fix the symbolic csgn function on complex input

[burcin]

Our wrapper of the csgn function from GiNaC (in sage/symbolic/expression.pyx) doesn't reflect it's real definition:

  /** Return the complex half-plane (left or right) in which the number lies.
   *  csgn(x)==0 for x==0, csgn(x)==1 for Re(x)>0 or Re(x)=0 and Im(x)>0,
   *  csgn(x)==-1 for Re(x)<0 or Re(x)=0 and Im(x)<0.
   *  */

Fix this and add doctests.

We should also consider using GiNaC's csgn() function for the top level sgn() and sign() functions. This should be on a different ticket though.

[burcin]

The new pynac package at #9201 changes the csgn() function according to the description. attachment:trac_9881-csgn.patch adds doctests for the new specification.

The pynac package includes patches for #9394, #9834, #9878, #9879, #9900 as well as this ticket. See the ticket description of #9901 for the list (and order) of patches associated to the new version.

[burcin]

Replying to burcin:

The new pynac package at #9201 changes the csgn() function according to the description.

That should have been "at #9901".

[kcrisman]

Just FYI - this appears to still apply cleanly after the review patch at #9879.

[kcrisman]

Okay, this looks good on both Pynac and Sage side - with the exception that I think the documentation needed slightly more clarity, and that some of the examples got misplaced to binomial for some reason. Positive review; apply reviewer patch after initial patch.

[kcrisman]

Apply after initial patch.