On Mar 18, 2011, at 10:24 PM, Ronan Lamy wrote: > 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.
Isn't a filter some kind of set of subsets that satisfies some properties? One of my professors introduced these to me when describing the hyperreal system. But I don't understand how that lets you define a "limit path" like you want. And I really don't understand how that could help with an implementation. I remember that when using filters to describe the hyperreal system, you have to use the axiom of choice to get what you want, i.e., it is only useful as a theoretical tool. Aaron Meurer -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
