#12455 closed enhancement (fixed)
Make Airy functions symbolic
Reported by:  Oscar Gerardo Lazo Arjona  Owned by:  Ralf Stephan 

Priority:  major  Milestone:  sage6.6 
Component:  symbolics  Keywords:  Airy functions sd40.5 sd48 
Cc:  KarlDieter Crisman, Burcin Erocal, Benjamin Jones, Fredrik Johansson, Eviatar Bach  Merged in:  
Authors:  Oscar Gerardo Lazo Arjona, Benjamin Jones, Douglas McNeil, Eviatar Bach, Ralf Stephan  Reviewers:  Eviatar Bach, KarlDieter Crisman, Burcin Erocal, Ralf Stephan, Jeroen Demeyer, Marc Mezzarobba 
Report Upstream:  N/A  Work issues:  
Branch:  2f6945a (Commits, GitHub, GitLab)  Commit:  
Dependencies:  #12289, #17130  Stopgaps: 
Description (last modified by )
As discussed in sagesupport.
Currently sage can evaluate airy functions numerically:
sage: airy_ai(1.4) 0.0820380498076
but it doesn't work symbolically
sage: airy_ai(x) ... TypeError: Cannot evaluate symbolic expression to a numeric value.
We should make it symbolical for both airy_ai and airy_bi, as well as their derivatives.
Attachments (8)
Change History (97)
comment:1 Changed 11 years ago by
Component:  PLEASE CHANGE → symbolics 

Owner:  changed from tbd to Burcin Erocal 
comment:2 Changed 11 years ago by
Owner:  changed from Burcin Erocal to Oscar Gerardo Lazo Arjona 

comment:3 Changed 11 years ago by
Description:  modified (diff) 

Changed 11 years ago by
Attachment:  trac_12455symbolic_airy.patch added 

comment:4 Changed 11 years ago by
comment:5 Changed 11 years ago by
Status:  new → needs_review 

comment:6 Changed 11 years ago by
Cc:  Fredrik Johansson added 

Status:  needs_review → needs_work 
Summary:  Make Airy functions symbolical → Make Airy functions symbolic 
Good start. A few responses.
 You'll need to have more methods. We should probably use mpmath to evaluate these functions in general, though using the SciPy version could be useful over RDF. See #11888 for a very recent example of this kind of thing and how to implement it.
 That should also fix precision issues, if properly done, I think.
 SciPy has evaluation for the airy primes. I think that Maxima has these too. (Cc:ing FJ in case he has plans to add these to mpmath.)
 We should have translations of these to Maxima and friends. That will probably help us name them. What do Mathematica and Maple call them?
 All methods, including initialization methods, need doctests. Many of the new symbolic functions added at wiki:symbolics/functions will have nice models to follow.
Thanks for getting us a start on this! That's great.
comment:7 followup: 8 Changed 11 years ago by
mpmath has the derivatives (as well as integrals)  just use the optional 'derivative' parameter.
comment:8 Changed 11 years ago by
mpmath has the derivatives (as well as integrals)  just use the optional 'derivative' parameter.
Ok, I didn't realize that was what that parameter was about. Though in retrospect it seems obvious!
comment:9 Changed 11 years ago by
On second thought, I think it would be better to use the airy equation to calculate derivatives or order higher than 1. Like
sage: airy_ai(2,x) x*airy_ai(x) sage: airy_ai(3,x) airy_ai(x)+x*airy_ai_prime(x) sage: diff(airy_ai(x),x,2) x*airy_ai(x) sage: diff(airy_ai(x),x,3) airy_ai(x)+x*airy_ai_prime(x)
which is very likey to be the way mpmath calculates higher order derivatives. Integrals however, would be returned as:
sage: airy_ai(1,x) airy_ai(1,x) sage: integral(airy_ai(x),x) airy_ai(1,x)
what do you think?
Changed 11 years ago by
Attachment:  trac_12455symbolic_airy2.patch added 

comment:10 followup: 11 Changed 11 years ago by
Status:  needs_work → needs_review 

