[Tracker Item 70] Delayed variables

http://bowmore.elyt.com/bugzilla/show_bug.cgi?id=70





--- Comment #2 from Andrew Miller 
<ak.miller-1/NbpDiVQt6SYBAHRPvY1A@xxxxxxxxxxxxxxxx>  2007-07-21 17:45:44 ---
(In reply to comment #1)
> Convolution with a shifted dirac delta is really just another way of saying
> y(t-k), since that is essentially one approach to defining the dirac delta
> generalised function.  Also, convolution would require us to specify the
> function arguments anyway.  So I think convolution is not the approach we
> should take.
> 
> Changing the specification so that y becomes y(t) (i.e. a function) seems the
> cleanest approach to me.
> 
I don't see the benefits of the convolution approach either.

It perhaps mathematically cleaner but there are other considerations which
might affect this:
1) Consistency with existing CellML specifications - how much do we want to
change the specification to support this?
2) Space requirements of the representation - will this be a major show-stopper
if every variable suddenly becomes <apply><ci>y</ci><ci>t</ci></apply> instead
of just <ci>y</ci>?
3) Consequences for software implementations - does this provide enough data
for a simulator to use - how do we define boundary conditions, and what sorts
of simulation metadata do we need to make such simulations work? How will they
interact with the new representation?

One option might be to introduce some sort of semantics where sometimes
<ci>y</ci> is a variable meaning y, and other times it is a function, but this
might cause headaches and ambiguity if we ever introduce functions as a type in
CellML (although we could add attributes to the 'variables' describing their
type it might be unambiguous).

Also, would a variable still be called a variable in the component if it is
actually a function, or do you propose that we have more than one type of
element?


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