The Polyhedra library is dedicated to solving problems dealing with the integer points of polyhedral sets. Such problems include decomposing the integer points of such sets, solving parametric integer programs, performing dependence analysis in for-loop nests and determining the validity of certain Presburger formulas.
{"title":"The polyhedra library in maple","authors":"Rui-Juan Jing, M. M. Maza","doi":"10.1145/3177795.3177798","DOIUrl":"https://doi.org/10.1145/3177795.3177798","url":null,"abstract":"The Polyhedra library is dedicated to solving problems dealing with the integer points of polyhedral sets. Such problems include decomposing the integer points of such sets, solving parametric integer programs, performing dependence analysis in for-loop nests and determining the validity of certain Presburger formulas.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"58 1","pages":"86-88"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84199935","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}
L. Kastner, Benjamin Lorenz, Andreas Paffenholz, Anna-Lena Winz
We give an overview of the application 'fulton' for toric geometry of the software framework polymake. Using two-dimensional cyclic quotient singularities as our main example, we will show how to create toric varieties and divisors on these. The Singular interface of polymake allows one to go back to the algebraic side in case there is no combinatorial algorithm known yet, in order to develop new conjectures and algorithms.
{"title":"Toric geometry in polymake","authors":"L. Kastner, Benjamin Lorenz, Andreas Paffenholz, Anna-Lena Winz","doi":"10.1145/3177795.3177800","DOIUrl":"https://doi.org/10.1145/3177795.3177800","url":null,"abstract":"We give an overview of the application 'fulton' for toric geometry of the software framework polymake. Using two-dimensional cyclic quotient singularities as our main example, we will show how to create toric varieties and divisors on these. The Singular interface of polymake allows one to go back to the algebraic side in case there is no combinatorial algorithm known yet, in order to develop new conjectures and algorithms.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"34 1","pages":"92-94"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90579317","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}
CoCoA-5 is an interactive Computer Algebra System for Computations in Commutative Algebra, particularly Gröbner bases. It offers a dedicated, mathematician-friendly programming language, with many built-in functions. Its mathematical core is a user-friendly C++ library, called CoCoALib; being a software library facilitates integration with other software. The software is free and open source (C++, GPL3). CoCoALib has been designed so that other "external" software libraries can be easily integrated with it, and also made accessible via CoCoA-5. We give an overview of CoCoA-5 and CoCoALib, highlighting the latest developments.
{"title":"CoCoA-5.2.2 and CoCoALib","authors":"J. Abbott, Anna Maria Bigatti","doi":"10.1145/3177795.3177801","DOIUrl":"https://doi.org/10.1145/3177795.3177801","url":null,"abstract":"CoCoA-5 is an interactive Computer Algebra System for Computations in Commutative Algebra, particularly Gröbner bases. It offers a dedicated, mathematician-friendly programming language, with many built-in functions. Its mathematical core is a user-friendly C++ library, called CoCoALib; being a software library facilitates integration with other software. The software is free and open source (C++, GPL3).\u0000 CoCoALib has been designed so that other \"external\" software libraries can be easily integrated with it, and also made accessible via CoCoA-5.\u0000 We give an overview of CoCoA-5 and CoCoALib, highlighting the latest developments.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"34 1","pages":"95-97"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87297598","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}
We will demonstrate software for fast computation of tropical varieties. We give a brief overview of the first techniques developed by Bogart-Jensen-Speyer-Sturmfels-Thomas and show how its bottlenecks can be avoided, relying theoretically on recent results on the intersection of tropical varieties and practically on well-known algorithms in computer algebra.
{"title":"Computing tropical varieties using Newton's polygon method","authors":"Yue Ren","doi":"10.1145/3177795.3177797","DOIUrl":"https://doi.org/10.1145/3177795.3177797","url":null,"abstract":"We will demonstrate software for fast computation of tropical varieties. We give a brief overview of the first techniques developed by Bogart-Jensen-Speyer-Sturmfels-Thomas and show how its bottlenecks can be avoided, relying theoretically on recent results on the intersection of tropical varieties and practically on well-known algorithms in computer algebra.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"16 1","pages":"83-85"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86885920","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}
We demonstrate some of the computations of Galois groups which are possible in Magma [1].
我们演示了一些在Magma中可能的伽罗瓦群的计算[1]。
{"title":"A demonstration of computing galois groups of polynomials in magma","authors":"Nicole Sutherland","doi":"10.1145/3177795.3177796","DOIUrl":"https://doi.org/10.1145/3177795.3177796","url":null,"abstract":"We demonstrate some of the computations of Galois groups which are possible in Magma [1].","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"63 1","pages":"81-82"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80313553","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}
Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA. Please send abstracts to the CCA editors for consideration.
{"title":"Abstracts of recent doctoral dissertations in computer algebra","authors":"Yusuf Baris Tuncer","doi":"10.1145/3177795.3177802","DOIUrl":"https://doi.org/10.1145/3177795.3177802","url":null,"abstract":"Each quarter we are pleased to present abstracts of recent doctoral dissertations in Computer Algebra and Symbolic Computation. We encourage all recent Ph.D. graduates who have defended in the past two years (and their supervisors), to submit their abstracts for publication in CCA.\u0000 Please send abstracts to the CCA editors <editors_SIGSAM@acm.org> for consideration.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"11 1","pages":"98"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86484275","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}
Professor Wen-Tsun Wu passed away on May 7, 2017, a few days ahead of his 98th birthday. Wu is one of the most influential Chinese mathematicians and computer scientists. In his early years, he made fundamental contributions to algebraic topology. In the late 1970s, Wu proposed the Wu's method of geometric theorem proving and founded the school of Mathematics Mechanization. His study on the ancient Chinese mathematics opened a new era in the field of history of Chinese mathematics. He also made contributions in the area of algebraic geometry, invariant theory, complex geometry, and game theory. His legacy consists not only of his academic work but also of several generations of scientists who learned from him the joy and enthusiasm of scientific research and the way to go about it.