I just added a new patch. The new version includes generalized derivatives, evaluation with mpmath, and special values of the functions and their derivatives. Just a one doubt, the coverage is:
oscar@oscarnetbook:~$ sage coverage airy.py SCORE /home/oscar/sage/my_patches/airy.py: 76% (20 of 26) Missing documentation: * __init__(self): * __init__(self): * __init__(self): * __init__(self): * __init__(self): * __init__(self): Possibly wrong (function name doesn't occur in doctests): * _derivative_(self, x, diff_param=None): * _eval_(self, x): * _evalf_(self, x, parent=None): * _derivative_(self, x, diff_param=None): * _eval_(self, x): * _evalf_(self, x, parent=None): * _derivative_(self, alpha, *args, **kwds): * _eval_(self, alpha, *args): * _evalf_(self, alpha, x, parent=None): * _derivative_(self, x, diff_param=None): * _eval_(self, x): * _evalf_(self, x, parent=None): * _derivative_(self, x, diff_param=None): * _eval_(self, x): * _evalf_(self, x, parent=None): * _derivative_(self, alpha, *args, **kwds): * _eval_(self, alpha, *args): * _evalf_(self, alpha, x, parent=None):
Is that important?
comment:11 followups: 12 14 Changed 11 years ago by
Is that important?
The second part isn't, as you are implicitly testing these 'hidden' functions. By the way,
Examples::
should be
EXAMPLES::
However, the first part (the initialization methods) is important for our coverage. You can just do a couple from the big examples that you have.
Do these pass doctests? I'm surprised that
sage: airy_ai_simple= FunctionAiryAiSimple()
would work when you run tests, assuming you didn't import FunctionAiryAiSimple
into the global namespace.
Anyway, overall on a quick glance this looks great; unfortunately, I won't have time to review it properly soon  hopefully someone else will, because you put a lot of great work into it and we should totally have these symbolic. Thanks!
comment:12 Changed 11 years ago by
Do these pass doctests? I'm surprised that
sage: airy_ai_simple= FunctionAiryAiSimple()would work when you run tests, assuming you didn't import
FunctionAiryAiSimple
into the global namespace.
It looks like they do:
oscar@oscarnetbook:~$ sage coverage airy.py sage t "/home/oscar/sage/my_patches/airy.py" [51.5 s]  All tests passed! Total time for all tests: 51.7 seconds
Why shouldn't they? I'll take care of the init functions.
comment:13 Changed 11 years ago by
I'm sorry, that should be:
oscar@oscarnetbook:~$ sage t airy.py sage t "/home/oscar/sage/my_patches/airy.py" [51.5 s]  All tests passed! Total time for all tests: 51.7 seconds
(the command was sage t)
comment:14 Changed 11 years ago by
Status:  needs_review → needs_work 

sage: airy_ai_simple= FunctionAiryAiSimple()
would work when you run tests, assuming you didn't import
FunctionAiryAiSimple
into the global namespace.
I'm just surprised this doesn't cause trouble.
On another note, this apparently does something weird when applied to 5.0.beta4. Namely, Sage won't start:
> 65 from sage.functions.all import sin, cos ImportError: cannot import name sin Error importing ipy_profile_sage  perhaps you should run %upgrade? WARNING: Loading of ipy_profile_sage failed.
I'll spare you the rest of the traceback. I think there is some kind of circular import thing going on here, but I don't understand imports that well. Perhaps moving the import of airy to further down (after trig functions) would help  that's a totally uninformed guess, of course.
Changed 11 years ago by
Attachment:  trac_12455symbolic_airy3.patch added 

comment:15 Changed 11 years ago by
Authors:  → Oscar Gerardo Lazo Arjona 

Status:  needs_work → needs_review 
I just added a new patch, now with 100 % test coverage, but I still get this message:
oscar@oscarnetbook:~$ sage coverage /home/oscar/sage/my_patches/airy.py  /home/oscar/sage/my_patches/airy.py ERROR: Please add a `TestSuite(s).run()` doctest. SCORE /home/oscar/sage/my_patches/airy.py: 100% (26 of 26) 
What is this TestSuite? thing? I also changed the order in which functions are initialized, so that airy_ai_general is initialized first. Doing it last made some symbolic operations, such as simplify not work (It said something about airy_ai requiring 2 arguments).
comment:16 Changed 11 years ago by
Reviewers:  → Benjamin Jones 

