Computer Mathematics : 9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012 ; contributed papers and invited talks

This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers. Front Matter....Pages i-xvi Front Matter....Pages 1-1 Symbolic Computation and Complexity Theory Transcript of My Talk....Pages 3-7 Factorization of Motions....Pages 9-11 Front Matter....Pages 13-13 Simplification of the Lattice Based Attack of Boneh and Durfee for RSA Cryptoanalysis....Pages 15-32 Real Root Isolation of Regular Chains....Pages 33-48 A Practical Implementation of a Modular Algorithm for Ore Polynomial Matrices....Pages 49-59 Computing Popov Forms of Matrices Over PBW Extensions....Pages 61-65 On the Simplest Quartic Fields and Related Thue Equations....Pages 67-85 On the Implementation of Boolean Gröbner Bases....Pages 87-92 Comprehensive Gröbner Bases in a Java Computer Algebra System....Pages 93-108 A Practical Method for Floating-Point Gröbner Basis Computation....Pages 109-124 Series-Expansion of Multivariate Algebraic Functions at Singular Points: Nonmonic Case....Pages 125-140 A Sequence of Nearest Polynomials with Given Factors....Pages 141-145 Digitization Workflow in the Czech Digital Mathematics Library....Pages 147-156 The Implementation and Complexity Analysis of the Branch Gröbner Bases Algorithm Over Boolean Polynomial Rings....Pages 157-169 Towards the Calculation of Casimir Forces for Inhomogeneous Planar Media....Pages 171-180 Front Matter....Pages 181-181 Sparse Polynomial Interpolation by Variable Shift in the Presence of Noise and Outliers in the Evaluations....Pages 183-197 An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions....Pages 199-221 Finding the Symbolic Solution of a Geometric Problem Through Numerical Computations....Pages 223-241 A Symbolic Approach to Compute a Null-Space Basis in the Projection Method....Pages 243-259 A Simple Quantifier-Free Formula of Positive Semidefinite Cyclic Ternary Quartic Forms....Pages 261-274 Front Matter....Pages 181-181 The Vanishing Ideal of a Finite Set of Points with Multiplicity Structures....Pages 275-296 Signature-Based Method of Deciding Program Termination....Pages 297-310 High-Precision Eigenvalue Bound for the Laplacian with Singularities....Pages 311-323 POLY: A New Polynomial Data Structure for Maple 17....Pages 325-348 Degree and Dimension Estimates for Invariant Ideals of $$P$$ -Solvable Recurrences....Pages 349-373 Real Root Isolation of Polynomial Equations Based on Hybrid Computation....Pages 375-396 Overview of the Mathemagix Type System....Pages 397-425 Resultant-Free Computation of Indefinite Hyperexponential Integrals....Pages 427-435 ImUp : A Maple Package for Uniformity-Improved Reparameterization of Plane Curves....Pages 437-451 The Diagonal Reduction Algorithm Using Fast Givens....Pages 453-465 Constructing Generalized Bent Functions from Trace Forms of Galois Rings....Pages 467-477 Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials....Pages 479-503 Preface; Conference Organization; Contents; Contributors; Part IInvited Talks of ASCM2012; 1 Symbolic Computation and Complexity Theory Transcript of My Talk; 1 The Setting; 1.1 NP-Completeness and Beyond; 1.2 Early Symbolic Computation Algorithms; 2 Cook's Thesis; 3 Faugère's Question; References; 2 Factorization of Motions; 1 Extended Abstract; References; Part IIContributed Papers of ASCM2009; 3 Simplification of the Lattice Based Attack of Boneh and Durfee for RSA Cryptoanalysis; 1 Introduction; 2 Preliminaries; 3 A New Lattice-Based Algorithm; 3.1 Canonical Replacement