Journal of Symbolic Computation最新文献_第3页

On arrangements of quadrics in decomposing the parameter space of 3D digitized rigid motions 论分解三维数字化刚性运动参数空间的四边形排列

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-04-14 DOI: 10.1016/j.jsc.2025.102447

Kacper Pluta , Guillaume Moroz , Yukiko Kenmochi , Pascal Romon

{"title":"On arrangements of quadrics in decomposing the parameter space of 3D digitized rigid motions","authors":"Kacper Pluta , Guillaume Moroz , Yukiko Kenmochi , Pascal Romon","doi":"10.1016/j.jsc.2025.102447","DOIUrl":"10.1016/j.jsc.2025.102447","url":null,"abstract":"<div><div>Computing the arrangement of quadrics in 3D is a fundamental problem in symbolic computation, with challenges arising when handling degenerate cases and asymptotic critical values. State-of-the-art methods typically require a generic change of coordinates to manage these asymptotes, rendering certain problems intractable. A specific instance of this challenge appears in digital geometry, where comparing 3D shapes up to isometry requires applying a 3D rigid motion on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and mapping the result back to <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, a process typically achieved via a digitization operator. However, such motions do not preserve the topology of digital objects, making the analysis of digitized rigid motions crucial. Our main contribution is the decomposition of the 6D parameter space of digitized rigid motions for image patches of radius up to three. This problem reduces to computing the arrangement of up to 741 quadrics, some of which are degenerate. To address the computational challenges, we introduce and implement a new algorithm for computing arrangements of quadrics in 3D, specifically designed to handle degenerate directions and asymptotic critical values. This approach allows us to overcome the limitations of existing methods, making the problem tractable in the context of digital geometry.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102447"},"PeriodicalIF":0.6,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855157","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

Geometric interpretations of compatibility for fundamental matrices 基本矩阵相容性的几何解释

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-04-02 DOI: 10.1016/j.jsc.2025.102446

Erin Connelly , Felix Rydell

引用次数: 0

Elimination by substitution 代入消去法

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-04-02 DOI: 10.1016/j.jsc.2025.102445

Martin Kreuzer , Lorenzo Robbiano

{"title":"Elimination by substitution","authors":"Martin Kreuzer , Lorenzo Robbiano","doi":"10.1016/j.jsc.2025.102445","DOIUrl":"10.1016/j.jsc.2025.102445","url":null,"abstract":"<div><div>Let <em>K</em> be a field and <span><math><mi>P</mi><mo>=</mo><mi>K</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span>. The technique of elimination by substitution is based on discovering a coherently <span><math><mi>Z</mi><mo>=</mo><mo>(</mo><msub><mrow><mi>z</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span>-separating tuple of polynomials <span><math><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span> in an ideal <em>I</em>, i.e., on finding polynomials such that <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> with <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mi>K</mi><mo>[</mo><mi>X</mi><mo>∖</mo><mi>Z</mi><mo>]</mo></math></span>. Here we elaborate on this technique in the case when <em>P</em> is non-negatively graded. The existence of a coherently <em>Z</em>-separating tuple is reduced to solving several <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-module membership problems. Best separable re-embeddings, i.e., isomorphisms <span><math><mi>P</mi><mo>/</mo><mi>I</mi><mo>⟶</mo><mi>K</mi><mo>[</mo><mi>X</mi><mo>∖</mo><mi>Z</mi><mo>]</mo><mo>/</mo><mo>(</mo><mi>I</mi><mo>∩</mo><mi>K</mi><mo>[</mo><mi>X</mi><mo>∖</mo><mi>Z</mi><mo>]</mo><mo>)</mo></math></span> with maximal #<em>Z</em>, are found degree-by-degree. They turn out to yield optimal re-embeddings in the positively graded case. Viewing <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>⟶</mo><mi>P</mi><mo>/</mo><mi>I</mi></math></span> as a fibration over an affine space, we show that its fibers allow optimal <em>Z</em>-separating re-embeddings, and we provide a criterion for a fiber to be isomorphic to an affine space. In the last section we introduce a new technique based on the solution of a unimodular matrix problem which enables us to construct automorphisms of <em>P</em> such that additional <em>Z</em>-separating re-embeddings are possible. One of the main outcomes is an algorithm which allows us to explicitly compute a homogeneous isomorphism between <span><math><mi>P</mi><mo>/</mo><mi>I</mi></math></span> and a non-negatively graded polynomial ring if <span><math><mi>P</mi><mo>/</mo><mi>I</mi></math></span> is regular.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"131 ","pages":"Article 102445"},"PeriodicalIF":0.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768989","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

Proof of some conjectural congruences involving products of two binomial coefficients 关于两个二项式系数乘积的若干猜想同余的证明