Hi Oscar, I haven't looked over your patch very closely yet, but I plan to. One comment on first glance: in several places you call
return mpmath_utils.call(airy_bi_mpmath, x, derivative=1, parent=RR)
but I think we want to preserve the parent of x
instead of forcing it to be RR
. Importing the parent
function from sage.structure.coerce
using a different name like sage_parent
(because as burcin pointed out in one of my tickets, parent is the name of the parameter in _evalf_
) and doing something like
from sage.structure.coerce import parent as sage_parent R = parent or sage_parent(x) return mpmath_utils.call(airy_bi_mpmath, x, derivative=1, parent=R)
would do the trick I think.
Other comment: can we add conversions to Maxima along with the Mma conversion you included? Here is a link to the appropriate chapter in the manual: http://maxima.sourceforge.net/docs/manual/en/maxima_15.html#SEC80
comment:17 Changed 11 years ago by
Status:  needs_review → needs_work 

The patch applies to 5.0.beta6 cleanly, but upon sage br
I get an import error ending with:
/home/jonesbe/sage/sage5.0.beta6/local/lib/python2.7/sitepackages/sage/gsl/dft.py in <module>() 63 from sage.rings.real_mpfr import RR 64 from sage.rings.all import I > 65 from sage.functions.all import sin, cos 66 from sage.gsl.fft import FastFourierTransform 67 from sage.gsl.dwt import WaveletTransform ImportError: cannot import name sin Error importing ipy_profile_sage  perhaps you should run %upgrade? WARNING: Loading of ipy_profile_sage failed.
Seems like the same thing kcrisman ran into with the previous patch applied to 5.0.beta4.
comment:18 Changed 11 years ago by
Work issues:  → circular import, doctest failures 

I found the cause of the problem in comment 17. There is a circular import going on because
from airy import airy_ai, airy_bi
occurs at the top of sage/functions/all.py
. If you move it to the bottom of the file, sage starts just fine.
There a several doctests that fail, however. Oscar, I think that running sage coverage
only checks to see if there are doctest for every function, it doesn't actually run the tests. Use
sage t devel/sage/sage/functions/airy.py
to run the tests and get feedback.
comment:19 Changed 11 years ago by
Authors:  Oscar Gerardo Lazo Arjona → Oscar Gerardo Lazo Arjona, Benjamin Jones 

Reviewers:  Benjamin Jones 
Here at SD 40.5, we're going to pick this ticket up, do the work, and get it into sage.
comment:20 Changed 11 years ago by
Keywords:  sd40.5 added 

comment:21 Changed 11 years ago by
Okay, I'm posting this for future reference. I've attempted to preserve as much as possible of the original code while switching to the "newstyle" dictionaryargument .n() approach we're working on in #12289, but I'm setting it to "needs work" myself while we think through some of the consequences of the switch. Some of the _evalf_ stuff violates DRY and I'm not yet sure of the best way to deal with it.
As well, the patch currently segfaults in testing when it computes beta(0.5, 0.5) due to some problem with the current #12289 package, which I suspect is unrelated. But I think the new approach is beginning to take shape.
Changed 11 years ago by
Attachment:  trac_12455_newstyle_airy.patch added 

newstyle rewrite, version 1
comment:22 Changed 11 years ago by
Dependencies:  → #12289 

comment:23 Changed 11 years ago by
Oh, yeah: and #13028 was a significant nuisance while working on this.
comment:24 Changed 9 years ago by
Cc:  Eviatar Bach added 

