Opened 6 years ago
Closed 4 years ago
#16697 closed defect (fixed)
implement symbolic lower incomplete gamma function
Reported by:  rws  Owned by:  

Priority:  major  Milestone:  sage7.2 
Component:  symbolics  Keywords:  gamma, incomplete, special, functions 
Cc:  kcrisman, nbruin  Merged in:  
Authors:  Ralf Stephan  Reviewers:  Buck Evan, Paul Masson 
Report Upstream:  N/A  Work issues:  
Branch:  157b268 (Commits)  Commit:  157b268d4ac45de049089e633809f89d2c3ab84e 
Dependencies:  #20185  Stopgaps: 
Description (last modified by )
This is actually a defect because we leave a result from Maxima undefined:
sage: hypergeometric([1],[b],x).simplify_hypergeometric() (b  1)*x^(b + 1)*e^x*gamma_greek(b  1, x) sage: gamma_greek  NameError Traceback (most recent call last) <ipythoninput186e90901bc5cb> in <module>() > 1 gamma_greek NameError: name 'gamma_greek' is not defined
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Lower_incomplete_Gamma_function
Mathematica seems to have Gamma[a,z] for upper and Gamma[a,0,z] for lower; Maple seems to have upper Gamma. gamma_inc
(the upper one in Sage) gets immediately converted to gamma(a,x)
. The symbolic functions gamma_inc==incomplete_gamma
are converted and never returned to the user as expression:
sage: gamma_inc(x,x,hold=True) gamma(x, x) sage: incomplete_gamma(x,x,hold=True) gamma(x, x) sage: assume(x>0) sage: integral(t^(s1)*e^(t),t,0,x) gamma(s, x) + gamma(s)
This ticket should deprecate "incomplete_gamma" and add the symbolic function gamma_inc_lower
, leaving open the question of the global alias for and the displayed name of Function_gamma_inc
.
Previous part of description:
 Provide all three "user input interfaces"
gamma_inc
,incomplete_gamma
andlower_incomplete_gamma
, and convert the Maximagamma_greek
togamma(a, x) + gamma(a)
 Provide all three "user input interfaces"
gamma_inc
,incomplete_gamma
andlower_incomplete_gamma
, and convert togamma(a,x)
andgamma(a,0,x)
n on output  Provide all three "user input interfaces"
gamma_inc
,incomplete_gamma
andlower_incomplete_gamma
, and haveincomplete_gamma
andlower_incomplete_gamma
as result instead of `gamma(...)'  Change the user interface completely to
lower_incomplete_gamma
andupper_incomplete_gamma
 Change the user interface completely to
gamma_inc_lower
andgamma_inc_upper
 Change the user interface completely to
gamma(a,x)
andgamma(a,0,x)
Attachments (2)
Change History (82)
comment:1 Changed 6 years ago by
 Cc kcrisman nbruin added
comment:2 Changed 6 years ago by
comment:3 Changed 6 years ago by
I don't underswtand. With "leave as is" you would keep gamma(a,x)
as returned expression for the upper function? Or would you make gamma_inc
fully symbolic in that it gets no longer converted to gamma(a,x)
?
comment:4 Changed 6 years ago by
The reason why gamma_inc(x,y)
gets output as gamma(x,y)
is not conversion as I thought but simple naming super in the constructor. It would be just as easy to make that gamma_inc
and change a few doctests such that then:
sage: f = exp_integral_e(1,x) sage: f.integrate(x)  Ei(x)  gamma(1, x) + Ei(x)  gamma_inc(1, x) sage: gamma_inc(3,2)  gamma(3, 2) + gamma_inc(3, 2) sage: gamma(3,2) gamma_inc(3, 2) sage: gamma(x,0) gamma(x) sage: gamma(x, 0, hold=True)  gamma(x, 0) + gamma_inc(x, 0)
I'm appending the patch that enables this here, so it is preserved.
comment:5 Changed 6 years ago by
 Branch set to u/rws/implement_symbolic_lower_incomplete_gamma_function
comment:6 Changed 6 years ago by
 Commit set to 93c2f94cb7e1ca7651a8a8de907bad09ae82428e
Branch pushed to git repo; I updated commit sha1. New commits:
93c2f94  16697: deprecate "incomplete_gamma"

