I think the absolute value of the Log function has a problem.
This is correct:
(%i1) assume(x>0,x<1)$
(%i2) abs(log(x));
(%o2) -log(x)
But for a negative value Maxima simplifies the same way:
(%i3) assume(y<0)$
(%i4) abs(log(y));
(%o4) -log(y)
Therefore we get (a complex value):
(%i1) abs(log(-1/2));
(%o1) -log(-1/2)
And not the expected real answer:
sqrt(%pi^2+log(2)^2);
We get this answer the following way:
(%i8) limit(log(x),x,-1/2);
(%o8) %i*%pi-log(2)
(%i9) abs(%);
(%o9) sqrt(log(2)^2+%pi^2)
But not using the abs function in the limit:
(%i13) limit(abs(log(x)),x,-1/2);
(%o13) -log(-1/2)
The simplification happens because $sign returns always neg for a number
which is less than 1:
(%i15) assume(y<1)$
(%i16) sign(log(y));
(%o16) neg
I think $sign should return $pnz for a negative argument to the Log
function to avoid an inconsistent simplification.
Dieter Kaiser