Bug with inverse hyperbolic cosine 'acosh'

[Arnaud Usciati]

Hello everybody,

I tried values with acosh function and I found an issue.

Suppose x = symbols('x', real=True) and f = lambda x: acosh(-x).

For instance :

> Input : f(1)

> Output : I*pi

  --> That's OK

> Input : f(-1)

> Output : 0

  --> That's OK

But f(x) returns -acosh(x) instead of acosh(-x) ! It's wrong because 'acosh' it's certainly not odd !!

Arnaud

[Joachim Durchholz]

Am 31.03.2015 um 15:06 schrieb Arnaud Usciati:
> Hello everybody,
>
> I tried values with acosh function and I found an issue.
> Suppose x = symbols('x', real=True) and f = lambda x: acosh(-x).

Just a heads-up: the x inside the lambda is unrelated to the symbol x.

> But f(x) returns -acosh(x) instead of acosh(-x) !

I did a bit more testing and found I wouldn't need f, or the real=True
assumption on x:

$ python
Python 2.6.9 (unknown, Dec 26 2014, 22:51:25)
[GCC 4.8.2] on linux3
Type "help", "copyright", "credits" or "license" for more information.
>>> from sympy import Symbol, acosh
>>> x = Symbol('x')
>>> acosh(-x)
-acosh(x)

This looks indeed like a bug to me.

[AMiT Kumar]

Yes, It is a bug Indeed.

Thanks for reporting.

Fixed in this PR:  https://github.com/sympy/sympy/pull/9231

Please have a look.

Reference:

http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/

http://www.wolframalpha.com/input/?i=ArcCosh%5B-z%5D