y = x - alpha(x)

is a map between the deflector plane (described by coordinate x) and the source plane (described by coordinate y.) The magnification of the lensed beams of light that follow the lens equation are magnified by a factor given by the Jacobian of the lens equation.

In spherically symmetric lenses, the determinant of the Jacobian can be written in a closed, and meaningful, form given in Equation (3.5) of the article. This Maple worksheet derives the result using the computer algebra software package Maple. Save this file as "detA.mws" (the default using Netscape's 'File/Save as...') and open the worksheet while running Maple (the worksheet was written using Maple 6, but should run under earlier versions, too.)