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-27 DOI: 10.1016/j.jsc.2025.102436

Guo-Shuai Mao , Xiran Zhang

引用次数: 0

Certified simultaneous isotopic approximation of algebraic curves via subdivision 通过细分的代数曲线的认证同时同位素近似

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-26 DOI: 10.1016/j.jsc.2025.102435

Michael Burr, Michael Byrd

引用次数: 0

A propositional encoding for first-order clausal entailment over infinitely many constants 无限多常数上一阶子句蕴涵的命题编码

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-19 DOI: 10.1016/j.jsc.2025.102434

Vaishak Belle

{"title":"A propositional encoding for first-order clausal entailment over infinitely many constants","authors":"Vaishak Belle","doi":"10.1016/j.jsc.2025.102434","DOIUrl":"10.1016/j.jsc.2025.102434","url":null,"abstract":"<div><div>There is a fundamental trade-off between the expressiveness of the language and the tractability of the reasoning task in knowledge representation. On the one hand it is widely acknowledged that relations and more generally, the expressiveness of first-order logic is extremely useful for capturing concepts required for common-sense reasoning. But at the same time the entailment problem is only semi-decidable.</div><div>There have been a wide range of approaches to deal with this trade-off, from restricting the language to propositional logic to limit the expressiveness of the language in terms of the arity of the predicates (as in description logics) or the use of negation (as in Horn logic) to limit reasoning by weakening the entailment relation using non-standard semantics.</div><div>In this work, we address a gap in this literature. We show that there is an intuitive fragment of first-order disjunctive knowledge, for which reasoning is decidable and can be reduced to propositional satisfiability. Knowledge bases in this fragment correspond to universally quantified first-order clauses, but without arity restrictions and without restrictions on the appearance of negation. Queries, however, are expected to be ground formulas. We achieve this result by showing how the entailment over infinitely many infinite-sized structures can be reduced to a search over finitely many finite-size structures. The crux of the argument lies in showing that constants not mentioned in the knowledge base and/or query behave identically (in a suitable formal sense). We then go on to also show that there is also an extension to this result for function symbols.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102434"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474775","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

Reduction systems and degree bounds for integration 积分的约简系统与度界

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-19 DOI: 10.1016/j.jsc.2025.102432

Hao Du , Clemens G. Raab

引用次数: 0

Congruence properties for Schmidt type d-fold partition diamonds Schmidt型d-fold分割菱形的同余性质

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-19 DOI: 10.1016/j.jsc.2025.102431

Olivia X.M. Yao, Xuan Yu

{"title":"Congruence properties for Schmidt type d-fold partition diamonds","authors":"Olivia X.M. Yao, Xuan Yu","doi":"10.1016/j.jsc.2025.102431","DOIUrl":"10.1016/j.jsc.2025.102431","url":null,"abstract":"<div><div>Recently, Dockery, Jameson, Sellers and Wilson introduced new combinatorial objects called <em>d</em>-fold partition diamonds, which generalize both the classical partition function and the plane partition diamonds of Andrews, Paule and Riese. They also investigated a partition function <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> which counts the number of Schmidt type <em>d</em>-fold partition diamonds of <em>n</em>. They presented the generating functions of <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and proved several congruences for <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. At the end of their paper, they posed a conjecture on congruences modulo 7 for <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. In this paper, we prove the conjectural congruences for <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> by using two methods: an elementary proof based on a result of Garvan and an algorithmic proof based on the Mathematica package RaduRK by Smoot. We also give an algorithmic proof of the conjectural congruences for <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> by utilizing Smoot's Mathematica package RaduRK. In addition, we prove new infinite families of congruences modulo 7 for <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and prove that <span><math><mfrac><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>6</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><mn>7</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>7</mn></mrow></mfrac></math></span> takes integer values with probability 1 for <span><math><mi>n</mi><mo>≥</mo><mn>0</mn></math></span>. Moreover, we show that there exist infinitely many integers <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> such that <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>12</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>≡</mo><mspace></mspace><mi>i</mi><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>13</mn><mo>)</mo></math></span> with <span><math><mn>0</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mn>12</mn></math></span>.</div></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"130 ","pages":"Article 102431"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509114","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

On other two representations of the C-recursive integer sequences by terms in modular arithmetic 关于c递归整数序列在模算术中的其他两种表示

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-02-19 DOI: 10.1016/j.jsc.2025.102433

Mihai Prunescu

引用次数: 0

Wilf-Zeilberger seeds and non-trivial hypergeometric identities Wilf-Zeilberger种子和非平凡超几何恒等式

IF 0.6 4区数学

Journal of Symbolic Computation Pub Date : 2025-01-28 DOI: 10.1016/j.jsc.2025.102421

Kam Cheong Au

引用次数: 0