Many kudos for this! Honestly, I don't actually know whether it means that much, but at this point I think that it could be useful for us to follow Mathematica in defining two different functions: Heaviside which is undefined in 0 and that is defined as the function whose derivative is the Dirac Delta ( see http://functions.wolfram.com/GeneralizedFunctions/HeavisideTheta/02/ ) and UnitStep, which is the piecewise version of this function, so it's numerically defined everywhere. It would be great if one could possibly change the desired value in 0.
I think it doesn't hurt now to carry on both, because it shouldn't be that difficult to merge them in future if we don't see any usefulness in having them separated. I can see that Maple use Heaviside undefined in 0, and then let the user the chance to convert it to a piecewise function if desired. This looks a bit unfriendly to me, and doesn't bring any real advantage. By the way, how do we represent Dirac Delta? I know that it's not defined in 0, but I want to point out an example. Please, remember that the Fourier transform of any periodic function (although the use of the transform is not proper in case of periodic functions, I know) is formed by the summation of Dirac Deltas at different location in the frequency spectrum, and I would love to have a graphical representation of the spectrum of a signal. So, do you think we can find a convenient way of plotting delta? I don't know much of them, but I'm sure there are many similar physical problems, that would take advantage of plotting deltas. Thanks again Maurizio On 23 Giu, 19:02, Golam Mortuza Hossain <gmhoss...@gmail.com> wrote: > Thanks David, Tim, Burcin! > > Correct me if I have missed your points. With your suggestions > here is the new conventions for Heaviside and unit step > > (2) Heaviside: > > (a) represented as: "heaviside" > (b) latex name : "\theta" > (c) heaviside(0): will return symbolic expression "heaviside(0)" > > (3) unit_step = heaviside (Just an alias) > > >> Will, for example, sin(t)*unit_step(t) be defined? > >> If so, will you provide a plotting and _latex_ method for it? > > > I really hope so. > > These functions are sub-class of PrimitiveFunctions of new > symbolics. So many methods are predefined. For example, > I didn't write any code for plotting but it works. > > Here is a screenshot from my Sage notebook. > > http://www.math.unb.ca/~ghossain/sage-generalized-functions.png > > Hopefully, it answers some of your questions. I am still working > on integration algorithm. > > Cheers, > Golam --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
