Add support for bidirectional limits (dir="real")

[skirpichev]

• Do we need this at all? 1) We don't have specific algorithms for bidirectional limits yet. 2) Not all CAS support this conception, see e.g. Mathematica.
• Better name for dir value? (variants: "0", "both" or just None); "real" is from the Maple.
• Raise different errors for discontinuities of different type.

[smichr]

Why are you wrapping dir in str to do the test here and throughout?

[skirpichev]

because dir is a Symbol

[smichr]

ok. I missed the sympification of the arg. Would dir.name be better than str(dir)?

[skirpichev]

I find this more cryptic.
On Oct 4, 2014 11:32 PM, "Christopher Smith" notifications@github.com
wrote:

In sympy/printing/latex.py:

@@ -562,8 +562,11 @@ def _print_Integral(self, expr):
def _print_Limit(self, expr):
e, z, z0, dir = expr.args

•    tex = r"\lim_{%s \to %s}" % (self._print(z),
  

•                                 self._print(z0))
  

•    tex = r"\lim_{%s \to " % self._print(z)
  

•    if str(dir) == "real" or z0 in (S.Infinity, S.NegativeInfinity):
  

ok. I missed the sympification of the arg. Would dir.name be better than
str(dir)?

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Reply to this email directly or view it on GitHub
https://github.com/sympy/sympy/pull/8194/files#r18431164.

[skirpichev]

rebased on top of #8201

[asmeurer]

I think it's better just in terms of usability. People expect limit to be bidirectional by default.

[skirpichev]

People expect limit to be bidirectional by default.

Maybe (any proofs?). Anyway, are you sure this worth a performance penalty right now?

[asmeurer]

There have been several issues about it. I do think it would be better if we could make this work on a low level in the Gruntz algorithm to avoid duplicate work.

[skirpichev]

On Tue, Oct 28, 2014 at 10:20:20AM -0700, Aaron Meurer wrote:

I do think it would be better if
we could make this work on a low level in the Gruntz algorithm to avoid
duplicate work.

Sure, but it's far from trivial and it will be not the Gruntz algorithm.

[skirpichev]

Feel free to pick up this work.

[cbm755]

@pelegm, @asmeurer I think this should be merged. Performance doesn't strike me as a big deal b/c this PR does not propose making it the default. Can one of you re-open this?

We can file an issue for improving the performance (although I'm not volunteering to do that) and/or making it default.

[cbm755]

Ok, maybe this is not so easy:

a = limit(sin(1/x**2), x, 0, '-')
# sin(oo)
b = limit(sin(1/x**2), x, 0, '+')
# sin(oo)
(a - b).equals(0)
# True

limit(sin(x), x, oo) should be NaN, or Eq(sin(oo), sin(oo)) should be False, something like that.

But probably there are similar silent failures where the left- and right-hand limit are unevaluated expressions.

[cbm755]

sin(oo) thing is #5299.

[amitsaha]

@asmeurer Strictly from a SymPy user's point of view (and writing about it for others to learn), is it possible that the default will be bidirectional in a future release?

[pelegm]

@amitsaha see discussion here. I personally agree with you.