{"title":"Wen-Tsun Wu: His Life and Legacy","authors":"X. Gao","doi":"10.1145/3151131.3151136","DOIUrl":"https://doi.org/10.1145/3151131.3151136","url":null,"abstract":"Professor Wen-Tsun Wu passed away on May 7, 2017, a few days ahead of his 98th birthday. Wu is one of the most influential Chinese mathematicians and computer scientists. In his early years, he made fundamental contributions to algebraic topology. In the late 1970s, Wu proposed the Wu's method of geometric theorem proving and founded the school of Mathematics Mechanization. His study on the ancient Chinese mathematics opened a new era in the field of history of Chinese mathematics. He also made contributions in the area of algebraic geometry, invariant theory, complex geometry, and game theory. His legacy consists not only of his academic work but also of several generations of scientists who learned from him the joy and enthusiasm of scientific research and the way to go about it.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"07 1","pages":"73-79"},"PeriodicalIF":0.0,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85859358","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}
A method for computing limits of quotients of real analytic functions in two variables was developed in [4]. In this article we generalize the results obtained in that paper to the case of quotients q = f(x, y, z)/g(x, y, z) of polynomial functions in three variables with rational coefficients. The main idea consists in examining the behavior of the function q along certain real variety X(q) (the discriminant variety associated to q). The original problem is then solved by reducing to the case of functions of two variables. The inductive step is provided by the key fact that any algebraic curve is birationally equivalent to a plane curve. Our main result is summarized in Theorem 2. In Section 4 we describe an effective method for computing such limits. We provide a high level description of an algorithm that generalizes the one developed in [4], now available in Maple as the limit/multi command.
[4]提出了一种计算二元实解析函数商极限的方法。本文将所得结果推广到具有有理系数的三元多项式函数商q = f(x, y, z)/g(x, y, z)的情况。其主要思想在于检查函数q沿某实变量X(q)(与q相关的判别变量)的行为。然后通过简化到两个变量函数的情况来解决原始问题。归纳步骤是由一个关键的事实提供的，即任何代数曲线都是等价于平面曲线的。定理2概括了我们的主要结果。在第4节中，我们描述了计算这种极限的有效方法。我们提供了一种算法的高级描述，它推广了[4]中开发的算法，现在可以在Maple中使用limit/multi命令。
{"title":"Limits of quotients of polynomial functions in three variables","authors":"J. D. Velez, Juan P. Hernandez, C. Cadavid","doi":"10.1145/3151131.3151132","DOIUrl":"https://doi.org/10.1145/3151131.3151132","url":null,"abstract":"A method for computing limits of quotients of real analytic functions in two variables was developed in [4]. In this article we generalize the results obtained in that paper to the case of quotients q = f(x, y, z)/g(x, y, z) of polynomial functions in three variables with rational coefficients. The main idea consists in examining the behavior of the function q along certain real variety X(q) (the discriminant variety associated to q). The original problem is then solved by reducing to the case of functions of two variables. The inductive step is provided by the key fact that any algebraic curve is birationally equivalent to a plane curve. Our main result is summarized in Theorem 2.\u0000 In Section 4 we describe an effective method for computing such limits. We provide a high level description of an algorithm that generalizes the one developed in [4], now available in Maple as the <code>limit/multi</code> command.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"4 1","pages":"42-56"},"PeriodicalIF":0.0,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73036964","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}
The workshop "Milestone in Computer Algebra 2016 (MICA 2016)" was in-cooperation of ACM and hosted by David R. Cheriton School of Computer Science at the University of Waterloo. The MICA 2016 took place from July 16 till 18, which was right before the annual premier computer algebra conference ISSAC 2016, also hosted in Waterloo by the nearby Wilfrid Laurier University from July 19 till 22.
“2016年计算机代数里程碑(MICA 2016)”研讨会由ACM与滑铁卢大学David R. Cheriton计算机科学学院合作举办。MICA 2016于7月16日至18日举行，就在年度顶级计算机代数会议ISSAC 2016之前，ISSAC 2016也由附近的威尔弗里德劳里埃大学于7月19日至22日在滑铁卢举办。
{"title":"Milestones in Computer Algebra (MICA 2016): a workshop celebrating the research of Erick Kaltofen","authors":"Wen-shin Lee","doi":"10.1145/3151131.3151133","DOIUrl":"https://doi.org/10.1145/3151131.3151133","url":null,"abstract":"The workshop \"Milestone in Computer Algebra 2016 (MICA 2016)\" was in-cooperation of ACM and hosted by David R. Cheriton School of Computer Science at the University of Waterloo. The MICA 2016 took place from July 16 till 18, which was right before the annual premier computer algebra conference ISSAC 2016, also hosted in Waterloo by the nearby Wilfrid Laurier University from July 19 till 22.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"11 1","pages":"57-65"},"PeriodicalIF":0.0,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78194027","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}
{"title":"East coast copmuter algebra day 2017","authors":"Daniel Lichtblau","doi":"10.1145/3151131.3151134","DOIUrl":"https://doi.org/10.1145/3151131.3151134","url":null,"abstract":"The East Coast Computer Algebra Day 2017 (ECCAD 2017) was hosted byWolfram Research on Saturday, April 29, 2017.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"45 1","pages":"66-69"},"PeriodicalIF":0.0,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85512056","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}
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