#3192 asksign: internal error, zeroa+zerob: integration prompts error

[Richard Fateman]

ex:sin(x)^2*log(4*cos(2*x)+5), exponentialize;
integrate(ex,x,0,%pi/2)

gives "asksign: internal error"

A little tracing shows that EPS-SIGN in src/compar.lisp has been called on ((MPLUS) $ZEROA $ZEROB).

wxMaxima version: 15.8.2
Maxima version: 5.37.2
Maxima build date: 2015-09-18 21:03:17
Host type: i686-pc-mingw32
System type: Win32 6.2.9200 X86
Lisp implementation type: SBCL
Lisp implementation version: 1.2.7

[Richard Fateman]

zeroa+zerob is arguably zero. This is the sum of two signed zeros +0 and -0.

[Robert Dodier]

Trying the example with commit ff883f32a (post 5.47) with SBCL 2.1.11 on Linux returns a result in terms of polylogarithm functions. I don't know if it's correct.

-(((%i*(12*li[2](2)-6*log(2)^2)+%pi*(24-12*log(2))+19*%i*%pi^2)/12-%i*li[2](-(1/2))-%i*li[2](-2))/4)

[Robert Dodier]

Copying message from RJF via email.

"""
I think this is wrong. Evaluated numerically and expanded Maxima gives -(4.934802200544679*%i)-1.5707963267948966
But the integral evaluated directly numerically (using romberg() ..) gets 0.696094....
Mathematica gets 1/8 \[Pi] (-1 + Log[16]) which is 0.696094...
Exploring whether li[2] is computed wrong.. Mathematica says PolyLog[2,-1/2]//N is -0.448..
Maxima says li[2](-1/2) is -0.448.. So that's not it.

Note that this expression ex can be anti-differentiated to give a messy expression, call it v.
ratsimp(diff(v,x)-ex) gives 0. So Maxima knows how to compute v, the indefinite integral.
Plotting the expression ex between 0 and pi/2 shows nothing bothersome for integrating. No singularities.

Using the Fundamental Theorem of Calculus evaluating v at 3.1415926/2 and 0.0 ...
gives
0.4712901434518321*%i+0.6960939634530774
and
0.47129014345183173*%i

so the difference is 0.69609.... and FTC gets the right answer.

But the definite integral seems to be using some other code, and comes up with something wrong.
"""