On Apr 13, 2011, at 2:22 PM, Hector wrote:
>
>
> On Wed, Apr 13, 2011 at 11:46 PM, Julien Rioux <julien.ri...@gmail.com> wrote:
> On Apr 13, 11:45 am, Hector <hector1...@gmail.com> wrote:
> > Hello groups,
> >
> > This is about the way limit has been defined in sympy. Currently, Sympy
> > gives following result.
> >
> > In [1]: limit(abs(x)/x,x,0)
> > Out[1]: 1
> >
> > But as we know, the right-hand and left-hand of limit at given function is
> > different.
> >
> > In [2]: limit(abs(x)/x, x, 0, dir = "+")
> > Out[2]: 1
> >
> > In [3]: limit(abs(x)/x, x, 0, dir = "-")
> > Out[3]: -1
> >
> > And hence mathematically speaking, limit doesn't exist at given point. Sympy
> > assumes dir = "+" by default and hence giving the wrong answer. The similar
> > type of discussions has been made some times ago in Issue1000[1]. As
> > suggested in discussions, the default dir should be " r " for real line
> > where it checks both right hand side and left hand side limit and returns
> > the answer iff both are equal. For this to happen, I am proposing that we
> > should rename current "limit" function by "limit_eval" and define new limit
> > function which checks both right hand limit and left hand limit.
> >
> > I made the necessary changes, and the corresponding pull request is #219[2].
> > If this changing definition things is fine with core developers, I would
> > like to proceed further for limts of bi-variant functions.
> >
> > --
> > -Regards
> > Hector
> >
> > Whenever you think you can or you can't, in either way you are right.
> >
> > [1]http://code.google.com/p/sympy/issues/detail?can=2&q=1000&colspec=ID%...
> > [2]https://github.com/sympy/sympy/pull/219
>
> I do appreciate when sympy's functions are based as closely as
> possible on the mathematical definition, so I am +1 on this general
> idea. However:
>
> - Introducing limit_eval is repetitive. Just use limit(..., dir="+") if that
> is the intended behavior.
>
> But in mathematical literature, limit always implies limit from both
> directions( on real line) unless until specified. So as discussed in
> Issue1000, limit (modified) will be 2x as much time consuming as limit ( with
> old definition) but that will give us mathematically correct answer and I
> believe that counts more than speed. Moreover, we can never think of limit of
> bi-variant functions or limit in complex plane if we go with current
> definition of limit.
At what point in the algorithm does it use the direction of the limit? Is it
from the outset, or is it after it has done some other things? If it's the
second case, then we could optimize it so it doesn't take 2x as long.
Aaron Meurer
>
> - The default for the dir argument should depend on the assumptions on
> x. So you would get dir="r" when x is declared Symbol("x", real=True)
> but dir=(complex plane, I don't know the key, c?) when x is declared
> Symbol("x", complex=True).
>
> Regards,
> Julien
>
>
> This seems reasonable to me and thanks for pointing it out. I don't think
> currently there is any method available to compute limit when variable is
> complex. I will fix this while writing (if people permit) limit for complex
> variable.
>
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>
>
>
> --
> -Regards
> Hector
>
> Whenever you think you can or you can't, in either way you are right.
>
>
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