On Fri, Mar 18, 2011 at 4:14 PM, Alexey U. Gudchenko <pr...@goodok.ru>wrote:
> 18.03.2011 13:26, Hector пишет: > > On Fri, Mar 18, 2011 at 3:34 PM, Alexey U. Gudchenko<pr...@goodok.ru >> >wrote: >> >> 18.03.2011 12:49, Hector пишет: >>> >>> >>> >>> Now mathematically, limit x tending to 0, abs(x)/x should not exist. >>> >>>> >>>> >>> Why not? (tendind from the right.) >>> >>> Consider definition of limit: >>> >>> "the limit of f as x approaches 0 is L if and only if for every real ε> >>> 0 >>> there exists a real δ> 0 such that 0< x< δ implies | f(x) − L |< ε" >>> >>> >> Hi Alexey, >> > > Hi, > > > When we say - "the limit of f as x *approaches* 0 ", we are allowing x to >> approach 0 from any side. ( Here are only two ways of approaching to 0 viz >> '+ve' and '-ve' but its not true always. For function f(x,y) there are >> infinitely many ways of approaching to (0,0)). >> > > Yes, it is a complexity (which involve "Directional derivative", or > "Directional limit") in case of many variable. > > Now in sympy only right and left limits as you cited: > > > """For dir="+" (default) it calculates the limit from the right""" > > So when x approaches from +ve side the value of function will approach to >> +1 >> and when it approaches from -ve side the value of function approaches to >> -1 >> and you will never be able to find L in your definition. >> > > Hope the attachment will make my point clear. > > Now implemented dir="+" as default (in master branch of git repository): > > In [2]: limit(abs(x)/x, x, 0) > Out[2]: 1 > > In [3]: limit(abs(x)/x, x, 0, dir="-") > Out[3]: -1 > > From your remarks I see that you want to define dir="unknown" or dir="both" > as default. And in this case of 'dir' limit should return "None" for > "abs(x)/x" (when result differ between dir="-" and dir="+"). Right? > > > 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. > >> >> >> > -- > 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. > > -- -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.
