Jérémy Berthomieu, S. Graillat, Dimitri Lesnoff, Théo Mary
The bottleneck of the SPARSE-FGLM algorithm for Gröbner bases change of order is an iterative matrix - tall and skinny matrix product over a finite prime field. Our contribution is twofold. First, we port existing CPU-only algorithms for matrix products over prime fields to GPU architectures, and carry out a performance analysis of our implementation that shows that we can nearly achieve the maximum theoretical throughput of the hardware. Second, existing CPU-only algorithms could not handle primes with more than 26 bits, other than the GMP-based implementation in FLINT; we overcome this limitation by proposing an efficient multiword matrix product algorithm that can deal with primes with at most 35 bits; we benchmarked it on GPU.
{"title":"Modular Matrix Multiplication on GPU for Polynomial System Solving","authors":"Jérémy Berthomieu, S. Graillat, Dimitri Lesnoff, Théo Mary","doi":"10.1145/3614408.3614411","DOIUrl":"https://doi.org/10.1145/3614408.3614411","url":null,"abstract":"The bottleneck of the SPARSE-FGLM algorithm for Gröbner bases change of order is an iterative matrix - tall and skinny matrix product over a finite prime field. Our contribution is twofold. First, we port existing CPU-only algorithms for matrix products over prime fields to GPU architectures, and carry out a performance analysis of our implementation that shows that we can nearly achieve the maximum theoretical throughput of the hardware. Second, existing CPU-only algorithms could not handle primes with more than 26 bits, other than the GMP-based implementation in FLINT; we overcome this limitation by proposing an efficient multiword matrix product algorithm that can deal with primes with at most 35 bits; we benchmarked it on GPU.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"35 - 38"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47952748","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 improvements, implemented in the software package GeoGebra Discovery, that combine symbolic computation and graphics algorithms to faithfully visualize (semi-)algebraic expressions. Our implementation allows fluid animation of set of (semi-)algebraic sets of dimension 1 in a desktop application or a web browser. We use the Tarski library to create a cylindrical algebraic decomposition of the input, and its plot2d command, which is processed further in GeoGebra Discovery, to provide the user with a familiar look and feel.
{"title":"Faithful Real-Time Animation of Parametrized (Semi-) Algebraic Expressions via Cylindrical Algebraic Decomposition","authors":"Christopher W. Brown, Z. Kovács, T. Recio","doi":"10.1145/3614408.3614413","DOIUrl":"https://doi.org/10.1145/3614408.3614413","url":null,"abstract":"We present some current improvements, implemented in the software package GeoGebra Discovery, that combine symbolic computation and graphics algorithms to faithfully visualize (semi-)algebraic expressions. Our implementation allows fluid animation of set of (semi-)algebraic sets of dimension 1 in a desktop application or a web browser. We use the Tarski library to create a cylindrical algebraic decomposition of the input, and its plot2d command, which is processed further in GeoGebra Discovery, to provide the user with a familiar look and feel.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"43 - 46"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43273615","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. Batkhin, A. Ryabenko, L. Sevastianov, Yvette Zonn, Min Wu
The fifth International Conference "Computer algebra" http://www.ccas.ru/ca/conference is organized in Moscow from 26 to 28 June 2023 jointly by the Dorodnicyn Computing Centre (Federal Research Center "Computer Science and Control") of Russian Academy of Science, the Russian University of Peoples' Friendship named after Patrice Lumumba and Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.
