Communications of the ACM · 1971 · 124 citations · 7 references
ComputingComputer ScienceMathematicsAlgorithmsDifferential EquationsTheory Of ComputationDefinite IntegralsIntegral Equation FormulationsIntegral EquationsNumerical AlgorithmsNumerical IntegrationSpecial FunctionsAlgebraic ManipulationDefinite Integral ApproximationDefinite Integral NotationHermite FunctionsIntegral RepresentationsProperties Of Definite IntegralsRational Function ComputationSymbolic Computation
Three approaches to symbolic integration in the 1960's are described. The first, from artificial intelligence, led to Slagle's SAINT and to a large degree to Moses' SIN. The second, from algebraic manipulation, led to Manove's implementation and to Horowitz' and Tobey's reexamination of the Hermite algorithm for integrating rational functions. The third, from mathematics, led to Richardson's proof of the unsolvability of the problem for a class of functions and for Risch's decision procedure for the elementary functions. Generalizations of Risch's algorithm to a class of special functions and programs for solving differential equations and for finding the definite integral are also described.
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Joel Moses · Communications of the ACM · 1971 · 138 citations · Full text
Joel Moses · NASA Technical Reports Server (NASA) · 1966 · 91 citations · Full text
The Integration of Functions of a Single Variable