"Source: Text/Ring/RngOrd.text";
"Line: 7613";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 7613
// Example: H39E31 ()
print "Example: H39E31";
ei := GetEchoInput();
SetEchoInput(true);
K := QuadraticField(10);
M := MaximalOrder(K);
U, mU := SUnitGroup(3*M);
U;
mU;
u := mU(U.3); u;
Decomposition(u);
U, mU, base := SUnitGroup(3*M:Raw);
mU;
mU(U.3);
PowerProduct(base, $1);
base[2]^2 * base[3]^1 * base[11]^-2;
K := NumberField(Polynomial([ 13824, -3894, -1723, 5, 1291, 1 ]));
L := LLL(MaximalOrder(K));
C, mC := ClassGroup(L : Proof:="GRH");
U, mU, base := SUnitGroup(1*L:Raw);
logs := Matrix([Logs(x) : x in Eltseq(base)]);
mU(U.3)*logs;
assert $1[1] - 2815256.9980908 lt 10^-7;
SetEchoInput(ei);
