International Symposium on Symbolic and Algebraic Computation最新文献_第3页

Efficient detection of redundancies in systems of linear inequalities✱ 高效检测线性不等式系统中的冗余✱

International Symposium on Symbolic and Algebraic Computation Pub Date : 2024-07-16 DOI: 10.1145/3666000.3669708

Rui-Juan Jing, M. M. Maza, Yan-Feng Xie, Chun-Ming Yuan

引用次数: 0

Decoding Simultaneous Rational Evaluation Codes 解码同步有理评估代码

International Symposium on Symbolic and Algebraic Computation Pub Date : 2024-07-16 DOI: 10.1145/3666000.3669686

Matteo Abbondati, Eleonora Guerrini, R. Lebreton

{"title":"Decoding Simultaneous Rational Evaluation Codes","authors":"Matteo Abbondati, Eleonora Guerrini, R. Lebreton","doi":"10.1145/3666000.3669686","DOIUrl":"https://doi.org/10.1145/3666000.3669686","url":null,"abstract":"In this paper, we deal with the problem of simultaneous reconstruction of a vector of rational numbers, given modular reductions containing errors (SRNRwE). Our methods apply as well to the simultaneous reconstruction of rational functions given evaluations containing errors (SRFRwE), improving known results [7, 9]. In the latter case, one can take advantage of techniques from coding theory [4, 10] and provide an algorithm that extends classical Reed-Solomon decoding. In recent works [7, 9], interleaved Reed-Solomon codes [3, 19] are used to correct beyond the unique decoding capability in the case of random errors at the price of positive but small failure probability. Our first contribution is to extend these works to the simultaneous reconstruction with errors of rational numbers instead of functions. Thus considering rational number codes [16], we provide an algorithm decoding beyond the unique decoding capability and, as a central result of this paper, we analyze in detail its failure probability. Our analysis generalizes for the first time the best known analysis for interleaved Reed-Solomon codes [19] to SRFRwE, improving on the existing bound [8], to interleaved Chinese remainder codes, also improving the known bound [1], and finally for the first time to SRNRwE.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"1 5","pages":"153-161"},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141641776","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

Enumerating polynomial colored permutation classes 枚举多项式彩色排列类

International Symposium on Symbolic and Algebraic Computation Pub Date : 2024-07-16 DOI: 10.1145/3666000.3669700

Saúl A. Blanco, Daniel E. Skora

引用次数: 0

Automated Reasoning For The Existence Of Darboux Polynomials 达布多项式存在性的自动推理

International Symposium on Symbolic and Algebraic Computation Pub Date : 2024-07-16 DOI: 10.1145/3666000.3669705

Khalil Ghorbal, Maxime Bridoux

引用次数: 0

Closed Form Solutions for Linear Differential and Difference Equations 线性微分与差分方程的闭形式解

International Symposium on Symbolic and Algebraic Computation Pub Date : 2017-07-23 DOI: 10.1145/3087604.3087660

M. V. Hoeij

{"title":"Closed Form Solutions for Linear Differential and Difference Equations","authors":"M. V. Hoeij","doi":"10.1145/3087604.3087660","DOIUrl":"https://doi.org/10.1145/3087604.3087660","url":null,"abstract":"Finding closed form solutions of differential equations has a long history in computer algebra. For example, the Risch algorithm (1969) decides if the equation y' = f can be solved in terms of elementary functions. These are functions that can be written in terms of exp and log, where \"in terms of\" allows for field operations, composition, and algebraic extensions. More generally, functions are in closed form if they are written in terms of commonly used functions. This includes not only exp and log, but other common functions as well, such as Bessel functions or the Gauss hypergeometric function. Given a differential equation L, to find solutions written in terms of such functions, one seeks a sequence of transformations that sends the Bessel equation, or the Gauss hypergeometric equation, to L. Although random equations are unlikely to have closed form solutions, they are remarkably common in applications. For example, if y = ∑n=0∞ an xn has a positive radius of convergence, integer coefficients an, and satisfies a second order homogeneous linear differential equation L with polynomial coefficients, then L is conjectured to be solvable in closed form. Such equations are common, not only in combinatorics, but in physics as well. The talk will describe recent progress in finding closed form solutions of differential and difference equations, as well as open questions.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125398348","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

Decision Procedures for Elementary Sublanguages of Set Theory. XIV. Three Languages Involving Rank Related Constructs 集合论初等子语言的决策过程。十四。涉及等级相关构念的三种语言

International Symposium on Symbolic and Algebraic Computation Pub Date : 2015-09-08 DOI: 10.1007/3-540-51084-2_39

D. Cantone, V. Cutello, A. Ferro

引用次数: 3

Randomized detection of extraneous factors 随机检测外来因素

International Symposium on Symbolic and Algebraic Computation Pub Date : 2014-07-23 DOI: 10.1145/2608628.2608631