comment:7 Changed 6 years ago by
 Description modified (diff)
comment:8 Changed 6 years ago by
 Commit changed from 93c2f94cb7e1ca7651a8a8de907bad09ae82428e to 5c1dd67bfa51d7c871b055c3272a94af9fdb68f2
Branch pushed to git repo; I updated commit sha1. New commits:
5c1dd67  16697: implement gamma_inc_lower

comment:9 Changed 6 years ago by
 Status changed from new to needs_review
comment:10 Changed 6 years ago by
 Commit changed from 5c1dd67bfa51d7c871b055c3272a94af9fdb68f2 to d8d7ee29d7d0f8cf9f884c4403fe5c36cdf3336d
Branch pushed to git repo; I updated commit sha1. New commits:
d8d7ee2  16697: use mpmath as default evalf algorithm

comment:11 followup: ↓ 12 Changed 6 years ago by
On sagesupport Rafael Greenblatt reports
sage: (incomplete_gamma(x,y).diff(x)).simplify() TypeError: ECL says: Error executing code in Maxima: gamma: wrong number of arguments.
The problem probably arises because the function ends up separated from its arguments:
sage: incomplete_gamma(x,y).diff(x) D[0](gamma)(x, y)
which might confuse the translator (the behaviour is consistent with just going by strings). The changes here might improve the situation. It's worth checking.
The following of course works because it does NOT primarily look at strings:
sage: from sage.interfaces.maxima_lib import * sage: maxima_calculus(sr_to_max(incomplete_gamma(x,y).diff(x))) 'diff(gamma_incomplete(x,y),x,1)
comment:12 in reply to: ↑ 11 ; followup: ↓ 13 Changed 6 years ago by
Replying to nbruin:
On sagesupport Rafael Greenblatt reports
sage: (incomplete_gamma(x,y).diff(x)).simplify() TypeError: ECL says: Error executing code in Maxima: gamma: wrong number of arguments.The problem probably arises because the function ends up separated from its arguments:
sage: incomplete_gamma(x,y).diff(x) D[0](gamma)(x, y)which might confuse the translator (the behaviour is consistent with just going by strings). The changes here might improve the situation. It's worth checking.
Does the same with the patch. Maybe include the fix here? Is it simple?
comment:13 in reply to: ↑ 12 Changed 6 years ago by
Replying to rws:
Does the same with the patch. Maybe include the fix here? Is it simple?
Might not be too bad. I think the problem is in sage.symbolic.expression_conversions.InterfaceInit.derivative (line 515 or so). You can see there that the string representation of a derivative expression gets assembled by using f.name()
. Replacing that by f._maxima_init_()
might already do a better job:
sage: gamma(x,y).operator().name() 'gamma' sage: gamma(x).operator().name() 'gamma' sage: gamma(x,y).operator()._maxima_init_() 'gamma_incomplete' sage: gamma(x).operator()._maxima_init_() 'gamma'
comment:14 followup: ↓ 15 Changed 6 years ago by
That gives:
sage: (incomplete_gamma(x,y).diff(x)).simplify() D[0](gamma)(x, y)
comment:15 in reply to: ↑ 14 Changed 6 years ago by
Replying to rws:
That gives:
sage: (incomplete_gamma(x,y).diff(x)).simplify() D[0](gamma)(x, y)
Cool! so it IS easy. Be sure to also test (I haven't checked the answer is correct, but at least it shouldn't raise an error):
sage: (incomplete_gamma(x,x+1).diff(x)).simplify().simplify() (x + 1)^(x  1)*e^(x  1) + D[0](gamma)(x, x + 1)
to check that both occurrences of f.name()
have been replaced. I check the rest of that file and didn't find any further suspicious uses of name
so after this, our maxima interface is probably perfect :).
comment:16 Changed 6 years ago by
See #16785 for a more complete fix.
comment:17 Changed 6 years ago by
 Commit changed from d8d7ee29d7d0f8cf9f884c4403fe5c36cdf3336d to a73c5e374b1ee694ba20af22654767cdf441c126
comment:18 Changed 6 years ago by
I also had to fix a doctest in integration where the given result didn't have enough precision because it came from maxima. Now the default is mpmath and that uncovered it.
comment:19 Changed 6 years ago by
 Commit changed from a73c5e374b1ee694ba20af22654767cdf441c126 to 1fc19e73cb83d39a17d2055ec9b661f1fb401dfd
comment:20 Changed 6 years ago by
 Merged in set to #16785
comment:21 Changed 6 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:22 Changed 6 years ago by
 Merged in #16785 deleted
Sorry, we should make this clearer  that field is one currently not used but which should be (!!!) that was for saying which version/beta of Sage a given ticket was merged in. I agree that might not be clear given the word "merge" meaning something else in git!
comment:23 Changed 6 years ago by
So, is there anything missing?
comment:24 Changed 6 years ago by
comment:25 Changed 6 years ago by
 Commit changed from 1fc19e73cb83d39a17d2055ec9b661f1fb401dfd to 9033be83a52eaabe0c0f896193923a040837e0cf
Branch pushed to git repo; I updated commit sha1. New commits:
9033be8  Merge branch 'develop' into t/16697/implement_symbolic_lower_incomplete_gamma_function

