"Source: Text/Commut/Ideal.text";
"Line: 1437";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/Ideal.text, line: 1437
// Example: H116E9 ()
print "Example: H116E9";
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>;
R := Radical(I);
Groebner(R);
R;
// Check that t*u is in the radical of I by another method:
IsInRadical(t*u, I);
assert $1;
SetEchoInput(ei);
