Journal of Symbolic Computation最新文献_第10页

An improved complexity bound for computing the topology of a real algebraic space curve 计算实代数空间曲线拓扑的改进复杂度约束

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-02-21 DOI: 10.1016/j.jsc.2024.102309

Jin-San Cheng , Kai Jin , Marc Pouget , Junyi Wen , Bingwei Zhang

{"title":"An improved complexity bound for computing the topology of a real algebraic space curve","authors":"Jin-San Cheng , Kai Jin , Marc Pouget , Junyi Wen , Bingwei Zhang","doi":"10.1016/j.jsc.2024.102309","DOIUrl":"10.1016/j.jsc.2024.102309","url":null,"abstract":"<div>We propose a new algorithm to compute the topology of a real algebraic space curve. The novelties of this algorithm are a new technique to achieve the lifting step which recovers points of the space curve in each plane fiber from several projections and a weaker notion of generic position. As distinct to previous work, our sweep generic position does not require that x-critical points have different x-coordinates. The complexity of achieving this sweep generic position property is thus no longer a bottleneck in term of complexity. The bit complexity of our algorithm is <math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>18</mn></mrow></msup><mo>+</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>17</mn></mrow></msup><mi>τ</mi><mo>)</mo></math> where d and τ bound the degree and the bitsize of the integer coefficients, respectively, of the defining polynomials of the curve and polylogarithmic factors are ignored. To the best of our knowledge, this improves upon the best currently known results at least by a factor of <math><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup></math>.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"125 ","pages":"Article 102309"},"PeriodicalIF":0.7,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139919633","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

Rational solutions to the first order difference equations in the bivariate difference field 二维差分场中一阶差分方程的有理解

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-02-09 DOI: 10.1016/j.jsc.2024.102308

Qing-Hu Hou , Yarong Wei

{"title":"Rational solutions to the first order difference equations in the bivariate difference field","authors":"Qing-Hu Hou , Yarong Wei","doi":"10.1016/j.jsc.2024.102308","DOIUrl":"https://doi.org/10.1016/j.jsc.2024.102308","url":null,"abstract":"<div>Inspired by Karr's algorithm, we consider the summations involving a sequence satisfying a recurrence of order two. The structure of such summations provides an algebraic framework for solving the difference equations of form <math><mi>a</mi><mi>σ</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>+</mo><mi>b</mi><mi>g</mi><mo>=</mo><mi>f</mi></math> in the bivariate difference field <math><mo>(</mo><mi>F</mi><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>,</mo><mi>σ</mi><mo>)</mo></math>, where <math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>f</mi><mo>∈</mo><mi>F</mi><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math> are known binary functions of α, β, and α, β are two algebraically independent transcendental elements, σ is a transformation that satisfies <math><mi>σ</mi><mo>(</mo><mi>α</mi><mo>)</mo><mo>=</mo><mi>β</mi></math>, <math><mi>σ</mi><mo>(</mo><mi>β</mi><mo>)</mo><mo>=</mo><mi>u</mi><mi>α</mi><mo>+</mo><mi>v</mi><mi>β</mi></math>, where <math><mi>u</mi><mo>,</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>∈</mo><mi>F</mi></math>. Based on it, we then describe algorithms for finding the universal denominator for those equations in the bivariate difference field under certain assumptions. This reduces the general problem of finding the rational solutions of such equations to the problem of finding the polynomial solutions of such equations.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"124 ","pages":"Article 102308"},"PeriodicalIF":0.7,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139901497","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

Tensor decompositions on simplicial complexes with invariance 具有不变性的简单复数上的张量分解

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-19 DOI: 10.1016/j.jsc.2024.102299

Gemma De las Cuevas , Matt Hoogsteder Riera , Tim Netzer

引用次数: 0

Computing the binomial part of a polynomial ideal 计算多项式理想的二项式部分

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-14 DOI: 10.1016/j.jsc.2024.102298

