Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation最新文献

Real quantifier elimination by cylindrical algebraic decomposition, and improvements by machine learning 圆柱代数分解的实量词消除，以及机器学习的改进

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3403981

M. England

引用次数: 0

Approximate GCD by bernstein basis, and its applications 用bernstein基近似GCD及其应用

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3403991

Kosaku Nagasaka

引用次数: 1

Computing the N-th term of a q-holonomic sequence 计算q-完整序列的第n项

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404060

A. Bostan

引用次数: 6

An extended GCD algorithm for parametric univariate polynomials and application to parametric smith normal form 参数一元多项式的扩展GCD算法及其在参数史密斯范式中的应用

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404019

Dingkang Wang, Hesong Wang, Fanghui Xiao

{"title":"An extended GCD algorithm for parametric univariate polynomials and application to parametric smith normal form","authors":"Dingkang Wang, Hesong Wang, Fanghui Xiao","doi":"10.1145/3373207.3404019","DOIUrl":"https://doi.org/10.1145/3373207.3404019","url":null,"abstract":"An extended greatest common divisor (GCD) algorithm for parametric univariate polynomials is presented in this paper. This algorithm computes not only the GCD of parametric univariate polynomials in each constructible set but also the corresponding representation coefficients (or multipliers) for the GCD expressed as a linear combination of these parametric univariate polynomials. The key idea of our algorithm is that for non-parametric case the GCD of arbitrary finite number of univariate polynomials can be obtained by computing the minimal Gröbner basis of the ideal generated by those polynomials. But instead of computing the Gröbner basis of the ideal generated by those polynomials directly, we construct a special module by adding the unit vectors which can record the representation coefficients, then obtain the GCD and representation coefficients by computing a Gröbner basis of the module. This method can be naturally generalized to the parametric case because of the comprehensive Gröbner systems for modules. As a consequence, we obtain an extended GCD algorithm for parametric univariate polynomials. More importantly, we apply the proposed extended GCD algorithm to the computation of Smith normal form, and give the first algorithm for reducing a univariate polynomial matrix with parameters to its Smith normal form.","PeriodicalId":186699,"journal":{"name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121411585","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: 1

What do sparse interpolation, padé approximation, gaussian quadrature and tensor decomposition have in common? 稀疏插值、帕德瓦近似、高斯正交和张量分解有什么共同之处?

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3403983

A. Cuyt

引用次数: 0

Syzygies of ideals of polynomial rings over principal ideal domains 主理想域上多项式环理想的合性

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404046

H. Charalambous, K. Karagiannis, Sotiris Karanikolopoulos, A. Kontogeorgis

引用次数: 0

Fast multipoint evaluation and interpolation of polynomials in the LCH-basis over FPr FPr上lch基多项式的快速多点求值与插值

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404009

Axel Mathieu-Mahias, Michaël Quisquater

{"title":"Fast multipoint evaluation and interpolation of polynomials in the LCH-basis over FPr","authors":"Axel Mathieu-Mahias, Michaël Quisquater","doi":"10.1145/3373207.3404009","DOIUrl":"https://doi.org/10.1145/3373207.3404009","url":null,"abstract":"Lin, Chung and Han introduced in 2014 the LCH-basis in order to derive FFT-based multipoint evaluation and interpolation algorithms with respect to this polynomial basis. Considering an affine space of n = 2j points, their algorithms require O(n · log2 n) operations in F2r. The LCH-basis has then been extended over finite fields of characteristic p by Lin et al. in 2016 and an n-point evaluation algorithm has been derived for n = pj with complexity O(n · logp n · p). However, the problem of interpolating polynomials represented in such a basis over FPr has not been addressed. In this paper, we fill this gap and also derive a faster algorithm for evaluating polynomials in the LCH-basis at multiple points over FPr. We follow a different approach where we represent the multipoint evaluation and interpolation maps by well-defined matrices. We present factorizations of such matrices into the product of sparse matrices which can be evaluated efficiently. These factorizations lead to fast algorithms for both the multipoint evaluation and the interpolation of polynomials represented in the LCH-basis at n = pj points with optimized complexity O(n · log2 n · log2 p · log2 log2 p). A particular attention is paid to provide in-place algorithms with high memory-locality. Our implementations written in C confirm that our approach improves the original transforms.","PeriodicalId":186699,"journal":{"name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129777187","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: 0

On a non-archimedean broyden method 非阿基米德布洛登法

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404045

X. Dahan, Tristan Vaccon

引用次数: 0

Robots, computer algebra and eight connected components 机器人，计算机代数和八个相连的组件

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404048

J. Capco, M. S. E. Din, J. Schicho

{"title":"Robots, computer algebra and eight connected components","authors":"J. Capco, M. S. E. Din, J. Schicho","doi":"10.1145/3373207.3404048","DOIUrl":"https://doi.org/10.1145/3373207.3404048","url":null,"abstract":"Answering connectivity queries in semi-algebraic sets is a longstanding and challenging computational issue with applications in robotics, in particular for the analysis of kinematic singularities. One task there is to compute the number of connected components of the complementary of the singularities of the kinematic map. Another task is to design a continuous path joining two given points lying in the same connected component of such a set. In this paper, we push forward the current capabilities of computer algebra to obtain computer-aided proofs of the analysis of the kinematic singularities of various robots used in industry. We first show how to combine mathematical reasoning with easy symbolic computations to study the kinematic singularities of an infinite family (depending on paramaters) modelled by the UR-series produced by the company \"Universal Robots\". Next, we compute roadmaps (which are curves used to answer connectivity queries) for this family of robots. We design an algorithm for \"solving\" positive dimensional polynomial system depending on parameters. The meaning of solving here means partitioning the parameter's space into semi-algebraic components over which the number of connected components of the semi-algebraic set defined by the input system is invariant. Practical experiments confirm our computer-aided proof and show that such an algorithm can already be used to analyze the kinematic singularities of the UR-series family. The number of connected components of the complementary of the kinematic singularities of generic robots in this family is 8.","PeriodicalId":186699,"journal":{"name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","volume":"232 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123108916","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: 8

A Gröbner-basis theory for divide-and-conquer recurrences 分治递归的Gröbner-basis理论

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI: 10.1145/3373207.3404055

F. Chyzak, P. Dumas

引用次数: 0