Dieter Kaiser wrote:
> Hello Robert,
Hi Dieter,
> there is a further report concerning the erf function on the Sage website.
> Because we have extended the erf function to calculate results for complex
> values we now get:
>
> (%i14) build_info();
> Maxima version: 5.16.0cvs
> Maxima build date: 0:34 12/23/2008
> host type: @host@
> lisp-implementation-type: GNU Common Lisp (GCL)
> lisp-implementation-version: GCL 2.6.8
>
> (%i15) erf(%i);
> (%o15) erf(%i)
>
> (%i16) erf(%i),numer;
> (%o16) 1.650425758797543 %i + 2.1207839599929513E-16
>
> That is the report from the Sage project:
>
> Expected:
> -.8862269254527579*%i*erf(%i)
> Got:
> -.8862269254527579*%i*(1.650425758797543*%i+1.110223024625156E-16)
>
> erf(%i) is now evaluated and the result for the above expression is
> approximately real.
>
> (%i17) erf(3*%i);
> (%o17) erf(3 %i)
>
> (%i18) erf(3*%i),numer;
> (%o18) 1629.99462260308 %i + 1.7793504802297391E-12
>
> That is the report from the Sage project
>
> Expected:
> Traceback (most recent call last):
> ...
> TypeError: unable to simplify to complex approximation
> Got:
> (1.110223024625156e-16+1629.9946226005709j)
>
> Thus, Sage now detect an unexpected complex result.
>
> Thus, I do not think that we have errors in Maxima, but Sage get unexpected
> results for the erf function with complex arguments.
Yes, the issue here is in Sage. The ticket referred to in this thread
was not meant as a bug report to Maxima, but just listed issues that
needed to be investigated due to using Maxima 5.17.1 instead of 5.16.3
in Sage. That is why I didn't mention those issues yet on the list until
I had taken a closer look where the problem was.
> Remark: We have small realparts in the results. This is due to the limited
> numerical accuracy of the routine.
>
> Dieter Kaiser
Cheers,
Michael