Make incomplete gamma function symbolic #7748

kcrisman · 2009-12-22T17:18:07Z

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 · 2009-12-22T23:09:31Z

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 · 2009-12-23T04:42:36Z

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 · 2009-12-24T20:17:13Z

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 · 2010-02-07T11:37:27Z

Make Ei symbolic.

sagetrac-fstan · 2010-02-07T11:38:07Z

Attachment: trac_7748-exp_integral.patch.gz

Attachment: trac_7748-incomplete_gamma.patch.gz

Make incomplete gamma function symbolic.

sagetrac-fstan · 2010-02-07T11:42:41Z

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 · 2010-02-07T11:42:41Z

Author: Flavia Stan

zimmermann6 · 2010-02-07T21:53:54Z

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 · 2010-02-08T02:19:09Z

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.

sagetrac-fstan · 2010-02-08T11:03:15Z

comment:7

Replying to @zimmermann6:

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?

Thank you for the review. I'll include the derivative and submit again. Integration looks more complicated.

Greetings,

Flavia

zimmermann6 · 2010-02-08T13:09:40Z

comment:8

I tried sage -t * with both patches, and I get one additional failure with respect to those I get
due to #7773:

tarte% sage -t "rings/complex_number.pyx"
sage -t  "rings/complex_number.pyx"                         
**********************************************************************
File "/usr/local/sage-4.3-core2/devel/sage-main/sage/rings/complex_number.pyx", line 1611:
    sage: gamma_inc(2, 5)
Expected:
    0.0404276819945128
Got:
    gamma(2, 5)

Consider also the following:

sage: gamma_inc(2, 5.)
0.0404276819945128
sage: gamma(2, 5) 
1

burcin · 2010-02-08T16:36:18Z

comment:9

Replying to @zimmermann6:

Consider also the following:

sage: gamma_inc(2, 5.)
0.0404276819945128
sage: gamma(2, 5) 
1

We should write a python function wrapping gamma_inc and gamma, similar to the provided for psi() in #6961.

The fact that gamma() accepts two arguments at the moment is a bug that I introduced in #7490. Looking at the code, it also doesn't handle the prec parameter correctly. I'll upload a patch with a wrapper gamma() function and a fix for the prec issue.

Replying to @sagetrac-fstan:

Integration looks more complicated.

Integration cannot be handled with a custom method in symbolic functions. The patches attached to #6465 should make this easier.

zimmermann6 · 2010-02-10T12:39:43Z

comment:10

Flavia, please can you fix the rings/complex_number.pyx issue?

sagetrac-fstan · 2010-02-15T23:27:28Z

Attachment: trac_7748-exp_integral_ver2.patch.gz

Added derivative method.

sagetrac-fstan · 2010-02-15T23:28:10Z

Fixed tests from complex_number.pyx

sagetrac-fstan · 2010-02-15T23:34:50Z

comment:11

Attachment: trac_7748-incomplete_gamma_ver2.patch.gz

I've uploaded new patches which should fix the docs and the derivative.

Greetings,

Flavia

burcin · 2010-02-20T17:51:19Z

Attachment: trac_7748-exp_integral_ver2.4.3.3.alpha1.patch.gz

rebased to 4.3.3.alpha1

burcin · 2010-02-20T17:51:53Z

rebased to 4.3.3.alpha1

burcin · 2010-02-20T17:52:27Z

Attachment: trac_7748-incomplete_gamma_ver2.4.3.3.alpha1.patch.gz

Attachment: trac_7748-gamma_wrapper.patch.gz

wrapper for gamma and incomplete gamma

burcin · 2010-02-20T17:57:02Z

Attachment: trac_7748-gamma_wrapper.2.patch.gz

wrapper for gamma and incomplete gamma

burcin · 2010-02-20T18:03:28Z

comment:12

attachment: trac_7748-gamma_wrapper.2.patch adds a new wrapper function to call gamma or incomplete gamma depending on the number of arguments. It also corrects the way prec parameter to gamma was handled.

Flavia's patches needed to be rebased to 4.3.3.alpha1 since the changes to random_tests.py didn't apply anymore.