Changed 9 years ago by
Attachment:  trac_12455_newstyle_airy2.patch added 

comment:25 Changed 9 years ago by
New patch, which should pass all doctests once #12289 is merged.
It makes the following changes:
 Changing an incorrect
airy_bi
identity  Adding
airy.py
to the documentation  Checking whether
n
is an integer (for some reason mpmath is able to evaluate numerically with nonintegraln
)  Formatting changes
 Removing the parent's precision check because it wasn't used
 Removing the check for the
parent
keyword because Burcin told me to
Patchbot apply trac_12455_newstyle_airy.patch trac_12455_newstyle_airy2.patch
comment:26 Changed 9 years ago by
Keywords:  sd48 added 

comment:27 Changed 9 years ago by
Authors:  Oscar Gerardo Lazo Arjona, Benjamin Jones → Oscar Gerardo Lazo Arjona, Benjamin Jones, Eviatar Bach 

Description:  modified (diff) 
Status:  needs_work → needs_review 
Needs review, then? Note that I had to rebase #12289.
comment:28 Changed 9 years ago by
Description:  modified (diff) 

Reviewers:  → Eviatar Bach, KarlDieter Crisman 
Patchbot apply trac_12455newstyleairyrebase.patch and trac_12455_newstyle_airy2.patch
I don't know that either of the needs work issues are still there...
comment:29 Changed 9 years ago by
This needs a trivial extra patch to fix
sage t sage/functions/special.py ********************************************************************** File "sage/functions/special.py", line 389, in sage.functions.special._init Failed example: spherical_harmonic(3,2,1,2) Expected: 15/4*sqrt(7/30)*e^(4*I)*sin(1)^2*cos(1)/sqrt(pi) Got: 15/4*sqrt(7/30)*cos(1)*e^(4*I)*sin(1)^2/sqrt(pi) **********************************************************************
which is really a rebase issue off of #9880, no worries.
comment:31 Changed 9 years ago by
Description:  modified (diff) 

Apply trac_12455newstyleairyrebase.patch and trac_12455newstyleairy2rebase.patch
comment:32 Changed 9 years ago by
Eviatar, how much would you say still needs to be reviewed? (In the sense that you have not yet given it positive review.) Just your patch?
(I'm running doctests now.)
comment:34 Changed 9 years ago by
I think I was fairly thorough, but I haven't positivereviewed since my patch hasn't been looked at by someone else.
Changed 9 years ago by
Attachment:  trac_12455newstyleairyrebase.patch added 

comment:35 Changed 9 years ago by
Okay, now I have to fix something in the other one... sigh. Final version coming soon, it does pass tests!
Changed 9 years ago by
Attachment:  trac_12455newstyleairy2rebase.patch added 

comment:36 Changed 9 years ago by
Patchbot, apply trac_12455newstyleairyrebase.patch and trac_12455newstyleairy2rebase.patch
comment:37 Changed 9 years ago by
(for some reason mpmath is able to evaluate numerically with nonintegral n)
But this is even in the documentation you wrote!
Return the `\alpha`th order fractional derivative with respect to `z`.
"Fractional", right? So ... ? Plus, you do not make this change in airy_bi, only airy_ai, for some reason.
Another question:
sage: (plot(airy_bi(x), (x, 10, 5)) +\
Are we allowing this kind of continuation in doctests still? I can't remember but seem to recall something about this being a problem.
Otherwise this all seems fine.
comment:38 Changed 9 years ago by
Status:  needs_review → needs_work 

I didn't write it. But looking at the mpmath documentation, it should work. It didn't work for most values before my patch anyway, but I'll see what I can do.
comment:39 Changed 9 years ago by
I didn't write it.
Good point, sorry! In fact, it's just copied from the mpmath doc. But now you have taken charge :) Unfortunately, I can't find a lot of independent implementations of this...
Changed 9 years ago by
Attachment:  trac_12455airy_review.patch added 

comment:40 Changed 9 years ago by
Authors:  Oscar Gerardo Lazo Arjona, Benjamin Jones, Eviatar Bach → Oscar Gerardo Lazo Arjona, Benjamin Jones, D. S. McNeil, Eviatar Bach 