comment:26 Changed 6 years ago by
 Commit changed from 9033be83a52eaabe0c0f896193923a040837e0cf to 05195e75302bb598d61d724d8635b08cc1712846
Branch pushed to git repo; I updated commit sha1. New commits:
05195e7  Merge branch 'develop' into t/16697/implement_symbolic_lower_incomplete_gamma_function

comment:27 Changed 6 years ago by
Just to let you know: this conflicts with #17130.
comment:28 Changed 6 years ago by
See also the information here, which seems to be more information than the documentation of Maxima gives.
Implementation of the Incomplete Gamma function New Maxima User function: gamma_incomplete(a,z) The following features are implemented:  Evaluation for real and complex numbers in double float and bigfloat precision  Special values for gamma_incomplete(a,0) and gamma_incomplete(a,inf)  When $gamma_expand T expand the following expressions: gamma_incomplete(0,z) gamma_incomplete(n+1/2) gamma_incomplete(1/2n) gamma_incomplete(n,z) gamma_incomplete(n,z) gamma_incomplete(a+n,z) gamma_incomplete(an,z)  Mirror symmetry  Derivative wrt the arguments a and z  Implementation of the Generalized Incomplete Gamma function New Maxima User function: gamma_incomplete_generalized(a,z1,z2) The following features are implemented:  Evaluation for real and complex numbers in double float and bigfloat precision  Special values for: gamma_incomplete_generalized(a,z1,0) gamma_incomplete_generalized(a,0,z2), gamma_incomplete_generalized(a,z1,inf) gamma_incomplete_generalized(a,inf,z2) gamma_incomplete_generalized(a,0,inf) gamma_incomplete_generalized(a,x,x)  When $gamma_expand T and n an integer expand gamma_incomplete_generalized(a+n,z1,z2)  Implementation of Mirror symmetry  Derivative wrt the arguments a, z1 and z2  Implementation of the Regularized Incomplete Gamma function New Maxima User function: gamma_incomplete_regularized(a,z) The following features are implemented:  Evaluation for real and complex numbers in double float and bigfloat precision  Special values for: gamma_incomplete_regularized(a,0) gamma_incomplete_regularized(0,z) gamma_incomplete_regularized(a,inf)  When $gamma_expand T and n a positive integer expansions for gamma_incomplete_regularized(n+1/2,z) gamma_incomplete_regularized(1/2n,z) gamma_incomplete_regularized(n,z) gamma_incomplete_regularized(a+n,z) gamma_incomplete_regularized(an,z)  Derivative wrt the arguments a and z  Implementation of Mirror symmetry
comment:29 Changed 6 years ago by
We don't have gamma_incomplete_regularized
either. This would be a different ticket.
comment:30 followup: ↓ 69 Changed 6 years ago by
I'm going back to Pari as default since mpmath has similar problems as earlier Pari, see #17328 and https://github.com/fredrikjohansson/mpmath/issues/301
comment:31 Changed 6 years ago by
 Commit changed from 05195e75302bb598d61d724d8635b08cc1712846 to 6f59f3a6133b9654f349a1228a6bc9fe9c90c944
Branch pushed to git repo; I updated commit sha1. New commits:
6d10729  Simplify numerical evaluation of BuiltinFunctions

b6e1ed4  Merge remotetracking branches 'origin/u/jdemeyer/ticket/17131' and 'origin/u/jdemeyer/ticket/17133' into ticket/17130

382f97a  Merge branch 'u/jdemeyer/ticket/17130' of trac.sagemath.org:sage into 6.5beta1