Martin Kreuzer, Florian Walsh

{"title":"Computing the binomial part of a polynomial ideal","authors":"Martin Kreuzer, Florian Walsh","doi":"10.1016/j.jsc.2024.102298","DOIUrl":"10.1016/j.jsc.2024.102298","url":null,"abstract":"<div>Given an ideal I in a polynomial ring <math><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> over a field K, we present a complete algorithm to compute the binomial part of I, i.e., the subideal <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> of I generated by all monomials and binomials in I. This is achieved step-by-step. First we collect and extend several algorithms for computing exponent lattices in different kinds of fields. Then we generalize them to compute exponent lattices of units in 0-dimensional K-algebras, where we have to generalize the computation of the separable part of an algebra to non-perfect fields in characteristic p. Next we examine the computation of unit lattices in finitely generated K-algebras, as well as their associated characters and lattice ideals. This allows us to calculate <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> when I is saturated with respect to the indeterminates by reducing the task to the 0-dimensional case. Finally, we treat the computation of <math><mrow><mi>Bin</mi></mrow><mo>(</mo><mi>I</mi><mo>)</mo></math> for general ideals by computing their cellular decomposition and dealing with finitely many special ideals called <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-binomial parts. All algorithms have been implemented in SageMath.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"124 ","pages":"Article 102298"},"PeriodicalIF":0.7,"publicationDate":"2024-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0747717124000026/pdfft?md5=bc32bb62dcb12f7f2c1d113994ec49bf&pid=1-s2.0-S0747717124000026-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139462707","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

A post-quantum key exchange protocol from the intersection of conics 来自圆锥交点的后量子密钥交换协议

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-05 DOI: 10.1016/j.jsc.2024.102297

Alberto Alzati, Daniele Di Tullio, Manoj Gyawali, Alfonso Tortora

引用次数: 0

An effective decomposition theorem for Schubert varieties 舒伯特变换的一个有效分解定理

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2024-01-01 DOI: 10.1016/j.jsc.2023.102238

Francesca Cioffi, Davide Franco, Carmine Sessa

引用次数: 0

Theta nullvalues of supersingular Abelian varieties 超星阿贝尔变体的 Theta 空值

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2023-12-29 DOI: 10.1016/j.jsc.2023.102296

Andreas Pieper

引用次数: 0

A note on the relation between recognisable series and regular sequences, and their minimal linear representations 关于可识别数列和正则表达式及其最小线性表示之间关系的说明

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2023-12-28 DOI: 10.1016/j.jsc.2023.102295

Clemens Heuberger , Daniel Krenn , Gabriel F. Lipnik

引用次数: 0

Axioms for a theory of signature bases 签名基础理论的公理

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2023-12-18 DOI: 10.1016/j.jsc.2023.102275

Pierre Lairez

引用次数: 0

Computing primitive idempotents in finite commutative rings and applications 计算有限交换环中的基元幂级数及其应用

IF 0.7 4区数学

Journal of Symbolic Computation Pub Date : 2023-12-15 DOI: 10.1016/j.jsc.2023.102294

Mugurel Barcau , Vicenţiu Paşol

{"title":"Computing primitive idempotents in finite commutative rings and applications","authors":"Mugurel Barcau , Vicenţiu Paşol","doi":"10.1016/j.jsc.2023.102294","DOIUrl":"10.1016/j.jsc.2023.102294","url":null,"abstract":"<div>In this paper, we compute an algebraic decomposition of black-box rings in the generic ring model. More precisely, we explicitly decompose a black-box ring as a direct product of a nilpotent black-box ring and unital local black-box rings, by computing all its primitive idempotents. The algorithm presented in this paper uses quantum subroutines for the computation of the p-power parts of a black-box ring and then classical algorithms for the computation of the corresponding primitive idempotents. As a by-product, we get that the reduction of a black-box ring is also a black-box ring. The first application of this decomposition is an extension of the work of Maurer and Raub (2007) on representation problem in black-box finite fields to the case of reduced p-power black-box rings. Another important application is an <math><msup><mrow><mtext>IND-CCA</mtext></mrow><mrow><mn>1</mn></mrow></msup></math> attack for any ring homomorphic encryption scheme in the generic ring model. Moreover, when the plaintext space is a finite reduced black-box ring, we present a plaintext-recovery attack based on representation problem in black-box prime fields. In particular, if the ciphertext space has smooth characteristic, the plaintext-recovery attack is effectively computable in the generic ring model.</div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"123 ","pages":"Article 102294"},"PeriodicalIF":0.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138688298","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