI: 10.1016/j.jsc.2024.102391

Amir Hashemi , Deepak Kapur

{"title":"A new algorithm for Gröbner bases conversion","authors":"Amir Hashemi , Deepak Kapur","doi":"10.1016/j.jsc.2024.102391","DOIUrl":"10.1016/j.jsc.2024.102391","url":null,"abstract":"<div><div>A new approach for Gröbner bases conversion of polynomial ideals (over a field) of arbitrary dimension is presented. In contrast to the only other approach based on Gröbner fan and Gröbner walk for positive dimensional ideals, the proposed approach is simpler to understand, prove, and implement. It is based on defining for a given polynomial, a truncated sub-polynomial consisting of all monomials that can possibly become the leading monomial with respect to the target ordering: the monomials between the leading monomial of the target ordering and the leading monomial of the initial ordering.</div><div>The main ingredient of the new algorithm is the computation of a Gröbner basis with respect to the target ordering for the ideal generated by such truncated parts of the input Gröbner basis. This is done using the extended Buchberger algorithm that also outputs the relationship between the input and output bases. That information is used in attempts to recover a Gröbner basis of the ideal with respect to the target ordering. In general, more than one iteration may be needed to get a Gröbner basis with respect to the target ordering since truncated polynomials may miss some leading monomials.</div><div>The new algorithm has been implemented in <span>Maple</span> and its operation is illustrated using an example. The performance of this implementation is compared with the implementations of other approaches in <span>Maple.</span> In practice, a Gröbner basis with respect to a target ordering can be computed in a single iteration on most examples.</div><div>Since the proposed basis conversion algorithm uses simple concepts of Gröbner basis theory, it can be easily taught in contrast to methods based on Gröbner walk.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"128 ","pages":"Article 102391"},"PeriodicalIF":0.6,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421939","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

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