By the way:
(%i4) load(abs_integrate)$
Correct antiderivative:
(%i5) 'integrate(x*signum(x^2-1/4),x);
(%o5) abs(x^2-1/4)/2
Correct definite integral
(%i6) 'integrate(x*signum(x^2-1/4),x,-1,0);
(%o6) -1/4
In Maxima 5.24.0:
(%i11) integrate(x*signum(x^2-1/4),x,-1,0);
1
(%o11) -
2
But the picture makes it pretty clear this should be -1/4.
Is this antideriv ok?
(%i15) integrate(x*signum(x^2-1/4),x);
! 2 1!
!x - -!
! 4!
(%o15) --------
2
This was originally reported at the Sage trac at http://trac.sagemath.org/sage_trac/ticket/11590
By the way:
(%i4) load(abs_integrate)$
Correct antiderivative:
(%i5) 'integrate(x*signum(x^2-1/4),x);
(%o5) abs(x^2-1/4)/2
Correct definite integral
(%i6) 'integrate(x*signum(x^2-1/4),x,-1,0);
(%o6) -1/4
Update: why doesn't regular integrate work? Only 'integrate does.
(%i5) display2d:false;
(%o5) false
(%i6) integrate(x*signum(x^2-1/4),x,-1,0);
(%o6) 1/2
(%i7) 'integrate(x*signum(x^2-1/4),x,-1,0);
(%o7) -1/4
Again, this doesn't fix the problem that the answer is just wrong currently :( but at least would help use get it to work right in Sage.
Fixed by commit 5a300aab, which also fixes related bug #3123.
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