require "algebra"

F13 = ResidueClassRing(Integer, 13)

P = Polynomial(F13, "x")
Q = LocalizedRing(P)
x = Q[P.var]
p ( 1 / (x**2 - 1) - 1 / (x**3 - 1) )

#This is equivalent to the following
F = RationalFunctionField(F13, "x")
x = F.var
p ( 1 / (x**2 - 1) - 1 / (x**3 - 1) )