7265989  17130: reviewer's patch: fix typo

c47dbd4  Fix Trac #17328 again in a better way

a486db2  Call the factorial() method of an Integer

9d3cbbd  Fix numerical noise

abab222  Fix more numerical noise

a383a5b  Merge branch 'u/jdemeyer/ticket/17130' of trac.sagemath.org:sage into t/16697/implement_symbolic_lower_incomplete_gamma_function

6f59f3a  16697: adaptations due to trac 17130

comment:32 Changed 6 years ago by
 Dependencies set to #17130
comment:33 Changed 5 years ago by
 Branch changed from u/rws/implement_symbolic_lower_incomplete_gamma_function to public/ticket/16697
 Commit changed from 6f59f3a6133b9654f349a1228a6bc9fe9c90c944 to 202b202c0fd19a4848997e7c18895a216d9ad57b
rebased on latest 6.5.beta3
also added one missing trac role
New commits:
202b202  Merge branch 'u/rws/implement_symbolic_lower_incomplete_gamma_function' of trac.sagemath.org:sage into 6.5.b3

comment:34 Changed 5 years ago by
 Commit changed from 202b202c0fd19a4848997e7c18895a216d9ad57b to f8fcbc25f545e412f6c1cf18d58e7f50f4e44cb3
Branch pushed to git repo; I updated commit sha1. New commits:
f8fcbc2  trac #16697 one more trac role missing was added

