Fix crash and remove pexpect-Maxima usage in Y(m,n)

[rwst]

sage: spherical_harmonic(3, 2, 1, 2*pi/3)
...
TypeError: ECL says: THROW: The catch MACSYMA-QUIT is undefined.

The eval function of SphericalHarmonic uses pexpect-Maxima. Since this needs only a formula the call to Maxima could be replaced by a few lines of Python.

http://dlmf.nist.gov/14.30.E1

Replacing pexpect-Maxima is part of #17753.

Depends on #21614
Depends on #21963

Upstream: Fixed upstream, in a later stable release.

Component: symbolics

Author: Ralf Stephan

Branch/Commit: bb4630f

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/20939

[rwst]

Dependencies: 16813

[rwst]

comment:1

This depends on the associated Legendre polynomials being implemented, e,g, #16813.

[rwst]

Changed dependencies from 16813 to #16813

[rwst]

comment:3

It won't be dependent on P(l,m,x) if the P special value formula is directly used in _eval_. The Y floating point evaluation is done via mpmath anyway.

[rwst]

Changed dependencies from #16813 to none

[rwst]

Branch: u/rws/remove_pexpect_maxima_usage_in_y_m_n_

[rwst]

Commit: f233afa

[rwst]

New commits:

f233afa

20939: Fix crash and remove pexpect-Maxima usage in Y(m,n)

[rwst]

Author: Ralf Stephan

[tscrim]

comment:7

LGTM modulo

         Check that :trac:`20939` is fixed::
 
             sage: spherical_harmonic(3,2,1,2*pi/3)
             1/240*sqrt(30)*(-15*I*sqrt(7)*sqrt(3) -
-            ...15*sqrt(7))*cos(1)*sin(1)^2/sqrt(pi)
+            ... + 15*sqrt(7))*cos(1)*sin(1)^2/sqrt(pi)
         """
         if n in ZZ and m in ZZ and n > -1:
             if abs(m) > n:
                 return ZZ(0)
-            if (m == 0 and theta.is_zero()):
+            if m == 0 and theta.is_zero():
                 return sqrt((2*n+1)/4/pi)

[tscrim]

Reviewer: Travis Scrimshaw

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1a5cf6b

20939: cosmetics

[sagetrac-git]

Changed commit from f233afa to 1a5cf6b

[rwst]

comment:9

That doesn't work as given. First the plus is a minus, and then the space after the ellipsis will make it fail too.

I'll assume the last commit is still what you wanted and set positive. Just revert if not. Thanks for the review.

[tscrim]

Changed commit from 1a5cf6b to a080e1e

[tscrim]

comment:10

So the ... is actually unneeded; I was thinking there was more than 2 terms. Please check my changes.

---

New commits:

a080e1e

Removing uncessary ... in doctest.

[tscrim]

Changed branch from u/rws/remove_pexpect_maxima_usage_in_y_m_n_ to u/tscrim/remove_pexpect_maxima_in_ymn-20939

[tscrim]

comment:23

Would it be possible to have a test to make sure this stays fixed?

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

04f79cd

20939: make sure atan2(0,0) returns always NaN

[sagetrac-git]

Changed commit from 31e6c64 to 04f79cd

[rwst]

comment:25

This commit contains a test for the specific NaN evaluation problem causing the second crash (the fix for the first crash is tested with #21614). The commit also fixes an inconsistency. As to a general test of the second problem I opened pynac/pynac#211

[tscrim]

comment:26

Thanks. Now back to the buildbots.

[kiwifb]

comment:27

I don know what Volker will report if anything but now I have a segfault in constant.py

sage: sig_on_count() # check sig_on/off pairings (virtual doctest) ## line 688 ##
0
sage: loads(dumps(NaN)) ## line 704 ##
------------------------------------------------------------------------
/usr/lib64/python2.7/site-packages/cysignals/signals.so(+0x4556)[0x7f4f180eb556]
/usr/lib64/python2.7/site-packages/cysignals/signals.so(+0x4a6c)[0x7f4f180eba6c]
/usr/lib64/python2.7/site-packages/cysignals/signals.so(+0x6d6f)[0x7f4f180edd6f]
/lib64/libpthread.so.0(+0x10d70)[0x7f4f1ce53d70]
/usr/lib64/python2.7/site-packages/sage/libs/pynac/pynac.so(+0x2940d)[0x7f4d3ece640d]
/usr/lib64/libpynac.so.8(_ZN5GiNaC8constant9unarchiveERKNS_12archive_nodeERNS_9containerINSt7__cxx114listEEE+0x196)[0x7f4d3e955dcc]
/usr/lib64/libpynac.so.8(_ZNK5GiNaC12archive_node9unarchiveERNS_9containerINSt7__cxx114listEEE+0xf4)[0x7f4d3e936836]
/usr/lib64/libpynac.so.8(_ZNK5GiNaC7archive12unarchive_exERKNS_9containerINSt7__cxx114listEEEj+0x130)[0x7f4d3e936a42]
/usr/lib64/python2.7/site-packages/sage/symbolic/expression.so(+0xec87f)[0x7f4d3e63787f]
/usr/lib64/python2.7/site-packages/sage/symbolic/expression.so(+0xecc2a)[0x7f4d3e637c2a]
/usr/lib64/libpython2.7.so.1.0(PyCFunction_Call+0xf1)[0x7f4f1d0ddbd9]
/usr/lib64/libpython2.7.so.1.0(PyObject_Call+0x5c)[0x7f4f1d0a8123]

[rwst]

comment:28

Confirmed. I'm sorry. With Pynac changes I have a testing procedure in place here, but with Python I was relying on patchbot. This issue is also somewhat unusual as to the surprising problems presented.

[vbraun]

comment:29

Same here...

[kiwifb]

comment:30

Positive stuff for me, it made me realise that some bits of cysignals are not currently working properly on Gentoo - even so the tests pass :(

[rwst]

Upstream: Fixed upstream, in a later stable release.

[rwst]

Changed dependencies from #21614 to #21614, pynac-0.7.1

[rwst]

Changed dependencies from #21614, pynac-0.7.1 to #21614, #21963

[sagetrac-git]

Changed commit from 04f79cd to bb4630f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

bb4630f

Merge branch 'develop' into t/20939/remove_pexpect_maxima_in_ymn-20939

[tscrim]

comment:34

Let's try again.

[vbraun]

Changed branch from u/rws/remove_pexpect_maxima_in_ymn-20939 to bb4630f