Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation最新文献

{"title":"Optimization Problems over Noncompact Semialgebraic Sets","authors":"L. Zhi","doi":"10.1145/2755996.2756638","DOIUrl":"https://doi.org/10.1145/2755996.2756638","url":null,"abstract":"In this talk, we will introduce some recent progress in dealing with optimization problems over noncompact semialgebraic sets. We will start with the problem of optimizing a parametric linear function over a noncompact real algebraic variety. Then we will introduce how to compute the semidefinite representation or approximation of the convex hull of a noncompact semialgebraic set. Finally, we will show how to characterize the lifts of noncompact convex sets by the cone factorizations of properly defined slack operators.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"123 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123070898","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}

{"title":"Probabilistic Algorithm for Computing the Dimension of Real Algebraic Sets","authors":"Ivan Bannwarth, M. S. E. Din","doi":"10.1145/2755996.2756670","DOIUrl":"https://doi.org/10.1145/2755996.2756670","url":null,"abstract":"Let fΕ Q[X1, …, Xn] be a polynomial of degree D. We consider the problem of computing the real dimension of the real algebraic set defined by f=0. Such a problem can be reduced to quantifier elimination. Hence it can be tackled with Cylindrical Algebraic Decomposition within a complexity that is doubly exponential in the number of variables. More recently, denoting by d the dimension of the real algebraic set under study, deterministic algorithms running in time DO(d(n-d)) have been proposed. However, no implementation reflecting this complexity gain has been obtained and the constant in the exponent remains unspecified. We design a probabilistic algorithm which runs in time which is essentially cubic in Dd(n-d). Our algorithm takes advantage of genericity properties of polar varieties to avoid computationally difficult steps of quantifier elimination. We also report on a first implementation. It tackles examples that are out of reach of the state-of-the-art and its practical behavior reflects the complexity gain.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115581010","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}

{"title":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","authors":"D. Robertz, S. Linton, K. Yokoyama","doi":"10.1145/2755996","DOIUrl":"https://doi.org/10.1145/2755996","url":null,"abstract":"The 2015 International Symposium on Symbolic and Algebraic Computation (ISSAC 2015) is the premier conference for research in symbolic computation and computer algebra. ISSAC 2015, held at the University of Bath, U.K., is the 40th meeting in the series, which began in 1966 with the seminal ACM Symposium on Symbolic and Algebraic Manipulation. ISSAC 2015 is sponsored by the Association for Computing Machinery (ACM), in particular, the ACM Special Interest Group in Symbolic and Algebraic Manipulation (SIGSAM). The meeting is also supported by donations from the London Mathematical Society (LMS) and Maplesoft. As a scientific satellite event, the workshop Parallel Symbolic Computation (PASCO) was held in Bath immediately following ISSAC 2015. \u0000 \u0000The ISSAC conference is a showcase for original research contributions on all aspects of computer algebra and symbolic mathematical computation, including: \u0000 \u0000Algorithmic aspects: \u0000Exact and symbolic linear, polynomial and differential algebra \u0000Symbolic-numeric, homotopy, perturbation and series methods \u0000Computational algebraic geometry, group theory and number theory \u0000Computer arithmetic \u0000Summation, recurrence equations, integration, solution of ODEs and PDEs \u0000Symbolic methods in other areas of pure and applied mathematics \u0000Complexity of algebraic algorithms and algebraic complexity \u0000 \u0000 \u0000 \u0000Software aspects: \u0000Design of symbolic computation packages and systems \u0000Language design and type systems for symbolic computation \u0000Data representation \u0000Consideration for modern hardware \u0000Algorithm implementation and performance tuning \u0000Mathematical user interfaces \u0000 \u0000 \u0000 \u0000Application aspects: \u0000Applications that stretch the current limits of computer algebra algorithms or systems, use computer algebra in new areas or new ways, or apply it in situations with broad impact. \u0000 \u0000 \u0000 \u0000The program of ISSAC 2015 features invited talks, tutorials, contributed research presentations, a poster session and a software exhibits session. These Proceedings contain all accepted contributed papers, as well as abstracts of the invited talks and tutorials. \u0000 \u0000The ISSAC Program Committee selected 43 papers appearing in these Proceedings. All papers submitted to ISSAC 2015 were judged, and accepted or rejected, solely according to their scientific novelty and excellence. Each submitted paper was assigned to three members of the Program Committee, and two or more referee reports were obtained for each submission. We gratefully acknowledge the thorough and important work of the Program Committee Members and external reviewers, whose names appear on the following pages, and thank all the authors and lecturers for their contribution.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"256 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129911899","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}

{"title":"Exact Linear Algebra Algorithmic: Theory and Practice","authors":"Clément Pernet","doi":"10.1145/2755996.2756684","DOIUrl":"https://doi.org/10.1145/2755996.2756684","url":null,"abstract":"Exact linear algebra is a core component of many symbolic and algebraic computations, as it often delivers competitive theoretical complexities and also better harnesses the efficiency of modern computing infrastructures. In this tutorial we will present an overview on the recent advances in exact linear algebra algorithmic and implementation techniques, and highlight the few key ideas that have proven successful in their design. As an illustration, we will study in more details the computation of some matrix normal forms over a finite field or the ring of polynomials, specific to computer algebra. In particular, we will give a special care to the design and implementation of parallel exact linear algebra routines, trying to emphasize the similarities and distinctness with parallel numerical linear algebra. We aim to provide the working computer algebraist with a set of best practices for the use or the design of exact linear algebra software, together with an overview on a few still unresolved algorithmic problems in the field.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126802143","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}