comment:35 followup: ↓ 36 Changed 5 years ago by
Frédéric, any comments on review, or was this just a driveby improvement?
Does the following (from the description) now come out better?
sage: hypergeometric([1],[b],x).simplify_hypergeometric()
Could we add the gamma(a,0,x)
interface for the lower gamma? Should we?
comment:36 in reply to: ↑ 35 ; followup: ↓ 37 Changed 5 years ago by
Replying to kcrisman:
Does the following (from the description) now come out better?
sage: hypergeometric([1],[b],x).simplify_hypergeometric()
(b  1)*x^(b + 1)*e^x*gamma_inc_lower(b  1, x)
Could we add the
gamma(a,0,x)
interface for the lower gamma? Should we?
A separate ticket, please?
comment:37 in reply to: ↑ 36 ; followup: ↓ 38 Changed 5 years ago by
sage: hypergeometric([1],[b],x).simplify_hypergeometric()
(b  1)*x^(b + 1)*e^x*gamma_inc_lower(b  1, x)
Nice.
Could we add the
gamma(a,0,x)
interface for the lower gamma? Should we?A separate ticket, please?
Seems quite reasonable. Do you agree this would be a useful addition? I only mention it because it seems that at least a couple 'competitors' support it, so presumably it is somewhat of a standard and not a surprise if Sage implements it.
comment:38 in reply to: ↑ 37 Changed 5 years ago by
Replying to kcrisman:
Could we add the
gamma(a,0,x)
interface for the lower gamma? Should we?A separate ticket, please?
Seems quite reasonable. Do you agree this would be a useful addition? I only mention it because it seems that at least a couple 'competitors' support it, so presumably it is somewhat of a standard and not a surprise if Sage implements it.
Any UI change that reduces surprise is fine with me. (Actually, I have a GUI development history and have read and care much about this subject)
comment:39 Changed 5 years ago by
For the record, I know nearly nothing about UI development! It was only a question. #17722
I'm going to hold off on looking at this in more detail in case chapoton already did but a brief glance looks good.
comment:40 Changed 5 years ago by
Note sympy apparently implements this as lowergamma
(?).
comment:41 Changed 5 years ago by
 Milestone changed from sage6.4 to sage6.6
 Status changed from needs_review to needs_work
Thanks, I was completely unaware. I think I will use their eval
. The diff
cannot be used in completeness because we don't know about the Meijer G function (EDIT: #17970), but I can steal half of it.
comment:42 Changed 5 years ago by
 Commit changed from f8fcbc25f545e412f6c1cf18d58e7f50f4e44cb3 to 5f4a7fbd8598ef3fb22d8cb61d199dfffea23a8c
comment:43 Changed 5 years ago by
 Dependencies changed from #17130 to #17130, sympy0.7.7
 Milestone changed from sage6.6 to sagepending
 Status changed from needs_work to needs_review
Three doctests fail now because we depend on sympy.erf._sage_()
which will be in Sympy0.7.7. So this is pending.
comment:44 followup: ↓ 45 Changed 5 years ago by
Is there a ticket for sympy0.7.7?
comment:45 in reply to: ↑ 44 Changed 5 years ago by
comment:46 Changed 5 years ago by
The diff link of this ticket shows not the correct diff but if you git trac checkout 16697
you get the right branch.
comment:47 followup: ↓ 48 Changed 5 years ago by
I tried to review this (per ticket:18210#comment:18) but quickly got confused. (This would be a lot easier on github.)
 Could one of you point me to the doc pertaining to
_sage_
? I did look, but the special sage functions page doesn't mention it.  There are some doctests regarding precision that have been obliterated. Was this intentional? Why?
 It seems like this new function (gamma_inc_lower) would be deprecated as soon as #17722 is implemented. Don't we want to take a minute to figure out a design that works for both issues?
I think if this patch implemented lowergamma as a special case of a single general gamma function we would end up with less if statements / edge cases / opportunities for bugs.
Edit: ... end up with *less* bugs
comment:48 in reply to: ↑ 47 Changed 5 years ago by
Replying to buck:
 Could one of you point me to the doc pertaining to
_sage_
?
https://github.com/sagemath/sage/blob/master/src/sage/structure/sage_object.pyx#L557 This is overridden where necessary so please see the resp. class. Probably you want to know about interfaces: https://github.com/sagemath/sage/blob/master/src/sage/interfaces/interface.py#L803 http://sagemath.org/doc/reference/interfaces/index.html
 There are some doctests regarding precision that have been obliterated. Was this intentional? Why?
Oh that's true, I don't know why that got ditched.
 It seems like this new function (gamma_inc_lower) would be deprecated as soon as #17722 is implemented. Don't we want to take a minute to figure out a design that works for both issues?
There should be no problem to support both interfaces, and without code duplication. We already have
sage: incomplete_gamma(1,2) e^(2) sage: gamma(1,2) e^(2) sage: gamma(2) 1
I think if this patch implemented lowergamma as a special case of a single general gamma function we would end up with less if statements / edge cases / opportunities for bugs.
Well that's the task for #17722, right. To have many doctests will help a good deal.
Note that even if you review this ticket (please add your real name to the ticket head in case) we would need to wait for Sympy0.7.7 to be released. But a review of the code and the math would leave only a make ptestlong
to finish it all.
EDIT: typos
comment:49 Changed 5 years ago by
 Reviewers set to Buck Evan
 Status changed from needs_review to needs_work
comment:50 Changed 5 years ago by
I left this as "needs work" because of your "Oh that's true, I don't know why that got ditched."
Could you merge this up with master and I'll attempt to review again?
Also, please show me how to run all the relevant tests, please?
I'm surprised sympy hasn't cut a release yet, still. If I'm counting correctly, it's been eight months since their last release.
comment:51 Changed 5 years ago by
Merged and attempted to run the doctests, and got this result:
./sage t src/sage/functions/other.py ⬆ ✱ ◼ too few successful tests, not using stored timings Running doctests with ID 2015072617395110ac5315. Git branch: master Using optional=mpir,python2,sage,scons Doctesting 1 file. sage t src/sage/functions/other.py ********************************************************************** File "src/sage/functions/other.py", line 1076, in sage.functions.other.Function_gamma_inc_lower._eval_ Failed example: gamma_inc_lower(1/2,2) Exception raised: Traceback (most recent call last): File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 496, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 858, in compile_and_execute exec(compiled, globs) File "<doctest sage.functions.other.Function_gamma_inc_lower._eval_[2]>", line 1, in <module> gamma_inc_lower(Integer(1)/Integer(2),Integer(2)) File "sage/symbolic/function.pyx", line 994, in sage.symbolic.function.BuiltinFunction.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875) res = super(BuiltinFunction, self).__call__( File "sage/symbolic/function.pyx", line 507, in sage.symbolic.function.Function.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887) res = g_function_eval2(self._serial, (<Expression>args[0])._gobj, File "sage/symbolic/pynac.pyx", line 185, in sage.symbolic.pynac.pyExpression_to_ex (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934) t = ring.SR.coerce(res) File "sage/structure/parent.pyx", line 1310, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682) cpdef coerce(self, x): File "sage/structure/parent.pyx", line 1339, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628) return (<map.Map>mor)._call_(x) File "sage/symbolic/ring.pyx", line 927, in sage.symbolic.ring.UnderscoreSageMorphism._call_ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428) return self.codomain()(a._sage_()) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sympy/core/mul.py", line 1467, in _sage_ s *= x._sage_() AttributeError: 'erf' object has no attribute '_sage_' ********************************************************************** File "src/sage/functions/other.py", line 1078, in sage.functions.other.Function_gamma_inc_lower._eval_ Failed example: gamma_inc_lower(1/2,1) Exception raised: Traceback (most recent call last): File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 496, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 858, in compile_and_execute exec(compiled, globs) File "<doctest sage.functions.other.Function_gamma_inc_lower._eval_[3]>", line 1, in <module> gamma_inc_lower(Integer(1)/Integer(2),Integer(1)) File "sage/symbolic/function.pyx", line 994, in sage.symbolic.function.BuiltinFunction.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875) res = super(BuiltinFunction, self).__call__( File "sage/symbolic/function.pyx", line 507, in sage.symbolic.function.Function.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887) res = g_function_eval2(self._serial, (<Expression>args[0])._gobj, File "sage/symbolic/pynac.pyx", line 185, in sage.symbolic.pynac.pyExpression_to_ex (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934) t = ring.SR.coerce(res) File "sage/structure/parent.pyx", line 1310, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682) cpdef coerce(self, x): File "sage/structure/parent.pyx", line 1339, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628) return (<map.Map>mor)._call_(x) File "sage/symbolic/ring.pyx", line 927, in sage.symbolic.ring.UnderscoreSageMorphism._call_ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428) return self.codomain()(a._sage_()) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sympy/core/mul.py", line 1467, in _sage_ s *= x._sage_() AttributeError: 'erf' object has no attribute '_sage_' ********************************************************************** File "src/sage/functions/other.py", line 1092, in sage.functions.other.Function_gamma_inc_lower._eval_ Failed example: gamma_inc_lower(9/2,37/7) Exception raised: Traceback (most recent call last): File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 496, in _run self.compile_and_execute(example, compiler, test.globs) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 858, in compile_and_execute exec(compiled, globs) File "<doctest sage.functions.other.Function_gamma_inc_lower._eval_[10]>", line 1, in <module> gamma_inc_lower(Integer(9)/Integer(2),Integer(37)/Integer(7)) File "sage/symbolic/function.pyx", line 994, in sage.symbolic.function.BuiltinFunction.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:10875) res = super(BuiltinFunction, self).__call__( File "sage/symbolic/function.pyx", line 507, in sage.symbolic.function.Function.__call__ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/function.cpp:6887) res = g_function_eval2(self._serial, (<Expression>args[0])._gobj, File "sage/symbolic/pynac.pyx", line 185, in sage.symbolic.pynac.pyExpression_to_ex (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/pynac.cpp:3934) t = ring.SR.coerce(res) File "sage/structure/parent.pyx", line 1310, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10682) cpdef coerce(self, x): File "sage/structure/parent.pyx", line 1339, in sage.structure.parent.Parent.coerce (/home/buck/trees/mine/sage/src/build/cythonized/sage/structure/parent.c:10628) return (<map.Map>mor)._call_(x) File "sage/symbolic/ring.pyx", line 927, in sage.symbolic.ring.UnderscoreSageMorphism._call_ (/home/buck/trees/mine/sage/src/build/cythonized/sage/symbolic/ring.cpp:10428) return self.codomain()(a._sage_()) File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sympy/core/add.py", line 732, in _sage_ s += x._sage_() File "/home/buck/trees/mine/sage/local/lib/python2.7/sitepackages/sympy/core/mul.py", line 1467, in _sage_ s *= x._sage_() AttributeError: 'erf' object has no attribute '_sage_' ********************************************************************** 1 item had failures: 3 of 12 in sage.functions.other.Function_gamma_inc_lower._eval_ [509 tests, 3 failures, 3.90 s]  sage t src/sage/functions/other.py # 3 doctests failed  Total time for all tests: 4.1 seconds cpu time: 2.5 seconds cumulative wall time: 3.9 seconds
comment:52 Changed 5 years ago by
I realized I needed to upgrade sympy for this branch to work. After that, the functions.other doctests pass, but a full ptest shows some failures that seem unrelated, but it's hard for me to be sure. I've attached the full result.
comment:53 Changed 5 years ago by
There's something not quite right with this branch. I get gamma_greek
if I use combine().
sage: e gamma(x, y) + gamma_inc_lower(x, y) sage: e.combine() gamma(x, y) + gamma_greek(x, y) sage: e(x=1, y=2) 1 sage: e.combine()(x=1, y=2) e^(2) + gamma_greek(1, 2)
comment:54 Changed 5 years ago by
 Branch changed from public/ticket/16697 to u/rws/166971
comment:55 Changed 5 years ago by
 Commit changed from 5f4a7fbd8598ef3fb22d8cb61d199dfffea23a8c to f3be6f16908734f6c6e752578653a3ca09189011
 Dependencies changed from #17130, sympy0.7.7 to sympy0.7.7
 Status changed from needs_work to needs_review
Cannot confirm your doctest failures (except those where sympy0.7.7 is needed), nor the combine problem. It looks like you tested with an older Sage the doctests of a newer Sage.
I have squashed all commits into one, and uploaded a new branch based on Sage6.8. In this branch the three missing doctests were added as well.
Really, a full test should only be done with sympy0.7.7 but if you think the rest is fine(?) then the missing long test eventually is done quickly by the patchbot.
New commits:
f3be6f1  16697: implement symbolic lower incomplete gamma function

