We introduce a new method for finding a non-realizability certificate of a simplicial sphere Σ. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Plücker relations that must be positive in any realization of Σ; but since this combination should also vanish identically, the realization cannot exist. Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples.
{"title":"Large final polynomials from integer programming","authors":"J. Pfeifle","doi":"10.1145/3511528.3511533","DOIUrl":"https://doi.org/10.1145/3511528.3511533","url":null,"abstract":"We introduce a new method for finding a non-realizability certificate of a simplicial sphere Σ. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos. The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Plücker relations that must be positive in any realization of Σ; but since this combination should also vanish identically, the realization cannot exist. Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"82 - 86"},"PeriodicalIF":0.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44654827","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 discuss how symbolic computations can be used to find functional equations for multiple polylogarithms and prove parts of Goncharov's depth conjecture. We present a custom-built C++ toolkit for polylogarithm symbol manipulations in Lie coalgebras and show how this approach compares favorably to the alternatives in terms of performance.
{"title":"Discovering multiple polylogarithm equations via symbolic computations","authors":"Andrei Matveiakin","doi":"10.1145/3511528.3511539","DOIUrl":"https://doi.org/10.1145/3511528.3511539","url":null,"abstract":"We discuss how symbolic computations can be used to find functional equations for multiple polylogarithms and prove parts of Goncharov's depth conjecture. We present a custom-built C++ toolkit for polylogarithm symbol manipulations in Lie coalgebras and show how this approach compares favorably to the alternatives in terms of performance.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"112 - 116"},"PeriodicalIF":0.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48543918","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}
Because of the pandemic, most of us have been teaching online. Some of us have taught courses in computer algebra and some of us recorded those lectures. Now is a good time to assemble a library of computer algebra lectures on various topics. This will be of benefit to us and to future students, faculty and practitioners. Over time the quality of the lectures should improve and the number of topics covered will grow. In this note I describe such a library based on my own computer algebra lectures from this last semester that I have made public. I invite others to contribute.
{"title":"A call to build a publicly accessible library of lecture recordings in computer algebra","authors":"M. Monagan","doi":"10.1145/3511528.3511529","DOIUrl":"https://doi.org/10.1145/3511528.3511529","url":null,"abstract":"Because of the pandemic, most of us have been teaching online. Some of us have taught courses in computer algebra and some of us recorded those lectures. Now is a good time to assemble a library of computer algebra lectures on various topics. This will be of benefit to us and to future students, faculty and practitioners. Over time the quality of the lectures should improve and the number of topics covered will grow. In this note I describe such a library based on my own computer algebra lectures from this last semester that I have made public. I invite others to contribute.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"65 - 67"},"PeriodicalIF":0.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46337513","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}
J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio
We introduce an algorithm for computing the ideals associated with some sumset semigroups. Our results allow us to study some additive properties of sumsets.
{"title":"Computing the ideals of sumset semigroups","authors":"J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio","doi":"10.1145/3511528.3511531","DOIUrl":"https://doi.org/10.1145/3511528.3511531","url":null,"abstract":"We introduce an algorithm for computing the ideals associated with some sumset semigroups. Our results allow us to study some additive properties of sumsets.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"73 - 76"},"PeriodicalIF":0.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44713401","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}
Involutive bases were introduced in [6] as a type of Gröbner bases with additional combinatorial properties. Pommaret bases are a particular kind of involutive bases with strong relations to commutative algebra and algebraic geometry[11, 12].
{"title":"Cellular reductions of the Pommaret-Seiler resolution for Quasi-stable ideals","authors":"Rodrigo Iglesias, E. Sáenz-de-Cabezón","doi":"10.1145/3511528.3511537","DOIUrl":"https://doi.org/10.1145/3511528.3511537","url":null,"abstract":"Involutive bases were introduced in [6] as a type of Gröbner bases with additional combinatorial properties. Pommaret bases are a particular kind of involutive bases with strong relations to commutative algebra and algebraic geometry[11, 12].","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"102 - 106"},"PeriodicalIF":0.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41444275","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}
R. Bradford, J. Davenport, M. England, AmirHosein Sadeghimanesh, A. Uncu
This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, through the integration of SAT/SMT technology, the extension of Lazard projection theory, and the development of new algorithms based on CAD technology but without producing CADs themselves. The project also seeks to develop applications of CAD and will focus on applications in the domains of economics and bio-network analysis.