{"title":"Computer Algebra Applied to a Solitary Waves Study","authors":"D. Clamond, D. Dutykh, A. Galligo","doi":"10.1145/2755996.2756659","DOIUrl":"https://doi.org/10.1145/2755996.2756659","url":null,"abstract":"We apply Computer algebra techniques, such as algebraic computations of resultants and discriminants, certified drawing (with a guaranteed topology) of plane curves, to a problem in Fluid dynamics: We investigate ``capillary-gravity'' solitary waves in shallow water, relying on the framework of the Serre-Green-Naghdi equations. So, we deal with 2 dimensional surface waves, propagating in a shallow water of constant depth. By a differential elimination process, the study reduces to describing the solutions of an ordinary non linear first order differential equation, depending on two parameters. The paper is illustrated with examples and pictures computed with the computer algebra system Maple.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131227110","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}

{"title":"Algebraic Diagonals and Walks","authors":"A. Bostan, L. Dumont, B. Salvy","doi":"10.1145/2755996.2756663","DOIUrl":"https://doi.org/10.1145/2755996.2756663","url":null,"abstract":"The diagonal of a multivariate power series $F$ is the univariate power series DiagF generated by the diagonal terms of F. Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. We study algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It is classical that in this case DiagF is an algebraic function. We propose an algorithm that computes an annihilating polynomial for DiagF. Generically, it is its minimal polynomial and is obtained in time quasi-linear in its size. We show that this minimal polynomial has an exponential size with respect to the degree of the input rational function. We then address the related problem of enumerating directed lattice walks. The insight given by our study leads to a new method for expanding the generating power series of bridges, excursions and meanders. We show that their first N terms can be computed in quasi-linear complexity in N, without first computing a very large polynomial equation.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134512826","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}

{"title":"Algorithms for Finite Field Arithmetic","authors":"É. Schost","doi":"10.1145/2755996.2756637","DOIUrl":"https://doi.org/10.1145/2755996.2756637","url":null,"abstract":"We review several algorithms to construct finite fields and perform operations such as field embedding. Following previous work by notably Shoup, de Smit and Lenstra or Couveignes and Lercier, as well as results obtained with De Feo and Doliskani, we distinguish between algorithms that build \"towers\" of finite fields, with degrees of the form l, l2, l3,... and algorithms for composita. We show in particular how techniques that originate from algorithms for computing with triangular sets can be useful in such a context.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"231 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122103707","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}

{"title":"Computation of Dimension in Filtered Free Modules by Gröbner Reduction","authors":"Christoph Fürst, G. Landsmann","doi":"10.1145/2755996.2756680","DOIUrl":"https://doi.org/10.1145/2755996.2756680","url":null,"abstract":"We present an axiomatic approach to Gröbner basis techniques in free multi-filtered modules over a not necessarily commutative multi-filtered ring. It is shown that classical Gröbner basis concepts can be viewed as models of our axioms. Within this theory it is possible to prove a general theorem about the dimension of filter spaces in multi-filtered modules. We use these ideas for computing the Hilbert function of finitely generated multi-filtered modules over difference-differential rings. Thus the presented method allows to compute a multivariate generalization of the univariate and the bivariate dimension polynomial considered in the papers of Winkler and Zhou.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123941815","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}

{"title":"Structure of Polyzetas and Explicit Representation on Transcendence Bases of Shuffle and Stuffle Algebras","authors":"V. Bui, G. Duchamp, V. H. N. Minh","doi":"10.1145/2755996.2756657","DOIUrl":"https://doi.org/10.1145/2755996.2756657","url":null,"abstract":"By an effective construction of pairs of bases in duality in shuffle and quasi-shuffle algebras, we identify the local coordinates of noncommutative generating series of polyzetas which are group-like. Algorithms lead to the ideal of homogeneous polynomial relations, in weight, among polyzetas and their explicit representation on irreducible elements.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127134933","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}

{"title":"An Algorithm to Check Whether a Basis of a Parametric Polynomial System is a Comprehensive Gröbner Basis and the Associated Completion Algorithm","authors":"D. Kapur, Yiming Yang","doi":"10.1145/2755996.2756676","DOIUrl":"https://doi.org/10.1145/2755996.2756676","url":null,"abstract":"Given a basis of a parametric polynomial ideal, an algorithm is proposed to test whether it is a comprehensive Gröbner basis or not. A basis of a parametric polynomial ideal is a comprehensive Gröbner basis if and only if for every specialization of parameters in a given field, the specialization of the basis is a Gröbner basis of the associated specialized polynomial ideal. In case a basis does not check to be a comprehensive Gröbner basis, a completion algorithm for generating a comprehensive Gröbner basis from it that is patterned after Buchberger's algorithm is proposed. Its termination is proved and its correctness is established. In contrast to other algorithms for computing a comprehensive Gröbner basis which first compute a comprehensive Gröbner system and then extract a comprehensive Gröbner basis from it, the proposed algorithm computes a comprehensive Gröbner basis directly. Further, the proposed completion algorithm always computes a minimal faithful comprehensive Gröbner basis in the sense that every polynomial in the result is from the ideal as well as essential with respect to the comprehensive Gröbner basis. A prototype implementation of the algorithm has been successfully tried on many examples from the literature. An interesting and somewhat surprising outcome of using the proposed algorithm is that there are example parametric ideals for which a minimal comprehensive Gröbner basis computed by it is different from minimal comprehensive Gröbner bases computed by other algorithms in the literature.","PeriodicalId":182805,"journal":{"name":"Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125693922","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}