Description:  modified (diff) 
Reviewers:  Eviatar Bach, KarlDieter Crisman → Eviatar Bach, KarlDieter Crisman, Burcin Erocal 
trac_12455airy_review.patch fixes a couple of problems:
airy_{a,b}i_general
should evaluate toairy_{a,b}i_simple
,airy_{a,b}i_prime
, etc. depending on the first parameter
 differentiating
airy_{a,b}i_general
in the first parameter is not allowed
_evalf_
should not raise errors for unrecognized algorithm argument
This is still needs work because we use indirect doctests everywhere. There is no reason to go through the airy_{a,b}i
wrapper functions. We should call the symbolic functions directly in the doctests. There are also a lot of code paths that are not tested. I changed the fractional order behavior, but didn't need to change any doctests.
It would be great if someone else can fix/add doctests. I will move on to something else now.
comment:41 Changed 9 years ago by
Milestone:  sage5.11 → sage5.12 

comment:42 Changed 9 years ago by
This patch depends on a new release of Pynac and other fixes to make the algorithm
keyword work sensibly. Also, I don't see much point in having the Maxima implementation as an option, considering the fact that it doesn't accept complex input, doesn't have arbitrary precision, and is slower than mpmath (doesn't appear to scale better either).
I'd hate to delay this patch longer, especially considering that the Airy functions are probably among the mostused special functions. Could we remove the Maxima option for now and perhaps add it in the future, maybe along with a patch that adds a SciPy? option as suggested in one of the comments?
comment:43 Changed 9 years ago by
I'm fine with removing Maxima from the options for numerical evaluation (numerical is not generally where Maxima shines). I agree with @burcin, though, that indirect doctests should be fixed wherever possible and become direct tests and that the branch coverage should be higher.
What exactly is the issue with having the Maxima option? Is it the limited precision and domain? We could always check that inputs are okay whenever Maxima is selected and raise an exception otherwise.
comment:44 Changed 9 years ago by
Milestone:  sage6.1 → sage6.2 

comment:45 Changed 9 years ago by
Milestone:  sage6.2 → sage6.3 

comment:46 Changed 8 years ago by
Branch:  → u/rws/make_airy_functions_symbolic 

comment:47 Changed 8 years ago by
Commit:  → 22731c9d5b976301d282e3b48e259f5f13d4b8bd 

comment:48 Changed 8 years ago by
Replying to benjaminfjones:
What exactly is the issue with having the Maxima option? Is it the limited precision and domain? We could always check that inputs are okay whenever Maxima is selected and raise an exception otherwise.
It's useless, especially when scipy is implemented as algorithm. OTOH, it introduces more code paths to test and deepens a dependency that is unwanted.
Oh, and scipy is a bit faster:
sage: timeit("airy_bi(2).n(algorithm='maxima')") 625 loops, best of 3: 685 µs per loop sage: timeit("airy_bi(2).n(algorithm='scipy')") 625 loops, best of 3: 124 µs per loop
comment:49 Changed 8 years ago by
Commit:  22731c9d5b976301d282e3b48e259f5f13d4b8bd → 515e343290448d2bbe5e75f88accea814be9215f 

comment:50 Changed 8 years ago by
Authors:  Oscar Gerardo Lazo Arjona, Benjamin Jones, D. S. McNeil, Eviatar Bach → Oscar Gerardo Lazo Arjona, Benjamin Jones, D. S. McNeil, Eviatar Bach, Ralf Stephan 

Status:  needs_work → needs_review 
Work issues:  circular import, doctest failures 
Everything was reviewed up to my recent changes:
 merged develop
 removal of maxima and inclusion of scipy for numerics
 replacement of indirect with direct doctests (still 100% coverage)
 removal of hold_derivate keyword from
airy_ai/bi_general()
where it wasn't implemented (it is still inairy_ai/bi()
wrapper functions  small index at the top of documentation for orientation, because of confusing presentation order of functions, which cannot be controlled, sadly
So please review.
comment:51 Changed 8 years ago by
Milestone:  sage6.3 → sage6.4 

