As a clarification of what I was talking about, see this: http://mathworld.wolfram.com/ImpulsePair.html
Regards Maurizio On 23 Giu, 23:45, Maurizio <maurizio.gran...@gmail.com> wrote: > 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 ( > seehttp://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 -~----------~----~----~----~------~----~------~--~---
