"Source: Text/Commut/GB.text";
"Line: 2700";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/GB.text, line: 2700
// Example: H115E12 ()
print "Example: H115E12";
ei := GetEchoInput();
SetEchoInput(true);
P<x, y, z, t, u> := PolynomialRing(RationalField(), 5);
I := ideal<P |
    x + y + z + t + u,
    x*y + y*z + z*t + t*u + u*x,
    x*y*z + y*z*t + z*t*u + t*u*x + u*x*y,
    x*y*z*t + y*z*t*u + z*t*u*x + t*u*x*y + u*x*y*z,
    x*y*z*t*u - 1>;
Groebner(I);
K<W> := CyclotomicField(5);
J := ChangeRing(I, K);
V := Variety(J);
#V;
assert $1 eq 70;
SetEchoInput(ei);
