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2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

24-27 Sept. 2016

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  • [Front cover]

    Publication Year: 2016, Page(s): c1
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  • [Title page i]

    Publication Year: 2016, Page(s): i
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  • [Title page iii]

    Publication Year: 2016, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2016, Page(s): iv
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  • Table of contents

    Publication Year: 2016, Page(s):v - x
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  • Preface

    Publication Year: 2016, Page(s):xii - xiii
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  • Preface

    Publication Year: 2016, Page(s):xi - xii
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  • Organizing Committees

    Publication Year: 2016, Page(s):xiv - xv
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  • Organizing Committees

    Publication Year: 2016, Page(s):xiii - xiv
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  • Program Committees

    Publication Year: 2016, Page(s):xvi - xviii
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  • Program Committees

    Publication Year: 2016, Page(s):xv - xvii
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  • Additional Reviewers

    Publication Year: 2016, Page(s): xix
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  • Additional Reviewers

    Publication Year: 2016, Page(s): xviii
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  • Symbolic Computation Techniques in Satisfiability Checking

    Publication Year: 2016, Page(s):3 - 10
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (351 KB) | HTML iconHTML

    Satisfiability Checking is a relatively young research area, aiming at the development of efficient software technologies for checking the satisfiability of existentially quantified logical formulas. Besides the success story of SAT solving for propositional logic, SAT-modulo-theories (SMT) solvers offer sophisticated solutions for different theories. When targeting arithmetic theories, SMT solver... View full abstract»

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  • Bridging Two Communities to Solve Real Problems

    Publication Year: 2016, Page(s):11 - 14
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (351 KB) | HTML iconHTML

    This paper describes a sort of case study of how ideas from computational logic (specifically, satisfiability modulo theory solving) provide new algorithms in symbolic computing. In particular, it describes how ideas from the NLSAT solver led to a new kind of Cylindrical Algebraic Decomposition. View full abstract»

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  • The Time Yards Model - Rethinking the Way to Look at Texts

    Publication Year: 2016, Page(s):15 - 22
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (608 KB) | HTML iconHTML

    This paper is about copying on artificial agents humans' perception of time and their ability to produce-condensed short stories out of large free texts. We propose a model intended to objectivize processes that help to achieve this reasoning behaviour on machines. View full abstract»

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  • Revisit of "Geometric Exercise in Paper Folding" from a Viewpoint of Computational Origami

    Publication Year: 2016, Page(s):23 - 28
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB) | HTML iconHTML

    We revisit the seminal classical work of T. Sundara Row on the geometry in paper folding published in 1893. After 123 years, the significance of the book remains. This note is intended to provide a short description of Sundara Row's masterpiece from the viewpoint of the current mathematical theory of origami and show how various geometrical shapes that Sundara Row drew in his book can be produced ... View full abstract»

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  • Structural vs. Cyclic Induction: A Report on Some Experiments with Coq

    Publication Year: 2016, Page(s):29 - 36
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (246 KB) | HTML iconHTML

    Structural and (Noetherian) cyclic induction are two instances of the Noetherian induction principle adapted to reason on first-order logic. From a theoretical point of view, every structural proof can be converted to a cyclic proof but the other way is only conjectured. From a practical point of view, i) structural induction principles are built-in or automatically issued from the analysis of rec... View full abstract»

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  • How to Build a Global Digital Mathematics Library

    Publication Year: 2016, Page(s):37 - 40
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (172 KB) | HTML iconHTML

    As with many other areas of study, mathematical knowledge has been produced for centuries and will continue to be produced for centuries to come. The records have taken many forms, from manuscripts, to printed journals, and now digital media. Unlike many other fields, however, much of mathematical knowledge has a high degree of precision and objectivity that both gives it permanent utility and mak... View full abstract»

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  • Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition with Groebner Bases

    Publication Year: 2016, Page(s):45 - 52
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (308 KB) | HTML iconHTML

    Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polyno... View full abstract»

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  • Polynomial GCDs by Syzygies

    Publication Year: 2016, Page(s):53 - 59
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (245 KB) | HTML iconHTML

    We provide a simple method, using Gröbner bases over modules, to compute multivariate polynomial greatest common divisors. The approach we show is flexible, adaptable to algebraic extensions of the rationals or prime fields, and is notably faster than prior methods that work with Gröbner bases. It can be used in situations where sparse interpolation might be difficult to implement,... View full abstract»

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  • Combinatorics of Hybrid Sets

    Publication Year: 2016, Page(s):60 - 64
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (192 KB) | HTML iconHTML

    Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. This construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets have been used by combinatorists to give combinatorial interpretations for several generalizations of binomial coefficients and Stirling numbers and by computer scientists to design ... View full abstract»

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  • Effective Nondeterministic Positive Definiteness Test for Unidiagonal Integral Matrices

    Publication Year: 2016, Page(s):65 - 71
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (214 KB) | HTML iconHTML

    For standard algorithms verifying positive definiteness of a matrix A ∈ Mn(R) based on Sylvester's criterion, the computationally pessimistic case is this when A is positive definite. We present an algorithm realizing the same task for A ∈ Mn(Z), for which the case when A is positive definite is the optimistic one. The algorithm relies on performing certain edge transforma... View full abstract»

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  • Parallel Integer Polynomial Multiplication

    Publication Year: 2016, Page(s):72 - 80
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (337 KB) | HTML iconHTML

    We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantage of this new approach. View full abstract»

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  • Various Enhancements for Extended Hensel Construction of Sparse Multivariate Polynomials

    Publication Year: 2016, Page(s):83 - 86
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (175 KB) | HTML iconHTML

    The extended Hensel construction (EHC) is a direct extension of the generalized Hensel construction (GHC), and it targets sparse multivariate polynomials for which the GHC breaks down. The EHC consists of two Hensel constructions which we call separation of "maximal" and "minimal" Hensel factors (see the text). As for the minimal Hensel factor separation, very recently, we enhanced the old algorit... View full abstract»

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