comment:52 Changed 8 years ago by
Status:  needs_review → needs_work 

one failing doctest, see patchbot report
comment:53 Changed 8 years ago by
Commit:  515e343290448d2bbe5e75f88accea814be9215f → 8e76828f9f5c988b0429230cd1050c6086fb730b 

comment:54 Changed 8 years ago by
Owner:  changed from Oscar Gerardo Lazo Arjona to Ralf Stephan 

comment:55 Changed 8 years ago by
Owner:  changed from Ralf Stephan to Oscar Gerardo Lazo Arjona 

comment:56 Changed 8 years ago by
Status:  needs_work → needs_review 

comment:57 Changed 8 years ago by
Branch:  u/rws/make_airy_functions_symbolic → public/ticket/12455 

Commit:  8e76828f9f5c988b0429230cd1050c6086fb730b → 95526065b2703e42378838747055bb6bbc409402 
comment:58 Changed 8 years ago by
Commit:  95526065b2703e42378838747055bb6bbc409402 → 7102227617bf289b2620636e397b92c081f9715a 

Branch pushed to git repo; I updated commit sha1. New commits:
7102227  Merge with 6.4.beta4

comment:59 Changed 8 years ago by
Commit:  7102227617bf289b2620636e397b92c081f9715a → 5b731d32d7aec6bdb88acf777253c777ccb6f509 

Branch pushed to git repo; I updated commit sha1. New commits:
5b731d3  trac #12455 change use of Airy as example of maxima function

comment:60 Changed 8 years ago by
Commit:  5b731d32d7aec6bdb88acf777253c777ccb6f509 → 39deab4d13c17120737a875a4b2744a67ce61227 

Branch pushed to git repo; I updated commit sha1. New commits:
39deab4  trac #12455 formatting doc and code

comment:61 Changed 8 years ago by
Reviewers:  Eviatar Bach, KarlDieter Crisman, Burcin Erocal → Eviatar Bach, KarlDieter Crisman, Burcin Erocal, Ralf Stephan 

Status:  needs_review → needs_work 
sage t long src/sage/functions/airy.py ********************************************************************** File "src/sage/functions/airy.py", line 404, in sage.functions.airy.airy_ai Failed example: plot(airy_ai(x), (x, 10, 5)) + plot(airy_ai_prime(x), (x, 10, 5), color='red') Expected nothing Got: Graphics object consisting of 2 graphics primitives ********************************************************************** File "src/sage/functions/airy.py", line 799, in sage.functions.airy.airy_bi Failed example: plot(airy_bi(x), (x, 10, 5)) + plot(airy_bi_prime(x), (x, 10, 5), color='red') Expected nothing Got: Graphics object consisting of 2 graphics primitives
comment:62 Changed 8 years ago by
Commit:  39deab4d13c17120737a875a4b2744a67ce61227 → fbd6c357dfdba94d7630d6f2becb411f6169f004 

Branch pushed to git repo; I updated commit sha1. New commits:
fbd6c35  trac #12455 plot output

comment:63 Changed 8 years ago by
Status:  needs_work → needs_review 

comment:64 Changed 8 years ago by
Description:  modified (diff) 

comment:65 Changed 8 years ago by
Just to make you aware: this conflicts with #17130. When either of these tickets gets positive_review, the other should be rebased.
comment:66 followup: 69 Changed 8 years ago by
Status:  needs_review → needs_info 

And why the change to def hypergeometric_U
? The new code seems quite hackish, why is it needed and how does it relate to this ticket?
comment:67 Changed 8 years ago by
Status:  needs_info → needs_work 

