"Source: Text/Ring/FldFunG.text";
"Line: 7458";
"Date: Thu Jun 16 15:04:46 2022";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Ring/FldFunG.text, line: 7458
// Example: H45E41 ()
print "Example: H45E41";
ei := GetEchoInput();
SetEchoInput(true);
Qc<c> := PolynomialRing(RationalField());
Qcs<s> := PolynomialRing(Qc);
F<s> := FunctionField(s^2 + c^2 - 1);
c := F!c;
Genus(F);
assert $1 eq 0;
Zeros(s);
Zeros(c-1);
P := Zeros(c-1)[1];
Degree(P);
assert $1 eq 1;
Dimension(1*P);
assert $1 eq 2;
Basis(1*P);
a := Basis(1*P)[1];
Degree(a);
assert $1 eq 1;
MinimalPolynomial(a);
(a^2 - 1)/(a^2 + 1);
a * ((a^2 - 1)/(a^2 + 1) - 1);
SetEchoInput(ei);
