On Jun 23, 2009, at 5:45 PM, Maurizio 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 ( 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. > Technically, the Heaviside can be considered to be a piecewise function where H(x) = 0 x<0, H(x) = 1, x>0. Maple just has a conversion between the various representations. It comes in handy when there are multiple pieces. > 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. Ploting Dirac deltas doesn't make much sense given its definition. When I work with Dirac deltas and their derivatives, I just ignore them for plotting purposes. I only plot their integrals and higher. 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 sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
