A study of alternative methods for the symbolic calculation of elliptic integrals

SYMSACC（1976）

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摘要

This presentation describes the study of several candidate methods for the symbolic integration of a class of irrational expressions R(x,y), where y2 is a polynomial in x and R is a rational function of x and y. Three of these methods came from classical investigations of Legendre, Jacobi, and Weierstrass whereas one came from recent investigations of Carlson. The present paper may be considered a progress report on preliminary algorithmic study and some efforts of implementation on MACSYMA. In this presentation, we describe the study of several candidate methods for the symbolic integration of a class of irrational expressions R(x,y), where y2 is a polynomial in x and R is a rational function of x and y. We shall also summarize some efforts of implementation on MACSYMA.

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关键词

progress report,preliminary algorithmic study,recent investigation,present paper,irrational expressions r,symbolic calculation,alternative method,elliptic integral,candidate method,symbolic integration,rational function,classical investigation,singularities,interval analysis,symmetry,monotonicity,convexity,qualitative analysis

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