These should be an error:
sage: airy_ai(3).n(algorithm='scipy', prec=200) 0.006591139357460719 sage: airy_ai(3).n(algorithm='whatever') 0.00659113935746072
And I don't like this either (parent should be RR
):
sage: parent(airy_ai(3).n(algorithm='scipy')) Real Double Field
comment:68 Changed 8 years ago by
What's the point of
if len(args) > 0: raise TypeError(("symbolic function airy_ai takes at most 3 arguments " "({} given)").format(len(args) + 3))
why not simply remove *args
completely then?
comment:69 Changed 8 years ago by
Replying to jdemeyer:
And why the change to
def hypergeometric_U
? The new code seems quite hackish, why is it needed and how does it relate to this ticket?
I think that unrelated patch can be safely removed because scipy evaluation is replaced by mpmath in #14896 (of course hoping that that gets reviewed at some time).
comment:70 Changed 8 years ago by
Commit:  fbd6c357dfdba94d7630d6f2becb411f6169f004 → 61847c43253572e53c6ed25fe208f4eb19fd1b87 

Branch pushed to git repo; I updated commit sha1. New commits:
15e7e34  Merge branch 'develop' into t/12455/public/ticket/12455

2c0931c  12455: remove fishy code in hypergeometric_U()

b4213d3  12455: with algorithm=scipy return reals for real argument

b0841c9  12455: catch attempts to exceed precision with algorithm=scipy

484a615  12455: catch unknown evalf algorithms

58e006c  12455: remove superfluous args and check

870e003  12455: fix plot doctests

61847c4  Merge branch 'public/ticket/12455' of trac.sagemath.org:sage into t/12455/public/ticket/12455

comment:71 Changed 8 years ago by
Status:  needs_work → needs_review 

comment:72 Changed 8 years ago by
Commit:  61847c43253572e53c6ed25fe208f4eb19fd1b87 → aac86a20bbb84df905e4000dfb79f125247cf85b 

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

01614f7  Merge branch 'u/jdemeyer/ticket/17130' of trac.sagemath.org:sage into t/12455/public/ticket/12455

aac86a2  12455: simplifications due to trac 17130

comment:73 Changed 8 years ago by
Dependencies:  #12289 → #12289, #17130 

comment:74 Changed 8 years ago by
Frédéric, how much of this did you positively review up to now? In principle you and rws can review each other's contributions here. It would take me a while to get up to speed here.
comment:75 Changed 8 years ago by
a typo in line 5 of the doc:
Airy functions are solutions to the differential equation `f''(z) +f(z)x=0`.
The differential equation is wrong, should be f''  x f = 0
comment:76 Changed 8 years ago by
Commit:  aac86a20bbb84df905e4000dfb79f125247cf85b → 070e72855b15c138e9d22ae8325633d84ef49f69 

comment:77 Changed 8 years ago by
Milestone:  sage6.4 → sage6.6 

Owner:  changed from Oscar Gerardo Lazo Arjona to Ralf Stephan 
comment:79 Changed 8 years ago by
What exactly still needs review here?
The code looks pretty good to me overall, but there are lots of things I don't understand in detail. (For a simple example, what is the motivation for splitting the implementation in so many unrelated classes?) And yet I'm tempted to give this ticket positive review (leaving possible remaining issues for later), since many other people have looked at it and it is clearly an improvement over what sage currently has.
comment:80 followups: 81 84 Changed 8 years ago by
More nitpicking, not necessarily for this ticket:
 Raising a
ValueError
inFunctionAiryAiGeneral._derivative_
whendiff_param == 0
may not be the most appropriate, since (if I'm not mistaken) the partial derivative would make sense mathematically.  Is it necessary to specialcase
alpha == 0
etc. inFunctionAiryAiGeneral._evalf_
?
comment:81 Changed 8 years ago by
Replying to mmezzarobba:
 Is it necessary to specialcase
alpha == 0
etc. inFunctionAiryAiGeneral._evalf_
?
Scratch that, I misread the code.
comment:82 Changed 8 years ago by
Commit:  070e72855b15c138e9d22ae8325633d84ef49f69 → 91530d08a7a37bc03876962c1a1ae0bca10bfd70 

