integral of ln(1+4/5*sin(x)) from -3.1415 to 3.1415 crashes Maxima and Sage

[kcrisman]

See extensive discussion at this sage-support thread.

Reported by Ben Jones:

sage: integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415)


;;;
;;; Binding stack overflow.
;;; Jumping to the outermost toplevel prompt
;;;

...

;;;
;;; Binding stack overflow.
;;; Jumping to the outermost toplevel prompt
;;;


/Users/jonesbe/sage/sage-5.1.beta2/spkg/bin/sage: line 335: 86594 Illegal instruction     sage-ipython "$@" -i

There don't seem to be any problems with Maxima. Although it's been traced down (thanks to Dan Drake) to 5.0.beta3, the only obvious candidate for a change in our interface is when we added abs_integrate, which doesn't seem to impact things.

(%i2) load(abs_integrate);
(%o2) /Users/.../sage-5.0/local/share/maxima/5.26.0/s\
hare/contrib/integration/abs_integrate.mac
(%i4) keepfloat:true;
(%o4)                                true
(%i7) integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415);
                          3.1415
                         /
                         [            4 sin(x)
(%o7)                    I         ln(-------- + 1) dx
                         ]               5
                         /
                          - 3.1415

And we have

sage: maxima_calculus(" integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415);")
'integrate(ln(4*sin(x)/5+1),x,-3.1415,3.1415)

so something must indeed be wrong in how we're sending this to Maxima.

Upstream: Fixed upstream, in a later stable release.

CC: @benjaminfjones @sagetrac-dsm

Component: calculus

Keywords: integral

Author: Dave Morris

Branch/Commit: 3f41b09

Reviewer: Karl-Dieter Crisman

Issue created by migration from https://trac.sagemath.org/ticket/13097

[kcrisman]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-See extensive discussion at 
+See extensive discussion at [this sage-support thread](https://groups.google.com/forum/?fromgroups#!topic/sage-support/dZFPiWRWSoc).
 
 Reported by Ben Jones:
 

[dimpase]

comment:2

Could it rather be something wrong in how we are receiving data from Maxima(lib)?

[nbruin]

comment:4

I don't think maxima understands ln. If you do

maxima_calculus(" integrate(log(1+4/5*sin(x)), x, -3.1415, 3.1415);")

you see the same thing happening. No problem in vanilla maxima. But when we load abs_integrate:

(%i1) load(abs_integrate);
(%o1) /usr/local/sage/5.0/local/share/maxima/5.26.0/share/contrib/integration/abs_integrate.mac
(%i2) integrate(log(1+4/5*sin(x)), x, -3.1415, 3.1415);
...
Condition of type: STACK-OVERFLOW
BINDING-STACK overflow at size 8448. Stack can probably be resized.

FYI: with

from sage.interfaces.maxima_lib import *
from sage.libs.ecl import *
args=(ln(1+4/5*sin(x)), x, -3.1415, 3.1415)
I=EclObject(([max_integrate],[sr_to_max(SR(a)) for a in args]))
I

you see what expression gets passed to maxima_lib. With

EclObject('#$integrate(log(1+4/5*sin(x)), x, -3.1415, 3.1415)$')

you see what maxima's parser would produce. With

maxima_eval(I)

you can trigger the same explosion. Note that with this trick, you can quickly see that

EclObject('#$integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415)$')

creates an essentially different expression.

[nbruin]

comment:5

The problem can be simplified to

integrate(log(sin(x)),x);

which maxima without abs_integrate can do (or at least it returns an answer).

This is now Maxima Artifact 3533723

[nbruin]

Upstream: Reported upstream. No feedback yet.

[kcrisman]

comment:6

I don't think maxima understands ln. If you do

Well, egg on my face! Sorry for that noise. I just don't use Maxima enough beyond trying to generate bug reports or find new functionality for Sage :)

And good diagnosis; I guess if I had tried log instead I would have gotten the same problem.

[dimpase]

comment:7

Replying to @nbruin:

I don't think maxima understands ln.

facepalm. Sorry for noise on sage-support

[nbruin]

Changed upstream from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

[nbruin]

comment:8

We really need more options for "upstream" ;-). How about "Developers acknowledge bug, propose fix, but haven't gotten around to merging it because they got the fix with less than 24 hours round trip time"? See Maxima tracker. I have no doubt this will be fixed in some future Maxima release.

[nbruin]

comment:9

We can monkey-patch Barton Willis's fix into sage's maxima:

sage: L="""signum_int(q,x) :=
....: block([w : 1, acc : [], sgn, v, f, listconstvars : true],
....:   q : convert_to_signum(q),
....:   if freeof('signum, q) then
....:     (false)
....:   else (
....:     q : almost_everywhere_simp(q),
....:     v : listofvars(q),
....:     q : block([expandwrt_denom : true], expandwrt(q,'signum)),
....:     if (f : abs_int_extra(q,x)) # false then f
....:     else if (f : partition_as_signum(q,x)) # false then (
....:       w : first(f),
....:       acc : second(f),
....:       if every(lambda([s], linear_in_p(s,x)), acc) then (
....:       sgn : xreduce("*", map(lambda([s], diff(s,x)),acc)),
....:       acc : map(lambda([s], rhs(first(linsolve(s, x)))),acc),
....:       signum_int_helper(signum(sgn) * w, sort(acc), x)))
....:     else if (safe_op(q) = "+") then (
....:         f : map(lambda([s], signum_int(s,x)), args(q)),
....:         if member(false, f) then false else xreduce("+", f))
....:       else block([extra_integration_methods : [],
....:         extra_definite_integration_methods : []],integrate(q,x))
....:   )
....: );"""
sage:  integrate(ln(1+4/5*sin(x)), x, -3.1415, 3.1415)
integrate(log(4/5*sin(x) + 1), x, -3.1415, 3.1415)
sage: integrate(ln(sin(x)),x)
1/2*I*x^2 - 1/2*x*log(sin(x)^2 + cos(x)^2 - 2*cos(x) + 1) - 1/2*x*log(sin(x)^2 + cos(x)^2 + 2*cos(x) + 1) + x*log(sin(x)) + I*x*arctan2(sin(x), -cos(x) + 1) - I*x*arctan2(sin(x), cos(x) + 1) + I*polylog(2, -e^(I*x)) + I*polylog(2, e^(I*x))

This just patches a routine defined in abs_integrate.mac. It's a LOT slower than in 4.7.1, though, so if performance is any concern, we might want to reconsider whether abs_integrate should be loaded by default. By manipulating the maxima variables extra_integration_methods and extra_definite_integration_methods it should be possible to control which integration methods maxima tries to use (this is what abs_integrate hooks into).