14.04.2011 00:59, Aaron S. Meurer пишет: > > 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 >
For algorithm optimization, as one variant, we must have a quick procedure, which give us the answer whether function is continues at this point or not. BTW, it will be useful for other topics. Alexey U. -- 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.
