Computers and Mathematics de Erich Kaltofen

Computers and Mathematics

Erich Kaltofen

Stephen M. Watt

Advances in computer technology have had a tremendous impact on mathematics in the last two decades. In June of 1989, an international conference was held at MIT, bringing together mathematicians and computer scientists, to survey the work that has been done in computational mathematics, to report recent results in this field, and to discuss research directions as well as educational issues. This book presents a fascinating collection of contributions on topics ranging from computational algebra, and parallel computing, to mathematics education. Mathematicians interested in the computational aspects of their discipline as well as computer scientists interested in mathematical applications will enjoy the integrative view provided by this book.

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Cuprins

Session 1, Track A.- A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra.- Summation of Harmonic Numbers.- Algorithm and Implementation for Computation of Jordan Form Over A[x1,…, xm].- Fast Group Membership Using a Strong Generating Test for Permutation Groups.- Finite-Basis Theorems and a Computation-Integrated Approach to Obstruction Set Isolation.- Session 1, Track B.- Practical Determination of the Dimension of an Algebraic Variety.- A Computer Generated Census of Cusped Hyperbolic 3-Manifolds.- Classicality of Trigonal Curves of Genus Five.- Symmetric Matrices with Alternating Blocks.- Cohomology to Compute.- Session 2, Track A.- Use of Symbolic Methods in Analyzing an Integral Operator.- Computer Algebraic Methods for Investigating Plane Differential Systems of Center and Focus Type.- An Example of Computer Enhanced Analysis.- An Algorithm for Symbolic Computation of Hopf Bifurcation.- Application of the Reduce Computer Algebra System to Stability Analysis of Difference Schemes.- Session 2, Track B.- Signs of Algebraic Numbers.- Efficient Reduction of Quadratic Forms.- A Story About Computing with Roots of Unity.- Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method.- Computation of Fourier Transforms on the Symmetric Group.- Session 3, Track A.- Integration in Finite Terms and Simplification with Dilogarithms: A Progress Report.- Why Integration is Hard.- Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients.- Recipes for Classes of Definite Integrals Involving Exponentials and Logarithms.- Session 3, Track B.- Logic and Computation in MATHPERT: An Expert System for Learning Mathematics.- Representation of Inference in Computer Algebra Systems with Applications to Intelligent Tutoring.-Bunny Numerics: A Number Theory Microworld.- Advanced Mathematics from an Elementary Viewpoint: Chaos, Fractal Geometry, and Nonlinear Systems.- Session 4, Track A.- Iterated Function Systems and the Inverse Problem of Fractal Construction Using Moments.- Working with Ruled Surfaces in Solid Modeling.- Using Macsyma to Calculate the Extrinsic Geometry of a Tube in a Riemannian Manifold.- Computer Algebra in the Theory of Ordinary Differential Equations of Halphen Type.- Session 4, Track B.- Symbolic Derivation of Equations for Mixed Formulation in Finite Element Analysis.- Semantics in Algebraic Computation.- Symbolic Computation with Symmetric Polynomials: An Extension to Macsyma.- Simultaneous Computations in Fields of Different Characteristics.