"Source: Text/Commut/AlgAff.text";
"Line: 126";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/AlgAff.text, line: 126
// Example: H118E1 ()
print "Example: H118E1";
ei := GetEchoInput();
SetEchoInput(true);
Q := RationalField();
A<x, y> := AffineAlgebra<Q, x, y | x^2 - y^2 + 2, y^3 - 5>;
A;
x^2;
x^-1;
P<z> := PolynomialRing(Q);
MinimalPolynomial(x); 
MinimalPolynomial(x^-1); 
MinimalPolynomial(y);    
F<t> := FunctionField(IntegerRing());
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;
MinimalPolynomial(x);
MinimalPolynomial(x^-1); 
SetEchoInput(ei);