{"title":"The DEWCAD project","authors":"R. Bradford, J. Davenport, M. England, AmirHosein Sadeghimanesh, A. Uncu","doi":"10.1145/3511528.3511538","DOIUrl":"https://doi.org/10.1145/3511528.3511538","url":null,"abstract":"This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, through the integration of SAT/SMT technology, the extension of Lazard projection theory, and the development of new algorithms based on CAD technology but without producing CADs themselves. The project also seeks to develop applications of CAD and will focus on applications in the domains of economics and bio-network analysis.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"107 - 111"},"PeriodicalIF":0.1,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48734535","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 present some current achievements in the software package GeoGebra Discovery that provides several symbolic tools and commands to mechanically discover (and verify symbolically) relationships on planar geometry constructions. Our presentation includes the novel Discover tool and command, the Relation tool and command, and the Compare command. Our proposal successfully makes the cycle 'conjecturing-checking-proving' in elementary geometry even more accessible for general users, focusing not only on educational uses but research as well.
{"title":"Automated reasoning tools in GeoGebra discovery","authors":"Z. Kovács, T. Recio, M. Vélez","doi":"10.1145/3493492.3493495","DOIUrl":"https://doi.org/10.1145/3493492.3493495","url":null,"abstract":"We present some current achievements in the software package GeoGebra Discovery that provides several symbolic tools and commands to mechanically discover (and verify symbolically) relationships on planar geometry constructions. Our presentation includes the novel Discover tool and command, the Relation tool and command, and the Compare command. Our proposal successfully makes the cycle 'conjecturing-checking-proving' in elementary geometry even more accessible for general users, focusing not only on educational uses but research as well.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"39 - 43"},"PeriodicalIF":0.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46859242","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}
Structural identifiability properties of models of ordinary differential equations help one assess if the parameter's value can be recovered from experimental data. This theoretical property can be queried without the need for data collection and is determined with help of differential algebraic tools. We present a web-based Structural Identifiability Toolbox that rigorously uncovers identifiability properties of individual parameters of ODE systems as well as their functions (also called identifiable combinations) using the apparatus of differential algebra. The application requires no installation and is readily available at https://maple.cloud/app/6509768948056064/
{"title":"Maple application for structural identifiability analysis of ODE models","authors":"Ilia Ilmer, A. Ovchinnikov, G. Pogudin","doi":"10.1145/3493492.3493497","DOIUrl":"https://doi.org/10.1145/3493492.3493497","url":null,"abstract":"Structural identifiability properties of models of ordinary differential equations help one assess if the parameter's value can be recovered from experimental data. This theoretical property can be queried without the need for data collection and is determined with help of differential algebraic tools. We present a web-based Structural Identifiability Toolbox that rigorously uncovers identifiability properties of individual parameters of ODE systems as well as their functions (also called identifiable combinations) using the apparatus of differential algebra. The application requires no installation and is readily available at https://maple.cloud/app/6509768948056064/","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"49 - 53"},"PeriodicalIF":0.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43852472","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}
S. Abramov, A. Ryabenko, L. Sevastianov, Yvette Zonn, Min Wu
The International Conference "Computer Algebra" was held online via Zoom on June 28-29, 2021 and the conference web-site is http://www.ccas.ru/ca/conference. Co-organized by the Dorodnicyn Computing Center of Federal Research Center "Computer Science and Control" of Russian Academy of Science and the Peoples' Friendship University of Russia, the conference was devoted to inspiring discussions on computer algebra and related topics. Researchers from different countries presented talks on their latest research work. This is the fourth edition of the conference, and the previous three were in 2016, 2017 and 2019, respectively.
{"title":"The fourth conference \"computer algebra\" in Moscow","authors":"S. Abramov, A. Ryabenko, L. Sevastianov, Yvette Zonn, Min Wu","doi":"10.1145/3493492.3493494","DOIUrl":"https://doi.org/10.1145/3493492.3493494","url":null,"abstract":"The International Conference \"Computer Algebra\" was held online via Zoom on June 28-29, 2021 and the conference web-site is http://www.ccas.ru/ca/conference. Co-organized by the Dorodnicyn Computing Center of Federal Research Center \"Computer Science and Control\" of Russian Academy of Science and the Peoples' Friendship University of Russia, the conference was devoted to inspiring discussions on computer algebra and related topics. Researchers from different countries presented talks on their latest research work. This is the fourth edition of the conference, and the previous three were in 2016, 2017 and 2019, respectively.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"30 - 38"},"PeriodicalIF":0.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43734384","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 present a SageMath implementation of the symbolic-numeric algorithm introduced by van der Hoeven in 2007 for factoring linear differential operators whose coefficients are rational functions.
{"title":"A sage package for the symbolic-numeric factorization of linear differential operators","authors":"Alexandre Goyer","doi":"10.1145/3493492.3493496","DOIUrl":"https://doi.org/10.1145/3493492.3493496","url":null,"abstract":"We present a SageMath implementation of the symbolic-numeric algorithm introduced by van der Hoeven in 2007 for factoring linear differential operators whose coefficients are rational functions.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"44 - 48"},"PeriodicalIF":0.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45845279","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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