If I had the expertise to implement it, I would do the following: The integration would return another Piecewise function in which the first interval is integrated normally, and the next ones would integrate the function in that interval and add the definite integral of the previous intervals. I think that makes some sense.
Ronan Paixão Em Sáb, 2008-12-06 às 11:39 -0500, Paul Butler escreveu: > Currently, taking the integral of a piecewise function in Sage gives > you the definite integral. I've proposed on trac that the integral of > piecewise functions be indefinite by default. This would be consistent > with how integration works on other functions in Sage, as well as > piecewise functions in Maple and Mathematica. > > The main concern is whether the integral of a piecewise function is > even well-defined. It seems to me that at least for continuous > piecewise functions, the indefinite integral is well-defined. The > anti-derivative is well defined, and by the fundamental theorem of > calculus, the indefinite integral of a continuous function is the > anti-derivative. As for discontinuous piecewise functions, I'm finding > it difficult to convince myself either way. > > The trac ticket is 4721 ( http://trac.sagemath.org/sage_trac/ticket/4721 ) > > -- Paul > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
