The Undecidability of the Existence of Zeros of Real Elementary Functions
Journal of the ACM (JACM)
Towards a general theory of special functions
Communications of the ACM
Applications of symbolic programs to complex analysis
ACM '72 Proceedings of the ACM annual conference - Volume 2
Qualitative analysis of mathematical expressions using computer symbolic mathematics
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Automatic symbolic solution of differential equations of first order and first degree
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
ACM SIGSAM Bulletin
Complex analysis in symbolic computing of some definite integrals
ACM SIGSAM Bulletin
ACM SIGSAM Bulletin
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A heuristic computer program for the evaluation of real definite integrals of elementary functions is described. This program, called WANDERER (WANg''s DEfinite integRal EvaluatoR), evaluates many proper and improper integrals. The improper integrals may have a finite or infinite range of integration. Evaluation by contour integration and residue theory is among the methods used. A program called DELIMITER (DEfinite LIMIT EvaluatoR) is used for the limit computations needed in evaluating some definite integrals. DELIMITER is a heuristic program written for computing limits of real or complex analytic functions. For real functions of a real variable, one-sided as well as two-sided limits can be computed. WANDERER and DELIMITER have been implemented in the MACSYMA system, a symbolic and algebraic manipulation system being developed at Project Mac, MIT. A typical problem in applied mathematics, namely asymptotic analysis of a definite integral, is solved using MACSYMA to demonstrate the usefulness of such a system and the facilities provided by WANDERER.