Journal of Symbolic Computation最新文献

Persistent components in Canny's generalized characteristic polynomial 坎尼广义特征多项式中的持久成分

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-30 DOI: 10.1016/j.jsc.2024.102397

Gleb Pogudin

引用次数: 0

Mixed volumes of networks with binomial steady-states 具有二项稳定状态的网络混合体积

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-11 DOI: 10.1016/j.jsc.2024.102395

Jane Ivy Coons , Maize Curiel , Elizabeth Gross

引用次数: 0

Coupled cluster degree of the Grassmannian 格拉斯曼的耦合群集度

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-11 DOI: 10.1016/j.jsc.2024.102396

Viktoriia Borovik , Bernd Sturmfels , Svala Sverrisdóttir

引用次数: 0

Creative telescoping for hypergeometric double sums 超几何双和的创造性伸缩

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-10 DOI: 10.1016/j.jsc.2024.102394

Peter Paule , Carsten Schneider

引用次数: 0

On nonnegative invariant quartics in type A 论 A 型非负不变四元数

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2024-10-09 DOI: 10.1016/j.jsc.2024.102393

Sebastian Debus , Charu Goel , Salma Kuhlmann , Cordian Riener

引用次数: 0

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":null,"pages":null},"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":null,"pages":null},"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

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":null,"pages":null},"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