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%20Type%20Status%20Priority%20Milestone%20Owner%20Summary%20Stars&id=1000
[2] https://github.com/sympy/sympy/pull/219
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