发布求助
文献互助 智能选刊 最新文献

Applicable Algebra in Engineering Communication and Computing最新文献

筛选
英文 中文
Dedicated to the Memory of Joos Heintz 纪念乔斯·海因茨
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-04-01 DOI: 10.1007/s00200-026-00731-y
Marc Giusti, Grégoire Lecerf, Guillermo Matera, Luis M. Pardo
{"title":"Dedicated to the Memory of Joos Heintz","authors":"Marc Giusti, Grégoire Lecerf, Guillermo Matera, Luis M. Pardo","doi":"10.1007/s00200-026-00731-y","DOIUrl":"10.1007/s00200-026-00731-y","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"199 - 205"},"PeriodicalIF":0.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Kronecker algorithm for locally closed sets over a perfect field 完美域上局部闭集的Kronecker算法
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-04-01 DOI: 10.1007/s00200-026-00726-9
Nardo Giménez, Joos Heintz, Guillermo Matera, Luis Miguel Pardo, Mariana Pérez, Melina Privitelli
{"title":"A Kronecker algorithm for locally closed sets over a perfect field","authors":"Nardo Giménez,&nbsp;Joos Heintz,&nbsp;Guillermo Matera,&nbsp;Luis Miguel Pardo,&nbsp;Mariana Pérez,&nbsp;Melina Privitelli","doi":"10.1007/s00200-026-00726-9","DOIUrl":"10.1007/s00200-026-00726-9","url":null,"abstract":"<div><p>We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety <i>V</i> defined over a perfect field <i>k</i>. The variety <i>V</i> is the Zariski closure of the set of common zeros <span>({F_1=0,ldots ,F_r=0,Gnot =0})</span> of multivariate polynomials <span>(F_1,ldots ,F_rin k[X_1,ldots ,X_n])</span> outside a prescribed hypersurface <span>({G=0})</span>. We assume that <span>(F_1,ldots ,F_r)</span> satisfy natural geometric conditions, such as regularity and radicality, in the localization <span>(k[X_1,ldots ,X_n]_G)</span>. Our approach combines homotopic deformation techniques with symbolic Newton–Hensel lifting and elimination. We discuss the concept of lifting curves as intermediate geometric objects that enable efficient computation.</p><p>The complexity of the algorithm is expressed in terms of the degrees and arithmetic size of the input and achieves soft-quadratic complexity in these parameters. We provide detailed complexity analyses for arbitrary perfect fields, as well as for two important cases in computer algebra: finite fields and the field of rational numbers. For each case, we obtain sharp bounds on the size of the base field or required primes.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"207 - 304"},"PeriodicalIF":0.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal solutions of tropical linear differential systems 热带线性微分系统的极小解
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-03-30 DOI: 10.1007/s00200-025-00722-5
Dima Grigoriev, Cristhian Garay López
{"title":"Minimal solutions of tropical linear differential systems","authors":"Dima Grigoriev,&nbsp;Cristhian Garay López","doi":"10.1007/s00200-025-00722-5","DOIUrl":"10.1007/s00200-025-00722-5","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce and study minimal (with respect to inclusion) solutions of finite systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential equation in a single unknown has either a solution, or a solution at infinity. For a generic system of <i>n</i> tropical linear differential equations in the same number of unknowns, upper and lower bounds on the number of minimal solutions are established. The upper bound involves inversions of a family of permutations, which generalize inversions of a single permutation. For <span>(n=1, 2)</span>, we show that the bounds are sharp.</p>\u0000 </div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"503 - 539"},"PeriodicalIF":0.6,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparse systems and algorithmic equidimensional decomposition 稀疏系统与算法等维分解
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-03-16 DOI: 10.1007/s00200-025-00721-6
María Isabel Herrero, Gabriela Jeronimo, Juan Sabia
{"title":"Sparse systems and algorithmic equidimensional decomposition","authors":"María Isabel Herrero,&nbsp;Gabriela Jeronimo,&nbsp;Juan Sabia","doi":"10.1007/s00200-025-00721-6","DOIUrl":"10.1007/s00200-025-00721-6","url":null,"abstract":"<div>\u0000 \u0000 <p>We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved.</p>\u0000 </div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"305 - 330"},"PeriodicalIF":0.6,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Towards a library for straight-line programs 走向一个直线程序库
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-03-10 DOI: 10.1007/s00200-025-00719-0
Joris van der Hoeven, Grégoire Lecerf
{"title":"Towards a library for straight-line programs","authors":"Joris van der Hoeven,&nbsp;Grégoire Lecerf","doi":"10.1007/s00200-025-00719-0","DOIUrl":"10.1007/s00200-025-00719-0","url":null,"abstract":"<div>\u0000 \u0000 <p>Straight-line programs have proved to be an extremely useful framework both for theoretical work on algebraic complexity and for practical implementations. In this paper, we expose ideas for the development of high performance libraries dedicated to straight-line programs, with the hope that they will allow to fully leverage the theoretical advantages of this framework for practical applications.</p>\u0000 </div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"331 - 387"},"PeriodicalIF":0.6,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erzeugungsgrad, VC-dimension and neural networks with rational activation function Erzeugungsgrad， vc维与有理激活函数的神经网络
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-01-28 DOI: 10.1007/s00200-025-00723-4
