Computer Aided Proofs in Analysis

1. Front Matter

   Pages i-xvi

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2. The Conversion of a High Order Programming Language from Floating-Point Arithmetic to Range Arithmetic

   • Oliver Aberth

   Pages 1-4

3. Sylvester’s form of the Resultant and the Matrix-Triangularization Subresultant PRS Method

   • Alkiviadis G. Akritas

   Pages 5-11

4. Computing the Tsirelson Space Norm

   • Johnnie W. Baker, Oberta A. Slotterbeck, Richard Aron

   Pages 12-21

5. Floating-Point Systems for Theorem Proving

   • G. Bohlender, J. Wolff von Gudenberg, W. L. Miranker

   Pages 22-32

6. Computer Algebra and Indefinite Integrals

   • Manuel Bronstein

   Pages 33-42

7. A Computer-Assisted Approach to Small-Divisors Problems Arising in Hamiltonian Mechanics

   • Alessandra Celletti, Luigi Chierchia

   Pages 43-51

8. On a Computer Algebra Aided Proof in Bifurcation Theory

   • Carmen Chicone, Marc Jacobs

   Pages 52-70

9. MACSYMA Program to Implement Averaging Using Elliptic Functions

   • Vincent T. Coppola, Richard H. Rand

   Pages 71-89

10. Validated Anti-Derivatives

    • George F. Corliss

    Pages 90-96

11. A Toolbox for Nonlinear Dynamics

    • Shannon Coffey, André Deprit, Étienne Deprit, Liam Healy, Bruce R. Miller

    Pages 97-115

12. Computer Assisted Proofs of Stability of Matter

    • R. de la Llave

    Pages 116-126

13. Accurate Strategies for K.A.M. Bounds and Their Implementation

    • R. De La Llave, D. Rana

    Pages 127-146

14. A Software Tool for Analysis in Function Spaces

    • J.-P. Eckmann, A. Malaspinas, S. Oliffson Kamphorst

    Pages 147-167

15. Equation Solving by Symbolic Computation

    • Anthony C. Hearn

    Pages 168-174

16. Deciding a Class of Euclidean Geometry Theorems with Buchberger’s Algorithm

    • Bernhard Kutzler

    Pages 175-189

17. Lie Transform Tutorial — II

    • Kenneth R. Meyer

    Pages 190-210

18. Interval Tools for Computer Aided Proofs in Analysis

    • Ramon E. Moore

    Pages 211-216

19. Tools for Mathematical Computation

    • L. B. Rall

    Pages 217-228

20. Shadowing Trajectories of Dynamical Systems

    • Tim Sauer, James A. Yorke

    Pages 229-234

This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu­ tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina­ torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

• Mathematica
• algebra
• algorithms
• bifurcation
• integration

• Departments of Mathematics and Computer Science, University of Cincinnati, Cincinnati, USA

  Kenneth R. Meyer

• Department of Computer Science, University of Cincinnati, Cincinnati, USA

  Dieter S. Schmidt

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