Le vendredi 18 mars 2011 à 16:29 +0530, Hector a écrit :

> Yes, exactly.
> It seems more consistent that way. Has this issue already been
> discussed? If not, do we need to report this?
> Since I am looking forward to apply for GSoC, and would love to work
> with SymPy, this would be good start for me.
> 
> If core developers/contributors agree, I would like to work on this
> regardless GSoC. Because with thing implemented, we can never go for
> limit of multi-variable functions. 

I thought about this before, but I didn't reach the point where I could
suggest a design. 

I think there needs to be an object describing the "destination" of a
limit (i.e. "0", "0+", "0-", "+oo", ...), so the syntax for limit would
be limit(f(x), x, <something that means "0+">) instead of limit(f(x), x,
0, dir="+"). These destination objects would also be used by series()
and the like and would be passed around in the internal code.

The proper mathematical notion corresponding to this is a filter[*]. It
applies also in the multivariate case and allows to describe limits when
|(x,y)| -> 0, or when (x,y) -> (0,0) along a particular ray or some more
complicated curve, etc.

[*]: See http://fr.wikipedia.org/wiki/Filtre_%28math%C3%A9matiques%29
(in French) - I couldn't find a good description in English. The
en.Wikipedia article in particular is so full of category-theoretic
abstract nonsense as to be useless.


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