Branch pushed to git repo; I updated commit sha1. New commits:
91530d0  Ai/Bi: doc fixes and clarifications

comment:83 Changed 8 years ago by
One last thing: IMO hold_derivative
should be True
by default in airy_ai
and airy_bi
, except perhaps when the differentiation order is one. But I don't know if that's consistent with the way things are done in other parts of sage symbolics. Thoughts?
comment:84 followup: 86 Changed 8 years ago by
Replying to mmezzarobba:
x should be z in the differential equation
Strange typo.
 Raising a
ValueError
inFunctionAiryAiGeneral._derivative_
whendiff_param == 0
may not be the most appropriate, since (if I'm not mistaken) the partial derivative would make sense mathematically.
A quick look at old and new code shows 1. ValueError
, 2. NotImplementedError
, 3. assert
. So, this needs to be unified to NotImplementedError
.
One last thing: IMO
hold_derivative
should beTrue
by default inairy_ai
andairy_bi
, except perhaps when the differentiation order is one. But I don't know if that's consistent with the way things are done in other parts of sage symbolics. Thoughts?
I believe the code of this ticket is the only one that has such a parameter, so please feel free to improve it.
I have looked at your patch and it's fine, so if you think the rest is OK please set positive.
comment:85 Changed 8 years ago by
Commit:  91530d08a7a37bc03876962c1a1ae0bca10bfd70 → 2f6945af73219458fb0a2745e2df9e2eea79b055 

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
347cd08  #12455 Airy functions: doc fixes and clarifications

6aaf2da  #12455 Airy funs: raise NotImplementedError on diff(airy_?i(α,x),α)

c80be63  #12455 Airy funs: hold_derivative by default

2f6945a  #12455 Airy functions: avoid calling deprecated function

comment:86 Changed 8 years ago by
Description:  modified (diff) 

Reviewers:  Eviatar Bach, KarlDieter Crisman, Burcin Erocal, Ralf Stephan → Eviatar Bach, KarlDieter Crisman, Burcin Erocal, Ralf Stephan, Jeroen Demeyer, Marc Mezzarobba 
Replying to rws:
 Raising a
ValueError
inFunctionAiryAiGeneral._derivative_
whendiff_param == 0
may not be the most appropriate, since (if I'm not mistaken) the partial derivative would make sense mathematically.A quick look at old and new code shows 1.
ValueError
, 2.NotImplementedError
, 3.assert
. So, this needs to be unified toNotImplementedError
.One last thing: IMO
hold_derivative
should beTrue
by default inairy_ai
andairy_bi
, except perhaps when the differentiation order is one. But I don't know if that's consistent with the way things are done in other parts of sage symbolics. Thoughts?I believe the code of this ticket is the only one that has such a parameter, so please feel free to improve it.
Both done (now rather than later to avoid breaking the interface).
I have looked at your patch and it's fine, so if you think the rest is OK please set positive.
I'm okay with everything prior to my commits. Could you (or someone else) have a quick look at my last changes and set the ticket to positive review? Thanks!
comment:87 Changed 8 years ago by
Status:  needs_review → positive_review 

Is fine and passes tests in functions/
. Thank you too.
comment:88 Changed 8 years ago by
Branch:  public/ticket/12455 → 2f6945af73219458fb0a2745e2df9e2eea79b055 

Resolution:  → fixed 
Status:  positive_review → closed 
comment:89 Changed 8 years ago by
Authors:  Oscar Gerardo Lazo Arjona, Benjamin Jones, D. S. McNeil, Eviatar Bach, Ralf Stephan → Oscar Gerardo Lazo Arjona, Benjamin Jones, Douglas McNeil, Eviatar Bach, Ralf Stephan 

Commit:  2f6945af73219458fb0a2745e2df9e2eea79b055 
I've added a patch, which should do the job, but it has a few shortcomings:
1.The resulting symbolic functions seem to remain on hold:
You need to force it to evaluate:
2. This doesn't work:
3. There is no evaluation for airy_ai_prime or airy_bi_prime
4. I'm not sure about how should the functions be called, some possible schemes are
{ai,bi,aip,bip} {ai,bai,aip,baip} {airy_ai,airy_bi,airy_ai_prime,airy_bi_prime}
And also whether the latex representation should be capitalized or not. I chose the third scheme, and capitalized typesetting.