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Integration of Elementary Functions by Manuel Bronstein is a Computer Science article available to read on EtoBox.

What is Integration of Elementary Functions about?

We extend a recent algorithm of Trager to a decision procedure for the indefinite integration of elementary functions. We can express the integral ns an elementa.ry function or prove theft it is not elementary. We show that if the l~roblom of integration in finite terms is solvable on a given elementary function field k, then it is solva.ble in any algebraic extension of k(O), where 0 is a. logarithm or exponential of an element of k. Our proof considers a.n element of such an extension field to be an algebraic function of one variable o v e r ~, In his a,lgorlthm for the integre.tion of s.lgebralc functlons~ Trager describes s, tiering,etype reduction to reduce the problem to an integrand with only simple finite poles on the associated YGemann surface. We genera.lize that technique to curves over liouvilllan ground fields, and use it to simplify our integrands. Once the multiple finite poles have been removed, we use the Puiseux expansions of the integrand a.t infinity and a generaliza.tion of the residues to compute the integral. We also generalize a result of R.othstein ths.t gives us a necessary condition for elementary integrabillty, s.nd provide examples of its use.

Who reads Integration of Elementary Functions?

Author

Manuel Bronstein

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0747-7171)

Published

1990

Language

EN

Field

Computer Science (Physical Sciences)