On Sat, Dec 6, 2008 at 3:56 PM, Ronan Paixão <[EMAIL PROTECTED]> wrote: > > 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.
This makes sense for compactly supported functions. How do you do that for something like f(x) = max(1,floor(x))? > > 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 -~----------~----~----~----~------~----~------~--~---
