Make incomplete gamma function symbolic

[kcrisman]

We don't appear to have this, though perhaps it is in Pynac/Ginac already. We also need to translate Maxima's gamma_incomplete to our gamma_inc or incomplete_gamma as part of this ticket.

CC: @sagetrac-mvngu

Component: symbolics

Author: Flavia Stan, Burcin Erocal

Reviewer: Paul Zimmermann

Merged: sage-4.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7748

[burcin]

comment:1

After a quick look at the GiNaC sources, I don't think there is an implementation of the incomplete gamma function in there.

Numerical evaluation of this can be done with the gammainc() function of mpmath.

The conversion should just work, if the conversions dictionary argument of BuiltinFunction.__init__ contains maxima='gamma_incomplete'.

[kcrisman]

comment:2

Replying to @burcin:

After a quick look at the GiNaC sources, I don't think there is an implementation of the incomplete gamma function in there.

Okay.

Numerical evaluation of this can be done with the gammainc() function of mpmath.

But will it give us symbolic evaluation ala gamma_inc(1,1)=1/e? That would be best.

The conversion should just work, if the conversions dictionary argument of BuiltinFunction.__init__ contains maxima='gamma_incomplete'.

Yes, of course, but we still have to do it :)

[williamstein]

comment:3

Numerical evaluation of this can be done with the gammainc() function of mpmath.

Doesn't PARI also have an incomplete gamma implementation (it's used by RR and CC, I think)?

[sagetrac-fstan]

Make Ei symbolic.

[sagetrac-fstan]

Attachment: trac_7748-exp_integral.patch.gz

Attachment: trac_7748-incomplete_gamma.patch.gz

Make incomplete gamma function symbolic.

[sagetrac-fstan]

comment:4

The 2 patches should make the incomplete gamma function symbolic. The exponential integral Ei was used in its symbolic evaluation, therefore it was also made symbolic.

[sagetrac-fstan]

Author: Flavia Stan

[zimmermann6]

comment:5

I tried the exponential integral patch and it works ok. However I don't understand the changes in
random_tests.py. Also the following could be evaluated:

sage: diff(Ei(x),x)
D[0](Ei)(x)
sage: integrate(Ei(x),x)
integrate(Ei(x), x)

Should this be in a separate ticket?

[kcrisman]

comment:6

Replying to @zimmermann6:

I tried the exponential integral patch and it works ok. However I don't understand the changes in
random_tests.py.

This makes a 'random' symbolic expression, and when we add new symbolic functions (and sometimes when we change them) this doctest needs to be changed, not because anything bad happened.