*To*: mathgroup@smc.vnet.net*Subject*: [mg10949] Re: [mg10603] Bivariate Integrations/Assumptions error/*From*: "Mario Sancho" <mario_sancho.graca@virgin.net>*Date*: Sat, 14 Feb 1998 00:53:21 -0500

I would like to point out that Integrate[ ] uses different algorithms depending on whether it is definite or indefinite integration (Roach 1992, 'Indefinite and Definite Integration, Mathematica Conference 1992). Indefinite integration is centred about the Risch Structure Theorem, definite integration involves contour integration. Therefore, depending on how Integrate[ ] is used, we will obtain different results. Paul Abbot in reply to [mg10603] noted that there was a numerical argument in the expression being integrated, and numerical evaluations are in this context not desired. Also note that changing the limits of the definite integral from infinities to {x, x1, x2}, {y, y1, y2}, results in an exact (and true) solution with no conditions. Your integral may be fairly basic, but it illustrates a few aspects of symbolic computation which need to be considered. I think you were trying to check the answer given by Mathematica for a simple problem, without realizing that the statement of the problem is not so easy to formulate. There is, also, a necessity for Mathematica to consider by default the arguments as broad as possible (i.e. Complex) because otherwise the algorithms would be meaningless. With due care, a symbolic engine like Mathematica can be very useful for the evaluation of complicated expressions.