Computers and Mathematics

Front Matter....Pages i-xi
A Completion Procedure for Computing a Canonical Basis for a k -Subalgebra....Pages 1-11
Summation of Harmonic Numbers....Pages 12-20
Algorithm and Implementation for Computation of Jordan Form over A [ x 1 ,..., x m ]....Pages 21-26
Fast Group Membership Using a Strong Generating Test for Permutation Groups....Pages 27-36
Finite-Basis Theorems and a Computation-Integrated Approach to Obstruction Set Isolation....Pages 37-45
Practical Determination of the Dimension of an Algebraic Variety....Pages 46-52
A Computer Generated Census of Cusped Hyperbolic 3-Manifolds....Pages 53-59
Classicality of Trigonal Curves of Genus Five....Pages 60-65
Symmetric Matrices with Alternating Blocks....Pages 66-72
Cohomology to Compute....Pages 73-81
Use of symbolic methods in analyzing an integral operator....Pages 82-90
Computer Algebraic Methods for Investigating Plane Differential Systems of Center and Focus Type....Pages 91-99
An Example of Computer Enhanced Analysis....Pages 100-108
An Algorithm for Symbolic Computation of Hopf Bifurcation....Pages 109-118
Application of the REDUCE Computer Algebra System to Stability Analysis of Difference Schemes....Pages 119-129
Signs of Algebraic Numbers....Pages 130-134
Efficient Reduction of Quadratic Forms....Pages 135-139
A Story About Computing with Roots of Unity....Pages 140-144
Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method....Pages 145-155
Computation of Fourier Transforms on the Symmetric Group....Pages 156-165
Integration in Finite Terms and Simplification with Dilogarithms: A Progress Report....Pages 166-171
Why Integration is Hard....Pages 172-181
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients....Pages 182-191
Recipes for Classes of Definite Integrals Involving Exponentials and Logarithms....Pages 192-201
Logic and Computation in MATHPERT: An Expert System for Learning Mathematics....Pages 202-214
Representation of Inference in Computer Algebra Systems with Applications to Intelligent Tutoring....Pages 215-227
Bunny Numerics....Pages 228-239
Advanced Mathematics from an Elementary Viewpoint: Chaos, Fractal Geometry, and Nonlinear Systems....Pages 240-249
Iterated Function Systems and the Inverse Problem of Fractal Construction Using Moments....Pages 250-259
Working with ruled surfaces in solid modeling....Pages 260-268
Using MACSyma to Calculate the Extrinsic Geometry of a Tube in a Riemannian Manifold....Pages 269-278
Computer Algebra in the Theory of Ordinary Differential Equations of Halphen Type....Pages 279-288
Symbolic Derivation of Equations for Mixed Formulation in Finite Element Analysis....Pages 289-298
Semantics in Algebraic Computation....Pages 299-307
Symbolic Computation with Symmetric Polynomials an Extension to MACSYMA....Pages 308-320
Simultaneous Computations in Fields of Different Characteristics....Pages 321-326