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.

Klappentext

This volume is the proceedings of a scientific conference on the use of computers to do exact mathematics which was held at the University of Cincinnati, March 22-25, 1989. One group of papers deals with the use of general algebraic processors like Macsyma, Reduce, Scratchpad etc. to do precise computations in bifurcation analysis and related areas of analysis. Another group of papers deals with the development of the software to solve equations exactly, carry of explicit integrations etc. for these general software packages. A third group discusses the use of interval arithmetic algorithms and software to give rigorous proofs of mathematical theorems and give precise estimates of stabililty regions.

Inhalt
The conversion of a high order programming language from floating-point arithmetic to range arithmetic.- Sylvester's form of the resultant and the matrix-triangularization subresultant PRS method.- Computing the Tsirelson space norm.- Floating-point systems for theorem proving.- Computer algebra and indefinite integrals.- A computer-assisted approach to small-divisors problems arising in Hamiltonian mechanics.- On a computer algebra aided proof in bifurcation theory.- MACSYMA program to implement averaging using elliptic functions.- Validated anti-derivatives.- A toolbox for nonlinear dynamics.- Computer assisted proofs of stability of matter.- Accurate strategies for K.A.M. bounds and their implementation.- A software tool for analysis in function spaces.- Equation solving by symbolic computation.- Deciding a class of Euclidean geometry theorems with Buchberger's algorithm.- Lie transform tutorial II.- Interval tools for computer aided proofs in analysis.- Tools for mathematical computation.- Shadowing trajectories of dynamical systems.- Transformation to versal normal form.- Computer assisted lower bounds for atomic energies.