Issue : limit(abs(log(x)),x,0,'+')

[Arnaud Usciati]

Hello,

limit(abs(log(x)), x, 0, '+') should return +oo, but it returns -oo*sign(log(_w)) !!!

[Aaron Meurer]

That's definitely a bug (Dummy values should never leak out of functions). Can you open an issue for it?

Aaron Meurer

On Sat, Jan 31, 2015 at 9:33 AM, Arnaud Usciati <rai...@gmail.com> wrote:

Hello,

limit(abs(log(x)), x, 0, '+') should return +oo, but it returns -oo*sign(log(_w)) !!!

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[Douglas Lohmann]

In my test it's not a bug. You can explain better?

In [9]: limit(abs(log(x)), x, 0, '+')

Out[9]: oo

It was already reported the bug to the bug list?

[Ondřej Čertík]

Git bisect reveals that it got broken in
https://github.com/sympy/sympy/commit/4995bff19ba29e4264ea2c7e5c2e112425f44924

Ondrej

[Aaron Meurer]

Be sure to test against SymPy master. As Ondrej pointed out, this used to work, but it got broken.

Aaron Meurer

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[Ondřej Čertík]

The limits will have to be debugged, essentially we just need to go
step by step and see which routine returns the wrong answer.

Ondrej

> https://groups.google.com/d/msgid/sympy/CAKgW%3D6L30%3Dh4-b6r2S_1c7tZ%3Deu8n7zFWcCBQOcTaN3f1MbnMA%40mail.gmail.com.

[Arnaud Usciati]

Hi,

I found another error limit :

If x = symbols('x', positive=True), limit(tan(abs(x))/acosh(x), x, pi/2, '-') returns oo --> OK

If x = symbols('x', real=True), limit(tan(abs(x))/acosh(x), x, pi/2, '-') returns oo*sign(1/Subs(Derivative(re(_x), _x), (_x,), (0,))) !!

I guess the first result is correct because sympy can evaluate abs(x) to x for x positive, but for x real it can't simplify the function and calculate the limit !

[Christophe Bal]

Hello.

Maybe, it could be useful to have a abssimplify method that will try to simplify abs expressions.

Christophe BAL

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[Arnaud Usciati]

Hello,

Maybe abs() function have to be reconsidered, because I found other issues with abs...

limit(abs(ln(x))-ln(x), x, 2) or limit(abs(ln(x))-ln(x), x, 2, '+') return 0 (OK), but limit(abs(ln(x))-ln(x), x, 2, '-') runs endless and I need to interrupt it to stop calculating.. Same way with functions : abs(cos(x))-cos(x) or abs(sin(x))-sin(x) or abs(sqrt(x))-sqrt(x) for x = symbols('x', real=True)

But if I try : limit(abs(ln(x))-ln(x), x, a, '-') with a = symbols('a', real=True), it returns (sign(log(a)) - 1)*log(a). Idem for the direction '+' and without direction.

[Sergey Kirpichev]

On Thursday, February 12, 2015 at 10:26:32 PM UTC+3, Arnaud Usciati wrote:

Maybe abs() function have to be reconsidered, because I found other issues with abs...

All examples above are solved with patch from
 https://github.com/skirpichev/omg/pull/82
(on top of the https://github.com/skirpichev/omg/pull/154)
That should work for sympy with trivial replacements (is_extended_real -> is_real).

limit(abs(ln(x))-ln(x), x, 2) or limit(abs(ln(x))-ln(x), x, 2, '+') return 0 (OK), but limit(abs(ln(x))-ln(x), x, 2, '-') runs endless and I need to interrupt it to stop calculating.. Same way with functions : abs(cos(x))-cos(x) or abs(sin(x))-sin(x) or abs(sqrt(x))-sqrt(x) for x = symbols('x', real=True)

The problem is that nseries constantly emits an Order term and lseries can't yield anything at all.  But for real,
positive _and finite_ x < 1: abs(ln(2-x))-ln(2-x) == 0.

But if I try : limit(abs(ln(x))-ln(x), x, a, '-') with a = symbols('a', real=True), it returns (sign(log(a)) - 1)*log(a). Idem for the direction '+' and without direction.

This is an example of lucky answer, due to a non-strict approach in the calculate_series routine to
the zero-decision problem.  I.e. if sympy can't simplify term to zero, it thinks term is nonzero.

Wrong idea in general, but in this particular case it happens to be right.