restore "/tmp/testsave";
System("rm -f /tmp/testsave");

assert #SecondaryInvariants(R) eq 5;
assert #PrimaryInvariants(R) eq 4;

C := Coefficients(PowerSeriesRing(IntegerRing())!HilbertSeries(R));
assert C[1..10] eq [ 1, 1, 3, 5, 10, 14, 22, 30, 43, 55];

ps;
pis;

K;
S;
DefiningPolynomial(K, S);
DefiningPolynomial(K);
K!S.1;
assert MinimalPolynomial($1) eq DefiningPolynomial(S);

E:=EllipticCurve([GF(NextPrime(10^20))|1,2]);
time #E;
assert #E eq 100000000017275263512;

E:=EllipticCurve([GF(NextPrime(10^20))|1,3]);
time #E;
assert #E eq 100000000009207625256;

/////////////////

assert #G eq 5616;
X := CharacterTable(G);
assert &+[x[1]^2: x in X] eq #G;

assert &+[x[1]^2: x in X2] eq #G2;

//XXX;
quit;