{"title":"The Fifth Conference \"Computer Algebra\" in Moscow","authors":"S. Abramov, A. Batkhin, A. Ryabenko, L. Sevastianov, Yvette Zonn, Min Wu","doi":"10.1145/3614408.3614418","DOIUrl":"https://doi.org/10.1145/3614408.3614418","url":null,"abstract":"The fifth International Conference \"Computer algebra\" http://www.ccas.ru/ca/conference is organized in Moscow from 26 to 28 June 2023 jointly by the Dorodnicyn Computing Centre (Federal Research Center \"Computer Science and Control\") of Russian Academy of Science, the Russian University of Peoples' Friendship named after Patrice Lumumba and Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"72 - 84"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44352206","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}
N. Zidarič, G. Gong, M. Aagaard, Aleksandar Jurisic, Olexandr Konovalov
In this work we present the new GAP package FFCSA - Finite Field Constructions, Search, and Algorithms. It was designed to enable Design Space Exploration for hardware implementations of cryptographic algorithms defined over finite fields. FFCSA constructions and searches are used to produce the design space, and FFCSA algorithms, parameterized for the current candidate field, are used to generate expressions needed for implementation in hardware.
{"title":"FFCSA - Finite Field Constructions, Search, and Algorithms","authors":"N. Zidarič, G. Gong, M. Aagaard, Aleksandar Jurisic, Olexandr Konovalov","doi":"10.1145/3614408.3614416","DOIUrl":"https://doi.org/10.1145/3614408.3614416","url":null,"abstract":"In this work we present the new GAP package FFCSA - Finite Field Constructions, Search, and Algorithms. It was designed to enable Design Space Exploration for hardware implementations of cryptographic algorithms defined over finite fields. FFCSA constructions and searches are used to produce the design space, and FFCSA algorithms, parameterized for the current candidate field, are used to generate expressions needed for implementation in hardware.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"57 - 64"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41702185","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 ISZ method (Interval-Symbol method with Zero rewriting) based on stabilization theory was proposed to reduce the amount of exact computations as much as possible but obtain the exact results by aid of floating-point computations. In this paper, we applied the ISZ method to Trager's algorithm which factors univariate polynomials over algebraic number fields. By Maple experiments, we show the efficiency of the ISZ method over the purely exact approach which uses exact computations throughout the execution of the algorithm. Furthermore, we propose a new method called the ISZ* method, which is similar to the ISZ method but beforehand excludes insufficient precisions of floating-point approximation by checking the correctness of the obtained supports. We confirmed that the ISZ* method is more effective than the ISZ method when the initially set precision is not sufficiently high.
{"title":"Using the Interval-Symbol Method with Zero Rewriting to Factor Polynomials over Algebraic Number Fields","authors":"Kazuki Okuda, Kiyoshi Shirayanagi","doi":"10.1145/3614408.3614409","DOIUrl":"https://doi.org/10.1145/3614408.3614409","url":null,"abstract":"The ISZ method (Interval-Symbol method with Zero rewriting) based on stabilization theory was proposed to reduce the amount of exact computations as much as possible but obtain the exact results by aid of floating-point computations. In this paper, we applied the ISZ method to Trager's algorithm which factors univariate polynomials over algebraic number fields. By Maple experiments, we show the efficiency of the ISZ method over the purely exact approach which uses exact computations throughout the execution of the algorithm. Furthermore, we propose a new method called the ISZ* method, which is similar to the ISZ method but beforehand excludes insufficient precisions of floating-point approximation by checking the correctness of the obtained supports. We confirmed that the ISZ* method is more effective than the ISZ method when the initially set precision is not sufficiently high.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"3 4","pages":"21 - 30"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41270628","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}
Yang-Hui He, Vishnu Jejjala, B. Nelson, H. Schenck, M. Stillman
The Standard Model of particle physics has been amazingly successful at explaining interactions between three of the four fundamental forces of physics: the strong force, the weak force, and electro-magnetism. But it is an incomplete theory, failing to incorporate gravity. The Minimal Supersymmetric Standard Model (MSSM) is an approach to including gravity and supersymmetry in the standard model, by adding new particle states and interactions to the standard model. For example, supersymmetry pairs fermions (such as electrons) with bosons (such as photons). A starting point in the study of the MSSM is the Vacuum Moduli Space, which is a highly complicated algebraic variety introduced by Witten: it is the image of an affine variety X ⊆ C49 under a symplectic quotient map to C973. We describe the Macaulay2 software package MSSM, which facilitates computational investigation of the Vacuum Moduli Space.
