I. Intzodu cUon Risch's landmarh paper [Ris89] presen ted the first decision proced~re for th... more I. Intzodu cUon Risch's landmarh paper [Ris89] presen ted the first decision proced~re for the integration of elementary functions. In that paper he required that the functions appearing in the integrand be algebraically independent. Shortly afterwards in [Risalg] and [RisTO] he relaxed that restriction and outlined a complete decision procedure for the integration of elemeniary functions in finite terms. Unfortunately his algorithms for dealing ~th algebraic functions required considerably more complex machinery than his earlier ones for purely transcendental functions. ~qeses' implementation of the earlier approach in ~%IACS~f]v!~ [MAC??] demonstrated its practicality, whereas the same has yet to be done for Risch's more recent approach.
I. Intzodu cUon Risch's landmarh paper [Ris89] presen ted the first decision proced~re for th... more I. Intzodu cUon Risch's landmarh paper [Ris89] presen ted the first decision proced~re for the integration of elementary functions. In that paper he required that the functions appearing in the integrand be algebraically independent. Shortly afterwards in [Risalg] and [RisTO] he relaxed that restriction and outlined a complete decision procedure for the integration of elemeniary functions in finite terms. Unfortunately his algorithms for dealing ~th algebraic functions required considerably more complex machinery than his earlier ones for purely transcendental functions. ~qeses' implementation of the earlier approach in ~%IACS~f]v!~ [MAC??] demonstrated its practicality, whereas the same has yet to be done for Risch's more recent approach.
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