Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation最新文献_第3页

GAP 4 at Twenty-one - Algorithms, System Design and Applications GAP 4在21 -算法，系统设计和应用

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209026

S. Linton

引用次数: 0

Thirty Years of Virtual Substitution: Foundations, Techniques, Applications 虚拟替代的三十年:基础、技术和应用

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209030

T. Sturm

引用次数: 15

Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases 任意正交多项式基稀疏多项式插值

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3208999

E. Imamoglu, E. Kaltofen, Zhengfeng Yang

{"title":"Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases","authors":"E. Imamoglu, E. Kaltofen, Zhengfeng Yang","doi":"10.1145/3208976.3208999","DOIUrl":"https://doi.org/10.1145/3208976.3208999","url":null,"abstract":"An algorithm for interpolating a polynomial f from evaluation points whose running time depends on the sparsity t of the polynomial when it is represented as a sum of t Chebyshev Polynomials of the First Kind with non-zero scalar coefficients is given by Lakshman Y. N. and Saunders [SIAM J. Comput., vol. 24, nr. 2 (1995)]; Kaltofen and Lee [JSC, vol. 36, nr. 3--4 (2003)] analyze a randomized early termination version which computes the sparsity t. Those algorithms mirror Prony's algorithm for the standard power basis to the Chebyshev Basis of the First Kind. An alternate algorithm by Arnold's and Kaltofen's [Proc. ISSAC 2015, Sec. 4] uses Prony's original algorithm for standard power terms. Here we give sparse interpolation algorithms for generalized Chebyshev polynomials, which include the Chebyshev Bases of the Second, Third and Fourth Kind. Our algorithms also reduce to Prony's algorithm. If given on input a bound B >= t for the sparsity, our new algorithms deterministically recover the sparse representation in the First, Second, Third and Fourth Kind Chebyshev representation from exactly t + B evaluations. Finally, we generalize our algorithms to bases whose Chebyshev recurrences have parametric scalars. We also show how to compute those parameter values which optimize the sparsity of the representation in the corresponding basis, similar to computing a sparsest shift.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122118068","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: 9

Polynomial Equivalence Problems for Sum of Affine Powers 仿射幂和的多项式等价问题

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3208993

Ignacio García-Marco, P. Koiran, Timothée Pecatte

引用次数: 9

A Newton-like Validation Method for Chebyshev Approximate Solutions of Linear Ordinary Differential Systems 线性常微分系统Chebyshev近似解的类牛顿验证方法

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209000

F. Bréhard

引用次数: 2

Modular Algorithms for Computing Minimal Associated Primes and Radicals of Polynomial Ideals 计算多项式理想最小关联素数和根的模算法

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209014

T. Aoyama, M. Noro

{"title":"Modular Algorithms for Computing Minimal Associated Primes and Radicals of Polynomial Ideals","authors":"T. Aoyama, M. Noro","doi":"10.1145/3208976.3209014","DOIUrl":"https://doi.org/10.1145/3208976.3209014","url":null,"abstract":"In this paper, we propose algorithms for computing minimal associated primes of ideals in polynomial rings over Q and computing radicals of ideals in polynomial rings over a field. They apply Chinese Remainder Theorem (CRT) to Laplagne's algorithm which computes minimal associated primes without producing redundant components and computes radicals. CRT reconstructs an object in a ring from its modular images in the quotient rings modulo some ideals. In Laplagne's algorithm, ideals are decomposed over rational function fields by regarding some variables as parameters. In our new algorithms, we compute the minimal associated primes and the radical of < φ(G) > for a given ideal I= < G >, where φ is a substitution map for a parameter. Then we construct candidates of the minimal associated primes and the radical of I by applying CRT for those of < φ(G) >'s. In order for this method to work correctly, the shape of each modular component must coincide with that of the corresponding component of the ideal for computations of minimal associated primes, and radicals of modular images of given ideals must coincide with modular images of radicals of given ideals for radical computations. The former is realized with a high probability because a multivariate irreducible polynomial over Q remains irreducible after a substitution of integers for variables with a high probability and the latter is realized except for a finite number of moduli.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129195606","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

What Can (and Can't) we Do with Sparse Polynomials? 用稀疏多项式我们能做什么(不能做什么)?

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209027

Daniel S. Roche

引用次数: 43

Algebraic Techniques in Geometry: The 10th Anniversary 几何中的代数技术:十周年纪念

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209028

M. Sharir

引用次数: 0

Extending the GVW Algorithm to Local Ring 将GVW算法扩展到本地环

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3208979

Dong Lu, Dingkang Wang, Fanghui Xiao, Jie Zhou

{"title":"Extending the GVW Algorithm to Local Ring","authors":"Dong Lu, Dingkang Wang, Fanghui Xiao, Jie Zhou","doi":"10.1145/3208976.3208979","DOIUrl":"https://doi.org/10.1145/3208976.3208979","url":null,"abstract":"A new algorithm, which combines the GVW algorithm with the Mora normal form algorithm, is presented to compute the standard bases of ideals in a local ring. Since term orders in local ring are not well-orderings, there may not be a minimal signature in an infinite set, and we can not extend the GVW algorithm from a polynomial ring to a local ring directly. Nevertheless, when given an anti-graded order in R and a term-over-position order in Rm that are compatible, we can construct a special set such that it has a minimal signature, where R , Rm are a local ring and a R -module, respectively. That is, for any given polynomial v0 ın R, the set consisting of signatures of pairs (u,v)ın Rm x R has a minimal element, where the leading power products of v and v0 are equal. In this case, we prove a cover theorem in R , and use three criteria (syzygy criterion, signature criterion and rewrite criterion) to discard useless J-pairs without any reductions. Mora normal form algorithm is also extended to do regular top-reductions in Rm x R, and the correctness and termination of the algorithm are proved. The proposed algorithm has been implemented in the computer algebra system Maple, and experiment results show that most of J-pairs can be discarded by three criteria in the examples.","PeriodicalId":105762,"journal":{"name":"Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114227150","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: 2

Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations 非线性微分方程离散系统的多项式系统

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation Pub Date : 2018-07-11 DOI: 10.1145/3208976.3209029

A. Sommese

引用次数: 0