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ACM Communications in Computer Algebra最新文献

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On sparse interpolation of rational functions and gcds 有理函数的稀疏插值与gcd
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-11-11 DOI: 10.1145/3466895.3466896
J. Hoeven, Grégoire Lecerf
{"title":"On sparse interpolation of rational functions and gcds","authors":"J. Hoeven, Grégoire Lecerf","doi":"10.1145/3466895.3466896","DOIUrl":"https://doi.org/10.1145/3466895.3466896","url":null,"abstract":"In this note, we present a variant of a probabilistic algorithm by Cuyt and Lee for the sparse interpolation of multivariate rational functions. We also present an analogous method for the computation of sparse gcds.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"1 - 12"},"PeriodicalIF":0.1,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3466895.3466896","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46329629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
CQF Magma package CQF Magma包
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-29 DOI: 10.1145/3427218.3427224
P. Koprowski
{"title":"CQF Magma package","authors":"P. Koprowski","doi":"10.1145/3427218.3427224","DOIUrl":"https://doi.org/10.1145/3427218.3427224","url":null,"abstract":"CQF is a free, open-source Magma package for doing computations in quadratic forms theory. We present some selected ingredients of the package.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"53 - 56"},"PeriodicalIF":0.1,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42753804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The 2019 Richard D. Jenks memorial prize 2019年理查德·d·詹克斯纪念奖
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-29 DOI: 10.1145/3427218.3427226
M. Monagan
{"title":"The 2019 Richard D. Jenks memorial prize","authors":"M. Monagan","doi":"10.1145/3427218.3427226","DOIUrl":"https://doi.org/10.1145/3427218.3427226","url":null,"abstract":"","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"61 - 61"},"PeriodicalIF":0.1,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427226","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42693273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Checkpoints in searching for rational solutions of linear ordinary difference and differential systems 寻找线性常差分和微分系统的有理解的检查点
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-29 DOI: 10.1145/3427218.3427219
S. Abramov, D. E. Khmelnov, A. Ryabenko
{"title":"Checkpoints in searching for rational solutions of linear ordinary difference and differential systems","authors":"S. Abramov, D. E. Khmelnov, A. Ryabenko","doi":"10.1145/3427218.3427219","DOIUrl":"https://doi.org/10.1145/3427218.3427219","url":null,"abstract":"It is quite common that search algorithms for those solutions of difference and differential equations and systems that belong to a fixed class of functions are designed so that nonexistence of solutions of the desired type is detected only in the last stages of the algorithm. However, performing additional tests on the intermediate results makes it possible to stop the algorithm as soon as these tests imply that no solutions of the desired type exist. This gives an opportunity to save time and other computing resources. So, it makes sense to equip algorithms with checkpoints and some tests. We consider these questions in connection with the search for rational solutions of linear homogeneous difference and differential systems with polynomial coefficients, and propose a scheme equipped with such checkpoints and tests, and also report results of experiments with our implementation of the scheme in Maple.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"18 - 29"},"PeriodicalIF":0.1,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427219","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47265975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PTOPO: a maple package for the topology of parametric curves PTOPO:一个枫包的拓扑参数曲线
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-29 DOI: 10.1145/3427218.3427223
Christina Katsamaki, F. Rouillier, Elias P. Tsigaridas, Zafeirakis Zafeirakopoulos
{"title":"PTOPO: a maple package for the topology of parametric curves","authors":"Christina Katsamaki, F. Rouillier, Elias P. Tsigaridas, Zafeirakis Zafeirakopoulos","doi":"10.1145/3427218.3427223","DOIUrl":"https://doi.org/10.1145/3427218.3427223","url":null,"abstract":"PTOPO is a maple package computing the topology and describing the geometry of a parametric plane curve. The algorithm behind PTOPO constructs an abstract graph that is isotopic to the curve. PTOPO exploits the benefits of the parametric representation and performs all computations in the parameter space using exact computing. PTOPO computes the topology and visualizes the curve in less than a second for most examples in the literature. Comparison of maple parametric plot vs PTOPO 1 Topology of Parametric Curves The study of parametric curves is a classical topic in computational algebra and geometry (Sendra and Winkler (1999); Boissonnat and Teillaud (2006)). The interest for computing with parametric curves has been motivated, among others, by the omnipresence of parametric representations in computer modeling and computer aided geometric design (Manocha and Canny (1992); Pérez-Dı́az (2006); Sendra et al. (2008)). ⇤Supported by the Fondation Sciences Mathématiques de Paris (FSMP)","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"49-52"},"PeriodicalIF":0.1,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427223","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64034674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Sage package comb_walks for walks in the quarter plane Sage包comb_walks用于四分之一平面的行走
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-29 DOI: 10.1145/3427218.3427220
Antonio Jiménez-Pastor, A. Bostan, F. Chyzak, Pierre Lairez
