On Sunday, February 15, 2015 at 3:55:28 PM UTC+3, Arnaud Usciati wrote:
>
> If x = symbols('x', real=True).
>
> I found wrong results for limits with sign() function.
> limit(sign(x), x, 0, '+') = 1, and limit(sign(x), x, 0, '-') = -1 ---> OK
>
> But :
> - limit(sign(ln(x)), x, 1, '+') = 1 (OK) but limit(sign(ln(x)), x, 1, '-')
> = 0 instead of -1 ;
> - limit(sign(sin(x)), x, 0, '+') = 0 and limit(sign(sin(x)), x, 0, '-') =
> 0, instead of 1 and -1 ;
> - limit(sign(tan(x)), x, 0, '+') = 0 and limit(sign(tan(x)), x, 0, '-') =
> 0, instead of 1 and -1 ;
> - limit(sign(cos(x)), x, pi/2, '+') = 0 and limit(sign(cos(x)), x, pi/2,
> '-') = 0, instead of 1 and -1 ;
> Etc......
>
Patch: https://github.com/skirpichev/omg/pull/154
(Should work for sympy with trivial replacement .is_extended_real ->
.is_real)
Please note that
> limit(sign(cos(x)), x, pi/2, '+') = 0 and limit(sign(cos(x)), x, pi/2,
'-') = 0, instead of 1 and -1 ;
is incorrect. Should be -1 and 1 instead, c.f. Mathematica output:
In[3]:= Limit[Sign[Cos[x]], x->Pi/2, Direction->-1] (* default, equivalent
to dir="+" *)
Out[3]=
-1
In[4]:= Limit[Sign[Cos[x]], x->Pi/2, Direction->+1]
Out[4]=
1
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