Computers and Mathematics

1. Front Matter

   Pages i-xi

   PDF

2. Track A (10:45am–12:30pm)

   1. A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra

      • Deepak Kapur, Klaus Madlener

      Pages 1-11

   2. Summation of Harmonic Numbers

      • Dominic Y. Savio, Edmund A. Lamagna, Shing-Min Liu

      Pages 12-20

   3. Algorithm and Implementation for Computation of Jordan Form over A[x ₁,...,x _m ]

      • Nicholas Strauss

      Pages 21-26

   4. Fast Group Membership Using a Strong Generating Test for Permutation Groups

      • Gene Cooperman, Larry Finkelstein, Paul Walton Purdom Jr.

      Pages 27-36

   5. Finite-Basis Theorems and a Computation-Integrated Approach to Obstruction Set Isolation

      • Michael R. Fellows, Nancy G. Kinnersley, Michael A. Langston

      Pages 37-45

3. Track B (10:45am–12:30pm)

   1. Practical Determination of the Dimension of an Algebraic Variety

      • André Galligo, Carlo Traverso

      Pages 46-52

   2. A Computer Generated Census of Cusped Hyperbolic 3-Manifolds

      • Martin Hildebrand, Jeffrey Weeks

      Pages 53-59

   3. Classicality of Trigonal Curves of Genus Five

      • Paulo Viana

      Pages 60-65

   4. Symmetric Matrices with Alternating Blocks

      • Abramo Hefez, Anders Thorup

      Pages 66-72

   5. Cohomology to Compute

      • D. Leites, G. Post

      Pages 73-81

4. Track A (4:00pm–5:45pm)

   1. Use of symbolic methods in analyzing an integral operator

      • H. F. Trotter

      Pages 82-90

   2. Computer Algebraic Methods for Investigating Plane Differential Systems of Center and Focus Type

      • Dongming Wang

      Pages 91-99

   3. An Example of Computer Enhanced Analysis

      • Peter J. Costa, Ruth Hampton Westlake

      Pages 100-108

   4. An Algorithm for Symbolic Computation of Hopf Bifurcation

      • Emilio Freire, Estanislao Gamero, Enrique Ponce

      Pages 109-118

   5. Application of the REDUCE Computer Algebra System to Stability Analysis of Difference Schemes

      • Victor G. Ganzha, Richard Liska

      Pages 119-129

5. Track B (4:00pm–5:45pm)

   1. Signs of Algebraic Numbers

      • Takis Sakkalis

      Pages 130-134

   2. Efficient Reduction of Quadratic Forms

      • Neil W. Rickert

      Pages 135-139

   3. A Story About Computing with Roots of Unity

      • F. Bergeron

      Pages 140-144

   4. Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method

      • Alkiviadis G. Akritas

      Pages 145-155

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.

• Permutation
• algebra
• calculus
• geometry
• logic
• mathematics
• number theory

• Department of Computer Science, Rensselaer Polytechnic, Troy, USA

  Erich Kaltofen

• IBM Watson Research Center, Yorktown Heights, USA

  Stephen M. Watt

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