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. > - 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. > -- > 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. > > -- -Regards Hector Whenever you think you can or you can't, in either way you are right. -- 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.
