On 7 feb, 04:48, Burcin Erocal <bur...@erocal.org> wrote:
> You need to add an _eval_() function which calls _evalf_() if the
> argument is not exact. See this patch for an example:
>
> http://trac.sagemath.org/sage_trac/attachment/ticket/4498/trac_4498-s...

Done :)

> The _evalf_() function in your patch hard codes RDF. You need to do
> something like this:
>
> sage: from sage.libs.mpmath import utils as mpmath_utils
> sage: import mpmath
> sage: mpmath_utils.call(mpmath.airyai, 1, parent=RR)
> 0.135292416312881

mpmath seems to be around 35 times faster than the RDF version, (which
was the way things were done before my patch).

> I don't think we want to have separate functions for the derivatives in
> Sage. These might help you get around the printing problem for now, but
> they are not useful in general.

I disagree here, Mathematica has got the AiryAiPrime function. And
mpmath supports calculating derivatives and integrals of arbitrary
order! I think it would be best if we could do something like:

sage: airy_ai(x)
airy_ai(x)
sage: airy_ai(x,1)
airy_ai_prime(x)
sage: airy_ai(x,-2)
airy_ai(x,-2)

that is, make a single object that returns arbitrary derivatives or
integrals.

Cheers!

Oscar

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