"Source: Text/Commut/Ideal.text";
"Line: 740";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/Ideal.text, line: 740
// Example: H116E3 ()
print "Example: H116E3";
ei := GetEchoInput();
SetEchoInput(true);
K<w> := GF(27);
P<x, y> := PolynomialRing(K, 2);
I := ideal<P | x^8 + y + 2, y^6 + x*y^5 + x^2>;
Groebner(I);
I;
V := Variety(I);
V;
// Check that the original polynomials vanish:
[
   <x^8 + y + 2, y^6 + x*y^5 + x^2> where x is v[1] where y is v[2]: v in V
];
// Note that the variety of I would be larger over an extension field of K:
VarietySizeOverAlgebraicClosure(I);
assert $1 eq 48;
SetEchoInput(ei);
