I'll give you a small example so hopefully you can figure out the rest.
The following code first defines the function custom_divide and then prints all
possible values of that function together with the input. You could also add
the values to a list or a set to process them later.
def custom_divide(x,y):
if y==0:
return 0
return x/y
F.<a>=GF(8)
for a,b in F^2:
print "a: ",a,"b: ",b,"a/b:",custom_divide(a,b)
#an example where we add the values to a set
values = set([])
for i,j in F^2:
values.add(custom_divide(i,j)^7)
print values
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