comment:56 followup: ↓ 57 Changed 5 years ago by
I did the full test with sympy0.7.7, only after I got your new doctests in functions.other passing.
I reproduced the combinegammagreek problem with sage br, which I would think should avoid any versionmismatch issues no? (Apparently the maxima writer forgot that uppercase gamma is also greek?)
That said, I can't reproduce it anymore after merging your branch and running another sage br.
Should this not come out as gamma_inc_lower?
./sage br sage: maxima('gamma_greek(x, y)') gamma_greek(x,y)
I do see that _sage_
of the same expression yields gamma_inc_lower. I suppose I don't know enough about the coersion going on here. I did try looking in the docs but didn't find anything that helped me understand this particular aspect.
sage: maxima('gamma_greek(x, y)') gamma_greek(x,y) sage: maxima('gamma_greek(x, y)')._sage_() gamma_inc_lower(x, y) sage: maxima('gamma_greek(x, y)').simplify() simplify(gamma_greek(x,y)) sage: maxima('gamma_greek(x, y)')._sage_().simplify() gamma_inc_lower(x, y)
comment:57 in reply to: ↑ 56 Changed 5 years ago by
Replying to buck:
I did the full test with sympy0.7.7, only after I got your new doctests in functions.other passing.
How did you do that. Are there release tarballs of sympy0.7.7? Note that having it on your machine does not mean Sage will use it. The version used is that in the upstream directory of Sage.
comment:58 followup: ↓ 59 Changed 5 years ago by
I installed their master branch to the local/ tree. Putting local/bin on the $PATH makes it close enough to a virtualenv that pip will Just Work.
I needed this to get the doctests working as well, so I presumed it was also your procedure. If not, how were you getting your tests to pass?
comment:59 in reply to: ↑ 58 Changed 5 years ago by
Replying to buck:
I needed this to get the doctests working as well, so I presumed it was also your procedure. If not, how were you getting your tests to pass?
Never said I did. The ticket has pending and dependency set as well. But thanks anyway 8) So, except from a final test, would you say your review is positive?
comment:60 Changed 5 years ago by
There's doctest coverage missing (for the deprecated function), and this patch doesn't fix the numerical instability in incomplete gamma as promised elsewhere.
sage: gamma_inc_lower(25, 14.5).n() 6.63538851954338e22 sage: gamma_inc_lower(25, 14.5).n(algorithm='mpmath') 6.63538851954338e22 sage: gamma_inc_lower(25, 14.5).n(algorithm='pari') 6.63538851954338e22
comment:61 Changed 5 years ago by
Of note, gamma (even incomplete) is strictly positive in the reals; it's an integral of a strictly positive function.
https://en.wikipedia.org/wiki/Incomplete_gamma_function#Definition
comment:62 Changed 5 years ago by
Wolfram gives the value of the same as 4.7e21, which seems correct.
http://www.wolframalpha.com/input/?i=Gamma%5B25%2C+0%2C+14.5%5D
comment:63 followup: ↓ 66 Changed 5 years ago by
Actually, if I ask pari directly, it gets the correct value, so maybe the algorithm argument is broken?
sage: pari('gamma(25)  incgam(25, 14.5)') 4.71197173824555 E21 sage: pari('incgamc(25, 14.5)') 4.71197173824555 E21
comment:64 followup: ↓ 65 Changed 5 years ago by
Same story if I ask mpmath directly. I can't imagine what's wrong.
sage: call(mpmath.gammainc, 25, 0, 14.5) 4.71197173824555e21
comment:65 in reply to: ↑ 64 Changed 5 years ago by
Replying to buck:
Same story if I ask mpmath directly. I can't imagine what's wrong.
'algorithm' isn't propagated to evalf
so we always get the buggy pari values. As we would have to switch the default anyway as soon as a later pari version fixes the bug, I'll now simply disable pari. We'll have to live with mpmath
's 53 bits for now.
comment:66 in reply to: ↑ 63 Changed 5 years ago by
Replying to buck:
Actually, if I ask pari directly, it gets the correct value, so maybe the algorithm argument is broken?
sage: pari('gamma(25)  incgam(25, 14.5)') 4.71197173824555 E21 sage: pari('incgamc(25, 14.5)') 4.71197173824555 E21
This works because it uses the gp interface (the libpari might be broken on our side). Ah, that's two different bugs. However, even if it is in our interface to libpari and we fix this, or if we use the gp interface, there is still the unfixed pari bug at http://pari.math.ubordeaux.fr/cgibin/bugreport.cgi?bug=1689PARI/GP
comment:67 Changed 5 years ago by
 Commit changed from f3be6f16908734f6c6e752578653a3ca09189011 to 86618379012a463b10f0d392f57403755300236a
Branch pushed to git repo; I updated commit sha1. New commits:
8661837  16697: change algorithm; add, fix doctests

