On Apr 11, 2011, at 3:56 PM, Ronan Lamy wrote: > Le lundi 11 avril 2011 à 15:42 -0600, Aaron S. Meurer a écrit : >> On Apr 11, 2011, at 2:25 AM, smichr wrote: >> >>> Should `Integral(x, (x, 1, 2)) == Integral(y, (y, 1, 2))` be True? If >>> so, smichr branch 2068b has a commit that makes this testing possible. >>> >> This is a good question. For one thing, == is not mathematical >> equality but exact equality, so there is no reason why it should have >> to be True. So my initial response is that no, it should not. >> > I think it should. x and y are bound symbols that have no meaning > outside the integrals, so their identity should be completely > irrelevant. In fact, they should probably be replaced with dummies upon > instantiation of the Integral. >
Well, of course, it does not matter mathematically, but it does matter for other reasons. For example, it matters for printing. You wouldn't want to have >>> Integral(xyz, (xyz, 0, 1)) Integral(x, (x, 0, 1)) Using dummies internally is a good idea. I think that they shouldn't compare equal unless we at least do that. And we can take it further. To take an example from a discussion from one of the pull requests, should Integral(f(x, y), (x, 0, 1), (y, 0, 1)) == Integral(f(x, y), (y, 0, 1), (x, 0, 1)) return True? At what point do we draw the line for the "exact equality" that == is supposed to be checking for? Anyway, I think if we do more work with manipulating integrals (like combining them), we will see if this is a good idea or not. Aaron Meurer -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
