#4765 gfactor not idempotent

[Stavros Macrakis]

gfactor((%i+1)^(-1/2)) =>
   ((1-%i)*sqrt(%i+1))/2
gfactor(%) =>
   -(((%i-1)*sqrt(%i+1))/2)
gfactor(%) =>
   -(((%i-1)*sqrt(%i+1))/2)   <<< stable

This is arguably outside the domain of gfactor, so this is a very low priority bug.
I hope priority=2 means that it is extra-low priority, not extra-high priority!

[David Scherfgen]

It is actually the regular factor that's not idempotent here:

(%i1) factor(1/(sqrt(a+1)), 1+a^2);
(%o1) ((1-a)*sqrt(a+1))/2

(%i2) factor(%, 1+a^2);
(%o2) -(((a-1)*sqrt(a+1))/2)

(%i3) factor(%, 1+a^2);
(%o3) -(((a-1)*sqrt(a+1))/2)

[Stavros Macrakis]

Well, yes, gfactor is just a short form

gfactor(ex) == factor(ex, 1+a^2)