comment:68 Changed 5 years ago by
Actually the 53bit restriction applies only to larger values, so all is not lost.
comment:69 in reply to: ↑ 30 Changed 4 years ago by
Replying to rws:
I'm going back to Pari as default since mpmath has similar problems as earlier Pari, see #17328 and https://github.com/fredrikjohansson/mpmath/issues/301
The mpmath issue is now fixed as well so we have both options, mpmath or Pari/GP.
comment:70 Changed 4 years ago by
You could also compute the incomplete gamma function with Arb.
comment:71 Changed 4 years ago by
 Branch changed from u/rws/166971 to u/rws/166972
comment:72 Changed 4 years ago by
 Commit changed from 86618379012a463b10f0d392f57403755300236a to c6be42fd29966c4b824010c998820c37169c89c0
 Dependencies changed from sympy0.7.7 to #20185
 Milestone changed from sagepending to sage7.2
New commits:
c6be42f  Merge branch 'u/rws/166971' of git://trac.sagemath.org/sage into i16697

comment:74 Changed 4 years ago by
Wanna review?
comment:75 Changed 4 years ago by
 Commit changed from c6be42fd29966c4b824010c998820c37169c89c0 to 157b268d4ac45de049089e633809f89d2c3ab84e
comment:76 Changed 4 years ago by
 Status changed from needs_work to needs_review
comment:77 Changed 4 years ago by
Current 7.3.beta5 Sage builds fine with these modifications. Doctests all pass. Documentation builds.
Random numeric tests accurate. Function plots. One curious difference from gamma_inc
:
sage: gamma_inc_lower(a,x).diff(x) x^(a  1)*e^(x) sage: gamma_inc(a,x).diff(x) D[1](gamma)(a, x)
Looks good to me. Sympy already updated: any other reason not to merge?
comment:78 Changed 4 years ago by
 Reviewers changed from Buck Evan to Buck Evan, Paul Masson
 Status changed from needs_review to positive_review
comment:79 Changed 4 years ago by
Thanks.
comment:80 Changed 4 years ago by
 Branch changed from u/rws/166972 to 157b268d4ac45de049089e633809f89d2c3ab84e
 Resolution set to fixed
 Status changed from positive_review to closed
We don't need all of
gamma, gamma_inc, incomplete_gamma
as symbolic function if they all mean the same. Some of them are probably there for user convenience or because of legacy. I think we want only one spelling forgamma_upper
, whatever it may be. Thegamma(a,x)
convention seems fairly prominent in computer algebra, but is a poor translation of math notation, where the difference between upper and lower is made with case (and indeed, the complete gamma function tends to be capital gamma. I don't think I've ever seen different).Because of tab completion, you definitely want a binding available that starts with
gamma
. I'd be fine withgamma_lower
but if you want to go withgamma_lower_incomplete
, that's fine with me too. So, I'd proposegamma(a,x)
andgamma_inc(a,x)
. Just implement a symbolic functiongamma_lower
(or modified spelling) to correspond to maxima's gamma_greek.