The patches to be applied are (in this order):

I'm changing this to needs review. :)

zimmermann6 · 2010-02-24T07:27:18Z

comment:13

a partial review against 4.3.3:

sage -t  "devel/sage-main/sage/schemes/elliptic_curves/ell_rational_field.py"
...
    sage: E.Lambda(1.4+0.5*I, 50)
      File "/usr/local/sage-4.3.3/sage/local/lib/python/site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line 3088, in Lambda
        Gamma_inc = transcendental.gamma_inc
    AttributeError: 'module' object has no attribute 'gamma_inc'

This test was ok with vanilla 4.3.3.

zimmermann6 · 2010-02-24T07:27:18Z

Work Issues: new test failure

zimmermann6 · 2010-02-24T08:40:32Z

comment:14

apart from the above failure, all tests pass with sage 4.3.3 (apart from the Fedora 12 Segfaults).

burcin · 2010-03-02T11:33:29Z

Attachment: trac_7748-gamma_wrapper.3.patch.gz

fix new doctest failure

burcin · 2010-03-02T11:37:17Z

comment:15

I added a fix for the doctest failure in comment:13 to my patch, attachment: trac_7748-gamma_wrapper.3.patch.

The patches to be applied are (in this order):

I am OK with Flavia's changes. If someone can review my patch this can still get in 4.3.4. :)

burcin · 2010-03-02T11:37:17Z

Reviewer: Paul Zimmermann

zimmermann6 · 2010-03-03T12:24:49Z

comment:16

Everything works now. Great work!

Paul

zimmermann6 · 2010-03-03T12:24:49Z

Changed author from Flavia Stan to Flavia Stan, Burcin Erocal

burcin · 2010-03-17T08:09:33Z

Changed work issues from new test failure to none

burcin · 2010-03-17T08:09:33Z

comment:17

Hi Minh,

What is holding up this ticket? Note that it has a positive review and the patches to be applied are listed in comment:15.

Cheers,

Burcin

sagetrac-mvngu · 2010-03-17T08:13:14Z

comment:18

Replying to @burcin:

What is holding up this ticket?

I can't merge this ticket. We are now in feature freeze.

jhpalmieri · 2010-04-15T20:15:07Z

comment:19

Merged in 4.4.alpha0:

trac_7748-exp_integral_ver2.4.3.3.alpha1.patch
trac_7748-incomplete_gamma_ver2.4.3.3.alpha1.patch
trac_7748-gamma_wrapper.3.patch

jhpalmieri · 2010-04-15T20:15:07Z

Merged: sage-4.4.alpha0

kcrisman added this to the sage-4.4 milestone Dec 22, 2009

kcrisman added c: symbolics labels Dec 22, 2009

kcrisman assigned burcin Dec 22, 2009

sagetrac-fstan mannequin added the s: needs review label Feb 7, 2010

sagetrac-fstan mannequin added s: needs work and removed s: needs review labels Feb 8, 2010

zimmermann6 assigned zimmermann6 and unassigned burcin Feb 8, 2010

burcin added s: needs review and removed s: needs work labels Feb 20, 2010

zimmermann6 added s: needs work and removed s: needs review labels Feb 24, 2010

burcin added s: needs review and removed s: needs work labels Mar 2, 2010

zimmermann6 added s: positive review and removed s: needs review labels Mar 3, 2010

jhpalmieri removed the s: positive review label Apr 15, 2010

jhpalmieri closed this as completed Apr 15, 2010

burcin mentioned this issue Apr 6, 2010

maxima interface gives precedence to function dictionary instead of local variables #7661

Closed

nathanncohen mannequin mentioned this issue Jan 14, 2023

Remove deprecated code from tickets <10000 #15568

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Make incomplete gamma function symbolic #7748

Make incomplete gamma function symbolic #7748

kcrisman commented Dec 22, 2009

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Make incomplete gamma function symbolic #7748

Make incomplete gamma function symbolic #7748

Comments

kcrisman commented Dec 22, 2009

burcin commented Dec 22, 2009

kcrisman commented Dec 23, 2009

williamstein commented Dec 24, 2009

sagetrac-fstan mannequin commented Feb 7, 2010

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