An integral solved by Mathematica, but not by Sage

[Omri]

Hi,

I have an integral that is solved by Mathematica, but not by Sage:

integrate( exp(-x^2/2)/sqrt(2*pi) * sign(x-1), x, -oo, oo )

This is actually part of a 3D integral, that mathematica also solves, and sage has problems with due to the lack of multivariate integration:

integrate   sign(x+y)*sign(x+z) ,  where x,y and z are gaussian variables. The result is 1/3.

Does anybody know why this happens, and how can I solve this in Sage?
Thanks,
Omri

[kcrisman]

Maxima can't do this one either, at least not without some package.

(%i8) integrate(%e^(-x^2/2)/sqrt(2*%pi) * signum(x-1),x,minf,inf);

(%o8) ('integrate(%e^-(x^2/2)*signum(x-1),x,minf,inf))/
(sqrt(2)*sqrt(%pi))

[Omri]

So is this an issue that can be resolved?
Omri

[kcrisman]

On Aug 20, 12:45 pm, Omri <omri.ba...@gmail.com> wrote:
> So is this an issue that can be resolved?
> Omri

Depends on what you mean by resolved.

It turns out that the abs_integrate package in Maxima will do this.


(%i1) load(abs_integrate);
STYLE-WARNING: redefining SIMP-ISREAL-P in DEFUN
(%o1) /Users/.../maxima-5.25.0/share/contrib/integrat\
ion/abs_integrate.mac
(%i2) integrate(%e^(-x^2/2)/sqrt(2*%pi) * signum(x-1),x,minf,inf);

(%o2) -erf(1/sqrt(2))


See http://trac.sagemath.org/sage_trac/ticket/11483, where we are
tracking adding this. We tried to add it once, and then apparently
didn't actually do so. Now we still need to do it, which requires the
usual process of review. Thanks for reminding us!

- kcrisman

[achrzesz]

sage: (integrate( exp(-x^2/2)/sqrt(2*pi) * sign(x-1), x, -oo, 1 )
+integrate( exp(-x^2/2)/sqrt(2*pi) * sign(x-1), x, 1,
oo )).simplify_full()

-erf(1/2*sqrt(2))

[Omri]

Thanks - this is exactly what I meant by resolved.
Omri

[kcrisman]

Interesting that this "just works", and I guess it makes sense.
Still, hopefully we'll get #11483 resolved as well soon.