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Proceedings of the 2005 international symposium on Symbolic and algebraic computation最新文献

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Algebraic general solutions of algebraic ordinary differential equations 代数常微分方程的代数通解
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073891
J. M. Aroca, J. Cano, Ruyong Feng, X. Gao
{"title":"Algebraic general solutions of algebraic ordinary differential equations","authors":"J. M. Aroca, J. Cano, Ruyong Feng, X. Gao","doi":"10.1145/1073884.1073891","DOIUrl":"https://doi.org/10.1145/1073884.1073891","url":null,"abstract":"In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For a first order autonomous ODE, we give an optimal bound for the degree of its algebraic general solutions and a polynomial-time algorithm to compute an algebraic general solution if it exists. Here an algebraic ODE means that an ODE given by a differential polynomial.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115443909","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: 32
Algorithms for the non-monic case of the sparse modular GCD algorithm 算法为非一元情况下的稀疏模GCD算法
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073903
Jennifer de Kleine, M. Monagan, A. Wittkopf
{"title":"Algorithms for the non-monic case of the sparse modular GCD algorithm","authors":"Jennifer de Kleine, M. Monagan, A. Wittkopf","doi":"10.1145/1073884.1073903","DOIUrl":"https://doi.org/10.1145/1073884.1073903","url":null,"abstract":"Let G = (4y2+2z)x2 + (10y2+6z) be the greatest common divisor (Gcd) of two polynomials A, B ∈ ℤ[x,y,z]. Because G is not monic in the main variable x, the sparse modular Gcd algorithm of Richard Zippel cannot be applied directly as one is unable to scale univariate images of G in x consistently. We call this the normalization problem.We present two new sparse modular Gcd algorithms which solve this problem without requiring any factorizations. The first, a modification of Zippel's algorithm, treats the scaling factors as unknowns to be solved for. This leads to a structured coupled linear system for which an efficient solution is still possible. The second algorithm reconstructs the monic Gcd x2 + (5y2+3z)/(2y2+z) from monic univariate images using a sparse, variable at a time, rational function interpolation algorithm.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125559087","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: 40
A BLAS based C library for exact linear algebra on integer matrices 基于BLAS的整数矩阵精确线性代数C库
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073899
Zhuliang Chen, A. Storjohann
{"title":"A BLAS based C library for exact linear algebra on integer matrices","authors":"Zhuliang Chen, A. Storjohann","doi":"10.1145/1073884.1073899","DOIUrl":"https://doi.org/10.1145/1073884.1073899","url":null,"abstract":"Algorithms for solving linear systems of equations over the integers are designed and implemented. The implementations are based on the highly optimized and portable ATLAS/BLAS library for numerical linear algebra and the GNU Multiple Precision library (GMP) for large integer arithmetic.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122554471","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: 66
Schur partition for symmetric ternary forms and readable proof to inequalities 对称三元形式的Schur划分和不等式的可读证明
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073911
Fangjian Huang, Shengli Chen
{"title":"Schur partition for symmetric ternary forms and readable proof to inequalities","authors":"Fangjian Huang, Shengli Chen","doi":"10.1145/1073884.1073911","DOIUrl":"https://doi.org/10.1145/1073884.1073911","url":null,"abstract":"In this paper, we give a way to partition the ternary symmetric forms. Based on this method, we get a sufficient condition for ternary form to be positive semi-definite. At the end of the paper, we will show the application of the partition.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132203305","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
Structure and asymptotic expansion of multiple harmonic sums 多重调和和的结构与渐近展开
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073900
Christian Costermans, Jean-Yves Enjalbert, V. H. N. Minh, M. Petitot
{"title":"Structure and asymptotic expansion of multiple harmonic sums","authors":"Christian Costermans, Jean-Yves Enjalbert, V. H. N. Minh, M. Petitot","doi":"10.1145/1073884.1073900","DOIUrl":"https://doi.org/10.1145/1073884.1073900","url":null,"abstract":"We prove that the algebra of multiple harmonic sums is isomorphic to a shuffle algebra. So the multiple harmonic sums Hs, indexed by the compositions s=(s1,...,sr), are ℝ-linearly independent as real functions defined over ℕ. We deduce then the algorithm to obtain the asymptotic expansion of multiple harmonic sums.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124492327","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: 28
On the complexity of factoring bivariate supersparse (Lacunary) polynomials 二元超稀疏(lacary)多项式分解的复杂性
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073914
E. Kaltofen, P. Koiran
