I know this sort of simplify question has been asked many times, but I still don't seem to have 'got it'. In a nutshell, there's a conservative real 2-D vector field (cartesian X,Y coordinates) with an extra non-positive parameter Z, and Maple 12 is able to compute the scalar potential. But it presents it in a long (6 lines), perversely complicated form, involving the imaginary sqrt(-Y^2). I tried to show it here using the Maple leaf Tag and pasting the expressions there, but all I got was indecipherable ascii. The vector field X and Y components are
vfX = (X-1)*(2*Rp-Z)/(Rp^2*(Rp-Z)) - (X+1)*(2*Rm-Z)/(Rm^2*(Rm-Z))
vfY = Y *(2*Rp-Z)/(Rp^2*(Rp-Z)) - Y *(2*Rm-Z)/(Rm^2*(Rm-Z))
where Rp,m = sqrt( (X -,+ 1)^2 + Y^2 + Z^2 ). The scalar potential was computed with the instruction
sp = ScalarPotential( vf )
It only took a page and a half to simplify 'sp' by hand to something pretty straightforward:
sp = ln( Rp/Rm * (Rp - Z)/(Rm - Z) )
But I couldn't find any combination of instructions that could reduce Maple's 'sp' to anywhere close to this. All were still 5 lines long Among the variations I tried were
sp = ScalarPotential( vf ) assuming real
sp = ScalarPotential( vf ) assuming X::real, Y::real, Z<=0
and various combinations of simplify, convert, combine, and assuming. In fact, using simplify and assuming as immediately above produced expressions involving imaginaries.
I would appreciate any recommendations, especially generally applicable ones.