Luis Miguel Pardo, Daniel Sebastián
{"title":"Erzeugungsgrad, VC-dimension and neural networks with rational activation function","authors":"Luis Miguel Pardo,&nbsp;Daniel Sebastián","doi":"10.1007/s00200-025-00723-4","DOIUrl":"10.1007/s00200-025-00723-4","url":null,"abstract":"<div><p>The notion of Erzeugungsgrad was introduced by Joos Heintz in (Theoret Comput Sci 24:239–277, 1983) to bound the number of non-empty cells occurring after a process of quantifier elimination. We extend this notion and the combinatorial bounds of Theorem 2 in Heintz (1983) using the degree for constructible sets defined in Pardo and Sebastián (J Complex 68:101588, 2022). We show that the Erzeugungsgrad is the key ingredient to connect affine Intersection Theory over algebraically closed fields and the VC-Theory of Computational Learning Theory for families of classifiers given by parameterized families of constructible sets. In particular, we prove that the VC-dimension and the Krull dimension are linearly related up to logarithmic factors based on Intersection Theory. Using this relation, we study the density of correct test sequences in evasive varieties. We apply these ideas to analyze parameterized families of neural networks with rational activation function.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"389 - 471"},"PeriodicalIF":0.6,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithms to decide the generalised alibi query for space-time prisms with stationary activity time 具有固定活动时间的时空棱镜广义不在场查询的确定算法
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-01-27 DOI: 10.1007/s00200-026-00725-w
Arthur Jansen, Bart Kuijpers
{"title":"Algorithms to decide the generalised alibi query for space-time prisms with stationary activity time","authors":"Arthur Jansen,&nbsp;Bart Kuijpers","doi":"10.1007/s00200-026-00725-w","DOIUrl":"10.1007/s00200-026-00725-w","url":null,"abstract":"<div><p>Space-time prisms provide a framework to model the uncertainty on the space-time location of a moving object between its measured space-time locations, based on a bound on the speed of the moving object. In this model, the <i>generalised alibi query</i> asks whether <span>(textsf{n})</span> moving objects, given by their respective measured space-time locations and speed bounds, may have met. An analytical solution for <span>(textsf{n}=2)</span> to this problem was first given by Kuijpers et al. (Int J Geogr Inf Sci 25(2):293–322, 2011) and later geometric and algorithmic solutions were proposed for aribtrary finite <span>(textsf{n})</span> in Jansen and Kuijpers (Comput Geom 127:102159, 2025). In this paper, we extend the previous methods to space-time prisms that include “stationary activity time”. We propose solutions that work via the spatial projection as well as methods that use the temporal projection, using techniques from convex and semi-algebraic geometry. We also address variants of the alibi query where it is asked whether the <span>(textsf{n})</span> moving objects may have met at a spatial location or at given moment in time.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"473 - 502"},"PeriodicalIF":0.6,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unified Newton’s method for matrix decompositions 矩阵分解的统一牛顿法
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-01-14 DOI: 10.1007/s00200-025-00720-7
Jean-Claude Yakoubsohn
{"title":"Unified Newton’s method for matrix decompositions","authors":"Jean-Claude Yakoubsohn","doi":"10.1007/s00200-025-00720-7","DOIUrl":"10.1007/s00200-025-00720-7","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a way to unify the construction of Newton’s methods for matrix decompositions. This construction is based on a perturbation analysis of a suitable system associated with matrix decompositions. Then it appears that the resolution of a linear Sylvester equation permits defining Newton’s method. We give a general result to analyze the quadratic convergence of this Newton’s method. We apply it to classical matrix decompositions: <i>LU</i> decomposition, <i>QR</i> decomposition, eigenproblem in the diagonalizable case, singular value decomposition, and Schur decomposition. Finally, we propose for future work a generalization of this construction to approximate matrix decomposition by high-order methods.</p>\u0000 </div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"37 :","pages":"541 - 570"},"PeriodicalIF":0.6,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-025-00720-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147661896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Best Paper Award in Memory of Jacques Calmet 纪念雅克·卡尔梅特最佳论文奖
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2025-10-03 DOI: 10.1007/s00200-025-00707-4
{"title":"Best Paper Award in Memory of Jacques Calmet","authors":"","doi":"10.1007/s00200-025-00707-4","DOIUrl":"10.1007/s00200-025-00707-4","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 6","pages":"1049 - 1049"},"PeriodicalIF":0.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145369946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction: In memoriam Kai-Uwe Schmidt 更正：为了纪念Kai-Uwe Schmidt
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2025-03-17 DOI: 10.1007/s00200-025-00685-7
Teo Mora
{"title":"Correction: In memoriam Kai-Uwe Schmidt","authors":"Teo Mora","doi":"10.1007/s00200-025-00685-7","DOIUrl":"10.1007/s00200-025-00685-7","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 3","pages":"593 - 593"},"PeriodicalIF":0.6,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书