On Sunday, July 1, 2012 3:39:15 AM UTC-4, Slumberland wrote:
>
> Thanks for all the help!
>
> One last concern, then *ticket*:
>
> {Yes! I will move all future questions of this kind to the devel/ group!}
>
>
> In a series of symbolic calculations, if I can redefine the answers to
>
>
> -is the current representation of a system piecewise?
>
> -is the variable discrete or continuous?
>
> -how do I plan on integrating each part?
>
> -what monotonic function am I using to integrate?
>
>
> ...without changing the structure of the system, I call that cheating.
> Signal processing books call it the dirac_delta. I have no problem with
> this. It's clever, and it works.
>
> In the context of a particular problem, even a purely mathematical one, we
> say its width is zero, and we usually mean it is a pulse of the minimum
> width and maximum height for the system in question, and with area 1. Or
> maybe I mean it is the derivative of the unit step. I'll probably open the
> width beyond zero; I might even change the impulse shape.
>
>
> Q4) Should the dirac_delta wait until such manipulations are *in general
> * defined to your satisfaction, across the packages; and then inherit
> these methods directly? For example, Piecewise() should be updated however
> it best suits SAGE, and the dirac_delta abstracted from it (among others).
>
>>
>>
Not sure of the answers to all your questions, but I would go minimalist
for now. Look at the output of
dirac_delta??
and note that it's defined in sage/functions/generalized.py as a symbolic
function already, and compare the code of other functions in the functions
module to see how to add the sympy method etc. I'm not sure what to do
about the Maxima issue, given that Maxima doesn't actually recognize delta
properly. But figuring these very basic things out would be a great way to
learn how the symbolics and calculus code works in Sage; don't worry about
piecewise functions in general at this stage. Good luck!
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