Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation最新文献_第4页

Order-Degree-Height Surfaces for Linear Operators 线性算子的阶次高曲面

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-05-12 DOI: 10.1145/3476446.3536187

Hui Huang, Manuel Kauers, G. Mukherjee

引用次数: 0

Computing Critical Points for Algebraic Systems Defined by Hyperoctahedral Invariant Polynomials 由高八面体不变多项式定义的代数系统的临界点计算

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-30 DOI: 10.1145/3476446.3536181

Thi Xuan Vu

引用次数: 3

Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry 用计算机代数和实代数几何算法确定机械臂的个性

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-09 DOI: 10.1145/3476446.3535477

D. Chablat, R'emi Pr'ebet, M. S. E. Din, Durgesh Haribhau Salunkhe, P. Wenger

{"title":"Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry","authors":"D. Chablat, R'emi Pr'ebet, M. S. E. Din, Durgesh Haribhau Salunkhe, P. Wenger","doi":"10.1145/3476446.3535477","DOIUrl":"https://doi.org/10.1145/3476446.3535477","url":null,"abstract":"Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data. In this paper we design an algorithm that, on input a polynomial map in n indeterminates, and s polynomials in the same indeterminates describing a real algebraic set of dimension d, decides the cuspidality of the restriction of the map to the real algebraic set under consideration. Moreover, if D and τ are, respectively the maximum degree and the bound on the bit size of the coefficients of the input polynomials, this algorithm runs in time log-linear in τ and polynomial in ((s+d)D)O(n2). It relies on many high-level algorithms in computer algebra which use advanced methods on real algebraic sets and critical loci of polynomial maps. As far as we know, this is the first algorithm that tackles the cuspidality problem from a general point of view.","PeriodicalId":130499,"journal":{"name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","volume":"178 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121899719","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}

引用次数: 4

Finding Nontrivial Zeros of Quadratic Forms over Rational Function Fields of Characteristic 2 特征为2的有理函数域上求二次型的非平凡零

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-08 DOI: 10.1145/3476446.3535485

P. Kutas, Mickaël Montessinos, Gergely Zábrádi, T'imea Csah'ok

引用次数: 2

On Realizing Differential-Algebraic Equations by Rational Dynamical Systems 用有理动力系统实现微分代数方程

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-07 DOI: 10.1145/3476446.3535492

D. Pavlov, G. Pogudin

{"title":"On Realizing Differential-Algebraic Equations by Rational Dynamical Systems","authors":"D. Pavlov, G. Pogudin","doi":"10.1145/3476446.3535492","DOIUrl":"https://doi.org/10.1145/3476446.3535492","url":null,"abstract":"Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs of the system can typically be related by more complicated differential-algebraic equations (DAEs). Therefore, a natural question (referred to as the realizability problem) is: given a differential-algebraic equation (say, fitted from data), does it come from a partially observed dynamical system? A special case in which the functions involved in the dynamical system are rational is of particular interest. For a single differential-algebraic equation in a single output variable, Forsman has shown that it is realizable by a rational dynamical system if and only if the corresponding hypersurface is unirational, and he turned this into an algorithm in the first-order case. In this paper, we study a more general case of single-input-single-output equations. We show that if a realization by a rational dynamical system exists, the system can be taken to have the dimension equal to the order of the DAE. We provide a complete algorithm for first-order DAEs. We also show that the same approach can be used for higher-order DAEs using several examples from the literature.","PeriodicalId":130499,"journal":{"name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117002972","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}

引用次数: 3

On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves 随机抽样误差:参数曲线上均匀分布的随机点

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-03-05 DOI: 10.1145/3476446.3536190

Apostolos Chalkis, Christina Katsamaki, Josué Tonelli-Cueto

引用次数: 1

Random Primes without Primality Testing 没有素数检验的随机素数

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-02-24 DOI: 10.1145/3476446.3536191

Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray, Daniel S. Roche

引用次数: 0

Extending Flat Motion Planning to Non-flat Systems. Experiments on Aircraft Models Using Maple 将平面运动规划扩展到非平面系统。用Maple制作飞机模型的实验

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-02-20 DOI: 10.1145/3476446.3536179

F. Ollivier

引用次数: 3

Mahler Discrete Residues and Summability for Rational Functions 有理函数的Mahler离散残数与可和性

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-02-20 DOI: 10.1145/3476446.3536186

Carlos E. Arreche, Yi Zhang

引用次数: 1

Faster Change of Order Algorithm for Gröbner Bases under Shape and Stability Assumptions 形状和稳定性假设下Gröbner基的快速换阶算法

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-02-18 DOI: 10.1145/3476446.3535484

Jérémy Berthomieu, Vincent Neiger, M. S. E. Din

{"title":"Faster Change of Order Algorithm for Gröbner Bases under Shape and Stability Assumptions","authors":"Jérémy Berthomieu, Vincent Neiger, M. S. E. Din","doi":"10.1145/3476446.3535484","DOIUrl":"https://doi.org/10.1145/3476446.3535484","url":null,"abstract":"Solving zero-dimensional polynomial systems using Gröbner bases is usually done by, first, computing a Gröbner basis for the degree reverse lexicographic order, and next computing the lexicographic Gröbner basis with a change of order algorithm. Currently, the change of order now takes a significant part of the whole solving time for many generic instances. Like the fastest known change of order algorithms, this work focuses on the situation where the ideal defined by the system satisfies natural properties which can be recovered in generic coordinates. First, the ideal has a shape lexicographic Gröbner basis. Second, the set of leading terms with respect to the degree reverse lexicographic order has a stability property; in particular, the multiplication matrix can be read on the input Gröbner basis. The current fastest algorithms rely on the sparsity of this matrix. Actually, this sparsity is a consequence of an algebraic structure, which can be exploited to represent the matrix concisely as a univariate polynomial matrix. We show that the Hermite normal form of that matrix yields the sought lexicographic Gröbner basis, under assumptions which cover the shape position case. Under some mild assumption implying n≤t, the arithmetic complexity of our algorithm is O~(tω-1D), where n is the number of variables, t is a sparsity indicator of the aforementioned matrix, D is the degree of the zero-dimensional ideal under consideration, and ω is the exponent of matrix multiplication. This improves upon both state-of-the-art complexity bounds O~(tD2) and O~(Dω, since ω<3 and t≤D. Practical experiments, based on the libraries msolve and PML, confirm the high practical benefit.","PeriodicalId":130499,"journal":{"name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132959416","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}

引用次数: 6