On Jun 23, 2009, at 11:59 AM, David Joyner wrote:
>
>
> On Tue, Jun 23, 2009 at 10:53 AM, Golam Mortuza Hossain <gmhoss...@gmail.com
> > wrote:
>
> Hi,
>
> I am seeking your opinion to finalize the conventions
> for three generalized functions that I am implementing currently.
>
> My proposals are:
>
> (1) These generalized functions be included in a new module as
>
> "sage.functions.generalized"
>
> (2) Dirac delta:
>
> (a) represented as: "dirac_delta" [ex. dirac_delta(x) ]
> (b) latex name : "\delta"
> (c) dirac_delta(0) : will return a symbolic expression
> "dirac_delta(0)"
>
>
> (3) Heaviside Theta:
>
> (a) represented as: "heaviside_theta"
> (b) latex name : "\theta"
> (c) heaviside_theta(0) = 1/2
>
>
>
> Why not just heaviside? I've never heard of Heaviside Theta. For most
> purposes, unit step and heaviside will have the same effect (eg, if
> you take
> their Laplace transforms) so you may not even need both.
>
>
>
>
>
>
> (3) Unit Step:
>
> (a) represented as: "unit_step"
> (b) latex name : "{\rm u}"
> (c) unit_step(0) = 1
>
What about a function undefined at 0? I use Dirac delta, Heaviside,
and the derivative
of the delta function. Having a definition at x=0 for Heaviside can
cause problems. I'd
like the limit of x=0^{-} be zero while x=0^{+} be 1. Having a
specific value at x=0
causes problems.
Also, I've never heard it called Heaviside theta, just Heaviside.
Also, the use of {\rm u} is obsolete (see Guide to LaTeX 4th edition)
and can cause
problems with the memoir class. It's better to use \mathrm{u}.
>
> Will these generalized functions form a vector space?
> 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. They provide the basic functions for the solution of
beam loading
problems. A Dirac delta represents an applied point load, a unit step
= distributed load,
and the derivative of a Dirac delta is a point moment.
I like the idea, but defining a value at x=0 is problematic. Different
conventions use
different values so making it an option and having it be undefined
would be my preference
as a default. I've seen conventions that define the unit step to be 0,
1/2, 1, undefined
at x = 0.
Cheers,
Tim.
---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://www.linkedin.com/in/timlahey
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