{"title":"The Sage package comb_walks for walks in the quarter plane","authors":"Antonio Jiménez-Pastor, A. Bostan, F. Chyzak, Pierre Lairez","doi":"10.1145/3427218.3427220","DOIUrl":"https://doi.org/10.1145/3427218.3427220","url":null,"abstract":"We present in this extended abstract a new software designed to work with generating functions that count walks in the quarter plane. With this software we offer a cohesive package that brings together all the required procedures for manipulating these generating functions, as well as a unified interface to deal with them. We also display results that this package offers on a public webpage.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"30 - 38"},"PeriodicalIF":0.1,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3427218.3427220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46492496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves 稳定曲线模空间中零环Chow群中单项式的微积分
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-01 DOI: 10.1145/3457341.3457344
Jiayue Qi
{"title":"A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves","authors":"Jiayue Qi","doi":"10.1145/3457341.3457344","DOIUrl":"https://doi.org/10.1145/3457341.3457344","url":null,"abstract":"We introduce an algorithm for computing the value of all monomials in the Chow group of zero cycles in the moduli space of stable curves.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"91 - 94"},"PeriodicalIF":0.1,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457344","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46735245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Improved divisor arithmetic on generic hyperelliptic curves 改进的一般超椭圆曲线除数算法
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-01 DOI: 10.1145/3457341.3457345
Sebastian Lindner, L. Imbert, M. Jacobson
{"title":"Improved divisor arithmetic on generic hyperelliptic curves","authors":"Sebastian Lindner, L. Imbert, M. Jacobson","doi":"10.1145/3457341.3457345","DOIUrl":"https://doi.org/10.1145/3457341.3457345","url":null,"abstract":"The divisor class group of a hyperelliptic curve defined over a finite field is a finite abelian group at the center of a number of important open questions in algebraic geometry, number theory and cryptography. Many of these problems lend themselves to numerical investigation, and as emphasized by Sutherland [14, 13], fast arithmetic in the divisor class group is crucial for their efficiency. Besides, implementations of these fundamental operations are at the core of the algebraic geometry packages of widely-used computer algebra systems such as Magma and Sage.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"95 - 99"},"PeriodicalIF":0.1,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457345","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44761796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal monomial quadratization for ODE systems ODE系统的最优单项二次化
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-09-01 DOI: 10.1145/3457341.3457350
A. Bychkov, G. Pogudin
{"title":"Optimal monomial quadratization for ODE systems","authors":"A. Bychkov, G. Pogudin","doi":"10.1145/3457341.3457350","DOIUrl":"https://doi.org/10.1145/3457341.3457350","url":null,"abstract":"Transformation of a polynomial ODE system to a special quadratic form has been successfully used recently as a preprocessing step for model order reduction methods. However, to the best of our knowledge, there has been no practical algorithm for performing this step automatically with any optimality guarantees. We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials of the original variables. The algorithm is guaranteed to produce an optimal transformation of this form. The algorithm is implemented, and we demonstrate it on examples from the literature.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"119 - 123"},"PeriodicalIF":0.1,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457350","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46707568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Computing one billion roots using the tangent Graeffe method 使用正切Graeffe方法计算十亿根
IF 0.1
ACM Communications in Computer Algebra Pub Date : 2020-07-25 DOI: 10.1145/3457341.3457342
J. Hoeven, M. Monagan
{"title":"Computing one billion roots using the tangent Graeffe method","authors":"J. Hoeven, M. Monagan","doi":"10.1145/3457341.3457342","DOIUrl":"https://doi.org/10.1145/3457341.3457342","url":null,"abstract":"Let p be a prime of the form p = σ2k + 1 with σ small and let Fp denote the finite field with p elements. Let P(z) be a polynomial of degree d in Fp[z] with d distinct roots in Fp. For p =5 · 255 + 1 we can compute the roots of such polynomials of degree 109. We believe we are the first to factor such polynomials of size one billion. We used a multi-core computer with two 10 core Intel Xeon E5 2680 v2 CPUs and 128 gigabytes of RAM. The factorization takes just under 4,000 seconds on 10 cores and uses 121 gigabytes of RAM. We used the tangent Graeffe root finding algorithm from [27, 19] which is a factor of O(log d) faster than the Cantor-Zassenhaus algorithm. We implemented the tangent Graeffe algorithm in C using our own library of 64 bit integer FFT based in-place polynomial algorithms then parallelized the FFT and main steps using Cilk C. In this article we discuss the steps of the tangent Graeffe algorithm, the sub-algorithms that we used, how we parallelized them, and how we organized the memory so we could factor a polynomial of degree 109. We give both a theoretical and practical comparison of the tangent Graeffe algorithm with the Cantor-Zassenhaus algorithm for root finding. We improve the complexity of the tangent Graeffe algorithm by a factor of 2. We present a new in-place product tree multiplication algorithm that is fully parallelizable. We present some timings comparing our software with Magma's polynomial factorization command. Polynomial root finding over smooth finite fields is a key ingredient for algorithms for sparse polynomial interpolation that are based on geometric sequences. This application was also one of our main motivations for the present work.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"54 1","pages":"65 - 85"},"PeriodicalIF":0.1,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3457341.3457342","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43840894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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