## Computer Mathematics: Proceedings of the Fifth Asian Symposium (ASCM 2001), Matsuyama, Japan, 26-28 September 2001This volume covers some of the most recent and significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software and computer-aided geometric design. Researchers, engineers, academics and graduate students interested in doing mathematics using computers will find this volume good reading and a valuable reference. Contents: Solution of a Linear Differential Equations in the Form of Power Series and Its Application (T Kitamoto); On the Specification for Solvers of Polynomial Systems (D Lazard); OMEI: An Open Mathematical Engine Interface (W Liao et al.); Polynomial Solutions of Algebraic Differential Equations (Y Ma & X-S Gao); FIGUE: Mathematical Formula Layout with Interaction and MathML Support (H Naciri & L Rideau); An Inductive Approach to Formalizing Notions of Number Theory Proofs (T M Rasmussen); A Generalized Algorithm for Computing Characteristic Sets (D Wang); Action Refinement for Timed LOTOS (J Wu); Exact Analytical Solutions to a Set of Coupled Nonlinear Differential Equations Using Symbolic Computation (R-X Yao & Z-B Li); and other papers. Readership: Researchers, engineers, academics and graduate students in numerical & computational mathematics, theoretical computer science, mathematical modeling, analysis & differential equations, software engineering/programming, algebra & number theory, and logic. |

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### Contents

On the Complexity of Computing Determinants Extended Abstract | 13 |

Papers | 28 |

Solution of a Linear Differential Equation in the Form of Power Series | 46 |

On the Specification for Solvers of Polynomial Systems | 66 |

An Open Mathematical Engine Interface | 82 |

The Design and Implementation of OpenXMRFC 100 and 101 | 102 |

Mathematical Formula Layout with Interaction | 112 |

Comparison of | 122 |

An Inductive Approach to Formalizing Notions of Number | 131 |

Application of Grobner Basis and Quantifier Elimination | 141 |

An API for Internet Accessible Mathematical Services | 151 |

Deformation of Double Cusp Singularity on an Irreducible Quartic | 161 |

Deciding Inclusion of Differential QuasiAlgebraic Varieties | 175 |

Action Refinement for Timed LOTOS | 183 |

Symbolic Computation and Abundant New Families of Exact | 193 |

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2acd 4ceA algebraic differential equation algorithm applied approximate ascending set called characteristic sets Chebyshev polynomials coefficients command complexity components compute engine computer algebra system Computer Science cusp singularity decomposition defined degree equations denote design parameters determinant differential polynomial differential quasi-algebraic E-mail eigenvalues element example factors FIGUE finite field formalized formulas Grobner basis IAMC ideal implementation inductive input interaction interface interval irreducible Isabelle/HOL Java JavaMath JMEI Lemma linear Maple Math mathematical engines MathML Matlab matrix minimal polynomial multiplication nomials obtained OMEI OpenMath OpenXM operations output p-polynomials paper polynomial sequence polynomial set polynomial solution PPML prime problem proof Proposition protocol pseudo-remainder real zeros refinement function roots satisfy Schur-Cohn Section server singularity solver solving stack machine Step Sturm sequences Symbolic Computation theory triangular sets truncated power series univariate polynomial variables Wang wave solutions Wilson's Theorem Wu's method