{"title":"On the complexity of factoring bivariate supersparse (Lacunary) polynomials","authors":"E. Kaltofen, P. Koiran","doi":"10.1145/1073884.1073914","DOIUrl":"https://doi.org/10.1145/1073884.1073914","url":null,"abstract":"We present algorithms that compute the linear and quadratic factors of supersparse (lacunary) bivariate polynomials over the rational numbers in polynomial-time in the input size. In supersparse polynomials, the term degrees can have hundreds of digits as binary numbers. Our algorithms are Monte Carlo randomized for quadratic factors and deterministic for linear factors. Our approach relies on the results by H. W. Lenstra, Jr., on computing factors of univariate supersparse polynomials over the rational numbers. Furthermore, we show that the problem of determining the irreducibility of a supersparse bivariate polynomial over a large finite field of any characteristic is co-NP-hard via randomized reductions.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127334920","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: 45
Application of Wu's method to symbolic model checking 吴氏方法在符号模型检验中的应用
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI: 10.1145/1073884.1073918
Weibo Mao, Jinzhao Wu
{"title":"Application of Wu's method to symbolic model checking","authors":"Weibo Mao, Jinzhao Wu","doi":"10.1145/1073884.1073918","DOIUrl":"https://doi.org/10.1145/1073884.1073918","url":null,"abstract":"Model checking is widely used in verifying properties of concurrent systems. As an improvement, symbolic model checking uses OBDDs to alleviate the state explosion problem. However, the size of OBDDs greatly increases with the system becoming larger and more complex. In symbolic computation Wu's method is efficient to solve algebraic equations, and has succeeded in geometry theorem proving. In this paper, we present a framework to apply Wu's method to symbolic model checking. Briefly, symbolic model checking is carried out by using Wu's method to calculate the characteristic sets of polynomials that represent Kripke structures as well as CTL formulas. This is a new approach to model checking, and is a new successful application of Wu's method.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"11 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116821230","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: 12
Approximation of dynamical systems using s-systems theory: application to biological systems 用s系统理论逼近动力系统:在生物系统中的应用
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-03-02 DOI: 10.1145/1073884.1073928
L. Tournier
{"title":"Approximation of dynamical systems using s-systems theory: application to biological systems","authors":"L. Tournier","doi":"10.1145/1073884.1073928","DOIUrl":"https://doi.org/10.1145/1073884.1073928","url":null,"abstract":"In this article we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm uses a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems). A numerical calculus is then performed to converge towards an equilibrium, giving at the same time a S-system approximating the initial system around this equilibrium. This algorithm has been applied to a real biological example in 14 dimensions which is a subsystem of a metabolic pathway in Arabidopsis Thaliana.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126691031","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: 13
Efficient computation of the characteristic polynomial 高效计算特征多项式
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-01-25 DOI: 10.1145/1073884.1073905
J. Dumas, Clément Pernet, Z. Wan
{"title":"Efficient computation of the characteristic polynomial","authors":"J. Dumas, Clément Pernet, Z. Wan","doi":"10.1145/1073884.1073905","DOIUrl":"https://doi.org/10.1145/1073884.1073905","url":null,"abstract":"We deal with the computation of the characteristic polynomial of dense matrices over word size finite fields and over the integers. We first present two algorithms for finite fields: one is based on Krylov iterates and Gaussian elimination. We compare it to an improvement of the second algorithm of Keller-Gehrig. Then we show that a generalization of Keller-Gehrig's third algorithm could improve both complexity and computational time. We use these results as a basis for the computation of the characteristic polynomial of integer matrices. We first use early termination and Chinese remaindering for dense matrices. Then a probabilistic approach, based on integer minimal polynomial and Hensel factorization, is particularly well suited to sparse and/or structured matrices.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"382 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126728202","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: 48
Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations 线性偏微分方程双曲型系统的广义拉普拉斯变换与积分
Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-01-15 DOI: 10.1145/1073884.1073929
S. P. Tsarev
{"title":"Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations","authors":"S. P. Tsarev","doi":"10.1145/1073884.1073929","DOIUrl":"https://doi.org/10.1145/1073884.1073929","url":null,"abstract":"We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure generalizes the classical theory of Laplace transformations of second-order equations in the plane.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121661812","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: 65
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