{"title":"MSSM: A Macaulay2 Package for the Vacuum Moduli Space","authors":"Yang-Hui He, Vishnu Jejjala, B. Nelson, H. Schenck, M. Stillman","doi":"10.1145/3614408.3614412","DOIUrl":"https://doi.org/10.1145/3614408.3614412","url":null,"abstract":"The Standard Model of particle physics has been amazingly successful at explaining interactions between three of the four fundamental forces of physics: the strong force, the weak force, and electro-magnetism. But it is an incomplete theory, failing to incorporate gravity. The Minimal Supersymmetric Standard Model (MSSM) is an approach to including gravity and supersymmetry in the standard model, by adding new particle states and interactions to the standard model. For example, supersymmetry pairs fermions (such as electrons) with bosons (such as photons). A starting point in the study of the MSSM is the Vacuum Moduli Space, which is a highly complicated algebraic variety introduced by Witten: it is the image of an affine variety X ⊆ C49 under a symplectic quotient map to C973. We describe the Macaulay2 software package MSSM, which facilitates computational investigation of the Vacuum Moduli Space.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"39 - 42"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44439953","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}
Nested binomial sums form a particular class of sums that arise in the context of particle physics computations at higher orders in perturbation theory within QCD and QED, but that are also mathematically relevant, e.g., in combinatorics. We present the package RICA (Rule Induced Convolutions for Asymptotics), which aims at calculating Mellin representations and asymptotic expansions at infinity of those objects. These representations are of particular interest to perform analytic continuations of such sums.
{"title":"Computing Mellin Representations and Asymptotics of Nested Binomial Sums in a Symbolic Way: The RICA Package","authors":"J. Blümlein, Nikolai Fadeev, Carsten Schneider","doi":"10.1145/3614408.3614410","DOIUrl":"https://doi.org/10.1145/3614408.3614410","url":null,"abstract":"Nested binomial sums form a particular class of sums that arise in the context of particle physics computations at higher orders in perturbation theory within QCD and QED, but that are also mathematically relevant, e.g., in combinatorics. We present the package RICA (Rule Induced Convolutions for Asymptotics), which aims at calculating Mellin representations and asymptotic expansions at infinity of those objects. These representations are of particular interest to perform analytic continuations of such sums.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"31 - 34"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49445894","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}
Miguel Ángel Marco Buzunáriz, A. Romero, Jose Divasón
We present an algorithm for constructing the effective homology for the universal cover of simplicial sets with effective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.
{"title":"Effective Homology of Universal Covers","authors":"Miguel Ángel Marco Buzunáriz, A. Romero, Jose Divasón","doi":"10.1145/3614408.3614414","DOIUrl":"https://doi.org/10.1145/3614408.3614414","url":null,"abstract":"We present an algorithm for constructing the effective homology for the universal cover of simplicial sets with effective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"47 - 50"},"PeriodicalIF":0.1,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42803592","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":"Drinfeld Modules in SageMath","authors":"D. Ayotte, X. Caruso, Antoine Leudiere, Joseph Musleh","doi":"10.1145/3614408.3614417","DOIUrl":"https://doi.org/10.1145/3614408.3614417","url":null,"abstract":"We present the first implementation of Drinfeld modules fully integrated in the SageMath ecosystem. First features were released with SageMath 10.0.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"65 - 71"},"PeriodicalIF":0.1,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46231111","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 function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients. Each command is a feature of our Maple package NLDE available at https://mathrepo.mis.mpg.de/DAlgebraicFunctions/NLDEpackage.
{"title":"Operations for D-Algebraic Functions","authors":"Bertrand Teguia Tabuguia","doi":"10.1145/3614408.3614415","DOIUrl":"https://doi.org/10.1145/3614408.3614415","url":null,"abstract":"A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients. Each command is a feature of our Maple package NLDE available at https://mathrepo.mis.mpg.de/DAlgebraicFunctions/NLDEpackage.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"51 - 56"},"PeriodicalIF":0.1,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64084223","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：