Pub Date : 2023-04-01DOI: 10.1007/978-3-031-41724-5_19
Weidong Wang, Jing Yang
{"title":"Two Variants of Bézout Subresultants for Several Univariate Polynomials","authors":"Weidong Wang, Jing Yang","doi":"10.1007/978-3-031-41724-5_19","DOIUrl":"https://doi.org/10.1007/978-3-031-41724-5_19","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122181213","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}
Pub Date : 2022-06-27DOI: 10.1007/978-3-031-14788-3_17
Tereso del R'io, M. England
{"title":"New heuristic to choose a cylindrical algebraic decomposition variable ordering motivated by complexity analysis","authors":"Tereso del R'io, M. England","doi":"10.1007/978-3-031-14788-3_17","DOIUrl":"https://doi.org/10.1007/978-3-031-14788-3_17","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":" 15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132124808","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}
Pub Date : 2022-05-15DOI: 10.48550/arXiv.2205.07380
J. Verschelde, Kylash Viswanathan
A polynomial homotopy is a family of polynomial systems, where the systems in the family depend on one parameter. If for one value of the parameter we know a regular solution, then what is the nearest value of the parameter for which the solution in the polynomial homotopy is singular? For this problem we apply the ratio theorem of Fabry. Richardson extrapolation is effective to accelerate the convergence of the ratios of the coefficients of the series expansions of the solution paths defined by the homotopy. For numerical stability, we recondition the homotopy. To compute the coefficients of the series we propose the quaternion Fourier transform. We locate the closest singularity computing at a regular solution, avoiding numerical difficulties near a singularity.
{"title":"Locating the Closest Singularity in a Polynomial Homotopy","authors":"J. Verschelde, Kylash Viswanathan","doi":"10.48550/arXiv.2205.07380","DOIUrl":"https://doi.org/10.48550/arXiv.2205.07380","url":null,"abstract":"A polynomial homotopy is a family of polynomial systems, where the systems in the family depend on one parameter. If for one value of the parameter we know a regular solution, then what is the nearest value of the parameter for which the solution in the polynomial homotopy is singular? For this problem we apply the ratio theorem of Fabry. Richardson extrapolation is effective to accelerate the convergence of the ratios of the coefficients of the series expansions of the solution paths defined by the homotopy. For numerical stability, we recondition the homotopy. To compute the coefficients of the series we propose the quaternion Fourier transform. We locate the closest singularity computing at a regular solution, avoiding numerical difficulties near a singularity.","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126304468","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}
Pub Date : 2022-05-06DOI: 10.48550/arXiv.2205.03185
Markus Lange-Hegermann, D. Robertz
Computer algebra can answer various questions about partial differential equations using symbolic algorithms. However, the inclusion of data into equations is rare in computer algebra. Therefore, recently, computer algebra models have been combined with Gaussian processes, a regression model in machine learning, to describe the behavior of certain differential equations under data. While it was possible to describe polynomial boundary conditions in this context, we extend these models to analytic boundary conditions. Additionally, we describe the necessary algorithms for Gr"obner and Janet bases of Weyl algebras with certain analytic coefficients. Using these algorithms, we provide examples of divergence-free flow in domains bounded by analytic functions and adapted to observations.
{"title":"On boundary conditions parametrized by analytic functions","authors":"Markus Lange-Hegermann, D. Robertz","doi":"10.48550/arXiv.2205.03185","DOIUrl":"https://doi.org/10.48550/arXiv.2205.03185","url":null,"abstract":"Computer algebra can answer various questions about partial differential equations using symbolic algorithms. However, the inclusion of data into equations is rare in computer algebra. Therefore, recently, computer algebra models have been combined with Gaussian processes, a regression model in machine learning, to describe the behavior of certain differential equations under data. While it was possible to describe polynomial boundary conditions in this context, we extend these models to analytic boundary conditions. Additionally, we describe the necessary algorithms for Gr\"obner and Janet bases of Weyl algebras with certain analytic coefficients. Using these algorithms, we provide examples of divergence-free flow in domains bounded by analytic functions and adapted to observations.","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124195298","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}
Pub Date : 2021-09-13DOI: 10.1007/978-3-030-85165-1_2
Evangelos Bartzos, I. Emiris, C. Tzamos
{"title":"The m-Bézout Bound and Distance Geometry","authors":"Evangelos Bartzos, I. Emiris, C. Tzamos","doi":"10.1007/978-3-030-85165-1_2","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_2","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121465452","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}
Pub Date : 2021-07-04DOI: 10.1007/978-3-030-85165-1_19
Hamid Rahkooy, T. Sturm
{"title":"Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner System","authors":"Hamid Rahkooy, T. Sturm","doi":"10.1007/978-3-030-85165-1_19","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_19","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130440506","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}
Pub Date : 2021-06-27DOI: 10.1007/978-3-030-85165-1_11
Hiromi Ishii
{"title":"Automatic Differentiation With Higher Infinitesimals, or Computational Smooth Infinitesimal Analysis in Weil Algebra","authors":"Hiromi Ishii","doi":"10.1007/978-3-030-85165-1_11","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_11","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"230 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131925107","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}
Pub Date : 2021-05-23DOI: 10.1007/978-3-030-85165-1_18
Hamid Rahkooy, T. Sturm
{"title":"Parametric Toricity of Steady State Varieties of Reaction Networks","authors":"Hamid Rahkooy, T. Sturm","doi":"10.1007/978-3-030-85165-1_18","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_18","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131276518","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}
Pub Date : 2021-05-22DOI: 10.1007/978-3-030-85165-1_6
Alexander Brandt, M. M. Maza
{"title":"On the Complexity and Parallel Implementation of Hensel's Lemma and Weierstrass Preparation","authors":"Alexander Brandt, M. M. Maza","doi":"10.1007/978-3-030-85165-1_6","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_6","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117281180","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}
Pub Date : 2021-02-22DOI: 10.1007/978-3-030-85165-1_9
Rémi Imbach, V. Pan
{"title":"Root Radii and Subdivision for Polynomial Root-Finding","authors":"Rémi Imbach, V. Pan","doi":"10.1007/978-3-030-85165-1_9","DOIUrl":"https://doi.org/10.1007/978-3-030-85165-1_9","url":null,"abstract":"","PeriodicalId":243130,"journal":{"name":"Computer Algebra in Scientific Computing","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124218731","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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