On Dec 6, 2008, at 11:39 AM, Paul Butler wrote:
> > 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 > ) > This crops up regularly in solid mechanics, in particular in the bending of beams. One can represent the loading of a beam as derivatives and integrals of Heaviside functions and then integrate the expression to get the shear force, bending moment, and deflection of the beam. It's also one of the parts of Maple that's problematic. I wrote some code for my students a few years back to help them, but unfortunately, there are problems with some integrals of Heaviside functions. These can be discontinuous piecewise functions, at least the shear and moment graphs. Cheers, Tim. --- Tim Lahey PhD Candidate, Systems Design Engineering University of Waterloo http://www.linkedin.com/in/timlahey --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
