We present some preliminary results on the integration of integro-differential equations using Deep Learning techniques.
我们提出了一些使用深度学习技术的积分微分方程的初步结果。
{"title":"Integral equation modelling and deep learning","authors":"F. Lemaire, Loic Roussel","doi":"10.1145/3572867.3572874","DOIUrl":"https://doi.org/10.1145/3572867.3572874","url":null,"abstract":"We present some preliminary results on the integration of integro-differential equations using Deep Learning techniques.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"51 - 55"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44827205","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}
Jorge García Fontán, A. Colotti, S. Briot, A. Goldsztejn, M. S. E. Din
Visual servoing refers to different methods used for robot motion control based on data from computer vision, in general the projection of a number of characteristics from the scene on a camera mounted on the robot. When the control is carried out in the space of parameters extracted from the image, we refer to Image-Based Visual Servoing (IBVS).
{"title":"Computer algebra methods for polynomial system solving at the service of image-based visual servoing","authors":"Jorge García Fontán, A. Colotti, S. Briot, A. Goldsztejn, M. S. E. Din","doi":"10.1145/3572867.3572871","DOIUrl":"https://doi.org/10.1145/3572867.3572871","url":null,"abstract":"Visual servoing refers to different methods used for robot motion control based on data from computer vision, in general the projection of a number of characteristics from the scene on a camera mounted on the robot. When the control is carried out in the space of parameters extracted from the image, we refer to Image-Based Visual Servoing (IBVS).","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"36 - 40"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49064278","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}
Undoubtedly the following fact is surprising when being first encountered with: It is possible to cut a hole in the unit cube such that another unit cube can pass through it.
{"title":"Extended abstract for","authors":"Jakob Steininger, S. Yurkevich","doi":"10.1145/3572867.3572870","DOIUrl":"https://doi.org/10.1145/3572867.3572870","url":null,"abstract":"Undoubtedly the following fact is surprising when being first encountered with: It is possible to cut a hole in the unit cube such that another unit cube can pass through it.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"32 - 35"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48744749","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}
Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is "simple" enough. Simplicity is related to the compactness of the formula due to the presence of algebraic numbers: "the smaller, the simpler". This poster showcases the capacity of recent updates on the Formal Power Series (FPS) algorithm, implemented in Maxima and Maple (convert/FormalPowerSeries), to find simple formulas for sequences like those from https://oeis.org/A307717, https://oeis.org/A226782, or https://oeis.org/A226784 by computing power series representations of their correctly guessed generating functions. We designed the algorithm for the more general context of univariate P-recursive sequences. Our implementations are available at http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm
{"title":"FPS in action","authors":"Bertrand Teguia Tabuguia, W. Koepf","doi":"10.1145/3572867.3572873","DOIUrl":"https://doi.org/10.1145/3572867.3572873","url":null,"abstract":"Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is \"simple\" enough. Simplicity is related to the compactness of the formula due to the presence of algebraic numbers: \"the smaller, the simpler\". This poster showcases the capacity of recent updates on the Formal Power Series (FPS) algorithm, implemented in Maxima and Maple (convert/FormalPowerSeries), to find simple formulas for sequences like those from https://oeis.org/A307717, https://oeis.org/A226782, or https://oeis.org/A226784 by computing power series representations of their correctly guessed generating functions. We designed the algorithm for the more general context of univariate P-recursive sequences. Our implementations are available at http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"46 - 50"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41496443","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}
Let K be a field and x1 < ··· < xn be ordered variables. Consider a set of polynomials F ⊂ K[x1,...,xn]. If the zero set V(F) of F is of positive dimension, then any triangular decomposition
设K是一个域，x1<··
{"title":"Algorithms for multivariate laurent series","authors":"J. P. Trochez, M. M. Maza, M. Calder, E. Postma","doi":"10.1145/3572867.3572877","DOIUrl":"https://doi.org/10.1145/3572867.3572877","url":null,"abstract":"Let K be a field and x1 < ··· < xn be ordered variables. Consider a set of polynomials F ⊂ K[x1,...,xn]. If the zero set V(F) of F is of positive dimension, then any triangular decomposition","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"64 - 67"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41799949","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}
Dynamical systems are commonly used to represent real-world processes. Model reduction techniques are among the core tools for studying dynamical systems models, they allow to reduce the study of a model to a simpler one. In this poster, we present an algorithm for computing exact nonlinear reductions, that is, a set of new rational function macro-variables which satisfy a self-consistent ODE system with the dynamics defined by algebraic functions. We report reductions found by the algorithm in models from the literature.