Manfred Minimair

引用次数: 1

Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbers 包含区间和/或浮点数的非数值表达式的模糊简化

International Symposium on Symbolic and Algebraic Computation Pub Date : 2014-07-23 DOI: 10.1145/2608628.2627489

D. R. Stoutemyer

{"title":"Fuzzy simplification of non-numeric expressions containing some intervals and/or floating point numbers","authors":"D. R. Stoutemyer","doi":"10.1145/2608628.2627489","DOIUrl":"https://doi.org/10.1145/2608628.2627489","url":null,"abstract":"This article describes a Mathematica package that improves simplification of general non-numeric expressions containing any mixture of Gaussian rational numbers, symbolic constants, machine and arbitrary-precision floating-point numbers, together with intervals having any mixture of such endpoints. Such generalized numbers are not automatically all converted to floats or to intervals. Expressions can be multivariate and non-polynomial. Techniques include:\u0000 • Recognition and unification of approximately similar and approximately proportional factors and terms.\u0000 • The option of infinity-norm normalization that is more robust than monic normalization.\u0000 • The option of a unit-normal quasi-primitive normalization that uses large rational approximate common divisors of mixed number types and intervals to nicely normalize sums.\u0000 • A polynomial division algorithm tolerant of terms with coefficients that are float zeros or intervals containing 0.\u0000 • The ability to round or underflow negligible terms while satisfying the inclusion property of interval arithmetic.\u0000 The package and a more detailed version of this article will be posted at arXiv.org.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114757371","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

Root counts of semi-mixed systems, and an application to counting nash equilibria 半混合系统的根计数及其在纳什均衡计数中的应用

International Symposium on Symbolic and Algebraic Computation Pub Date : 2014-07-23 DOI: 10.1145/2608628.2608679

I. Emiris, R. Vidunas

{"title":"Root counts of semi-mixed systems, and an application to counting nash equilibria","authors":"I. Emiris, R. Vidunas","doi":"10.1145/2608628.2608679","DOIUrl":"https://doi.org/10.1145/2608628.2608679","url":null,"abstract":"Semi-mixed algebraic systems are those where the equations can be partitioned into subsets with common Newton polytopes. We are interested in counting roots of semi-mixed multihomogeneous systems, where both variables and equations can be partitioned into blocks, and each block of equations has a given degree in each block of variables. The motivating example is counting the number of totally mixed Nash equilibria in games of several players. Firstly, this paper relates and unifies the BKK and multivariate Bézout bounds for semi-mixed systems, through mixed volumes and matrix permanents. Permanent expressions for BKK bounds hold for all multihomogeneous systems, without any requirement of semi-mixed structure, as well as systems whose Newton polytopes are products of polytopes in complementary subspaces. Secondly, by means of a novel asymptotic analysis, the complexity of a combinatorial geometric algorithm for semi-mixed volumes (i.e., mixed volumes of semi-mixed systems) is explored and juxtaposed to the complexities of computing permanents, or using generating functions (via MacMahon's Master theorem), or orthogonal polynomials.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134003578","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: 18

Sparse multivariate function recovery with a high error rate in the evaluations 评价错误率高的稀疏多元函数恢复

International Symposium on Symbolic and Algebraic Computation Pub Date : 2014-07-23 DOI: 10.1145/2608628.2608637

E. Kaltofen, Zhengfeng Yang

{"title":"Sparse multivariate function recovery with a high error rate in the evaluations","authors":"E. Kaltofen, Zhengfeng Yang","doi":"10.1145/2608628.2608637","DOIUrl":"https://doi.org/10.1145/2608628.2608637","url":null,"abstract":"In [Kaltofen and Yang, Proc. ISSAC 2013] we have generalized algebraic error-correcting decoding to multivariate sparse rational function interpolation from evaluations that can be numerically inaccurate and where several evaluations can have severe errors (\"outliers\"). Here we present a different algorithm that can interpolate a sparse multivariate rational function from evaluations where the error rate is 1/q for any q > 2, which our ISSAC 2013 algorithm could not handle. When implemented as a numerical algorithm we can, for instance, reconstruct a fraction of trinomials of degree 15 in 50 variables with non-outlier evaluations of relative noise as large as 10-7 and where as much as 1/4 of the 14717 evaluations are outliers with relative error as small as 0.01 (large outliers are easily located by our method).\u0000 For the algorithm with exact arithmetic and exact values at non-erroneous points, we provide a proof that for random evaluations one can avoid quadratic oversampling. Our argument already applies to our original 2007 sparse rational function interpolation algorithm [Kaltofen, Yang and Zhi, Proc. SNC 2007], where we have experimentally observed that for T unknown non-zero coefficients in a sparse candidate ansatz one only needs T +O(1) evaluations rather than the proven O(T2) (cf. Candès and Tao sparse sensing). Here we finally can give the probabilistic analysis for this fact.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129580231","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: 11