PolMods in GP??

[Tim French <tfrench@tartarus.uwa.edu.au>]

 I'm a student in Western Australia and as part of my honours thesis I am
intending to implement Schoof's algorithm for counting pts on elliptic
curves over finite fields in Pari, (more specifically GP).

 However I have come across some problems with the modular arithmetic.

For example if

f1 = Mod(5,7)x^12+Mod(4,7)x^10+Mod(1,7)x^7+Mod(3,7)x^6+Mod(4,7)x^5+Mod(6,7)x^4
       +Mod(1,7)x^3+Mod(1,7)x^2+Mod(1,7)x

f2 = Mod(4,7)x^6+Mod(4,7)x^4+Mod(5,7)x^3+Mod(2,7)x^2+Mod(4,7)+Mod(3,7)

(with asterixs where appropriate)

then GP returns Mod(f2,f1)=0, and gcd(f1,f2)=Mod(4,7).

I feel this is a contradiction.
I am using version 2.0.12 on a PC with MS-DOS, and 32 meg of RAM.
Does anyone know what is going on???
Thanks a lot.
 
Tim.

Then GP returns Mod(f2,f1)=0, and gcd(f1,f2)=Mod(4,7).