{"title":"Computing exact nonlinear reductions of dynamical models","authors":"Antonio Jiménez-Pastor, G. Pogudin","doi":"10.1145/3572867.3572869","DOIUrl":"https://doi.org/10.1145/3572867.3572869","url":null,"abstract":"Dynamical systems are commonly used to represent real-world processes. Model reduction techniques are among the core tools for studying dynamical systems models, they allow to reduce the study of a model to a simpler one. In this poster, we present an algorithm for computing exact nonlinear reductions, that is, a set of new rational function macro-variables which satisfy a self-consistent ODE system with the dynamics defined by algebraic functions. We report reductions found by the algorithm in models from the literature.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"25 - 31"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41943963","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}
Given a system of polynomial equations with parameters, we present a new interpolation algorithm for computing its Dixon resultant R. Our algorithm interpolates the monic square-free factors of R one at a time from monic univariate polynomial images of R using sparse rational function interpolation. We have implemented our new Dixon resultant algorithm in Maple with some subroutines coded in C for efficiency. Experimental results show that our algorithm significantly outperforms Zippel's sparse interpolation algorithm.
{"title":"A new interpolation algorithm for computing dixon resultants","authors":"Ayoola Jinadu, M. Monagan","doi":"10.1145/3572867.3572883","DOIUrl":"https://doi.org/10.1145/3572867.3572883","url":null,"abstract":"Given a system of polynomial equations with parameters, we present a new interpolation algorithm for computing its Dixon resultant R. Our algorithm interpolates the monic square-free factors of R one at a time from monic univariate polynomial images of R using sparse rational function interpolation. We have implemented our new Dixon resultant algorithm in Maple with some subroutines coded in C for efficiency. Experimental results show that our algorithm significantly outperforms Zippel's sparse interpolation algorithm.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"88 - 91"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41726830","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}
Ignacio García-Marco, Irene Márquez-Corbella, E. Martínez-Moro, Yuriko Pitones
In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support that provides us some information about the GHWs. We prove that the first and second generalized Hamming weight of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated to a binomial ideal related with the code. Moreover, the remaining weights are bounded by the Betti numbers for that set.
{"title":"Computing generalized hamming weights of binary linear codes via free resolutions","authors":"Ignacio García-Marco, Irene Márquez-Corbella, E. Martínez-Moro, Yuriko Pitones","doi":"10.1145/3572867.3572868","DOIUrl":"https://doi.org/10.1145/3572867.3572868","url":null,"abstract":"In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support that provides us some information about the GHWs. We prove that the first and second generalized Hamming weight of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated to a binomial ideal related with the code. Moreover, the remaining weights are bounded by the Betti numbers for that set.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"19 - 24"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44243774","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}
E. Hubert, Tobias Metzlaff, Philippe Moustrou, C. Riener
We present the results of our recent article [4] and discuss its applications [5]. A finite group with an integer representation has a multiplicative action on the ring of Laurent polynomials, which is induced by a nonlinear action on the compact torus. We study the structure of the orbit space as the image of the fundamental invariants. For the Weyl groups associated to crystallographic root systems of types A, B, C, D, this image is a compact basic semi-algebraic set. We give the defining polynomial inequalities explicitly as the positivity-locus of a Hermite matrix polynomial. As an application, we consider the problem of computing the optimal value of an exponential function and solve it with algebraic methods under symmetry assumptions.
{"title":"T-orbit spaces of multiplicative actions and applications","authors":"E. Hubert, Tobias Metzlaff, Philippe Moustrou, C. Riener","doi":"10.1145/3572867.3572879","DOIUrl":"https://doi.org/10.1145/3572867.3572879","url":null,"abstract":"We present the results of our recent article [4] and discuss its applications [5]. A finite group with an integer representation has a multiplicative action on the ring of Laurent polynomials, which is induced by a nonlinear action on the compact torus. We study the structure of the orbit space as the image of the fundamental invariants. For the Weyl groups associated to crystallographic root systems of types A, B, C, D, this image is a compact basic semi-algebraic set. We give the defining polynomial inequalities explicitly as the positivity-locus of a Hermite matrix polynomial. As an application, we consider the problem of computing the optimal value of an exponential function and solve it with algebraic methods under symmetry assumptions.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"72 - 75"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47597591","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 version of Smale's α-theory for ultrametric fields, such as the p-adics and their extensions, which gives us a multivariate version of Hensel's lemma.
{"title":"Ultrametric smale's α-theory","authors":"Jazz G. Suchen, Josué Tonelli-Cueto","doi":"10.1145/3572867.3572875","DOIUrl":"https://doi.org/10.1145/3572867.3572875","url":null,"abstract":"We present a version of Smale's α-theory for ultrametric fields, such as the p-adics and their extensions, which gives us a multivariate version of Hensel's lemma.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"56 1","pages":"56 - 59"},"PeriodicalIF":0.1,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46412898","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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