"Source: Text/Commut/GB.text";
"Line: 2607";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/GB.text, line: 2607
// Example: H115E11 ()
print "Example: H115E11";
ei := GetEchoInput();
SetEchoInput(true);
P<a,b,c,d> := PolynomialRing(RationalField(), [4,3,2,1]);
L := [a*b - c^2*d^3, b*c*d + c^3, c^2*d - d^5, a*d - b*c];
[IsHomogeneous(f): f in L];
[Degree(f): f in L];
G:=GroebnerBasis(L);
G;
#G;
assert $1 eq 10;
[Degree(f): f in G];
for D := 1 to 10 do
    T := GroebnerBasis(L, D);
    printf "D = %o, #GB = %o, contains all degree-D polynomials: %o\n",
        D, #T, {f: f in G | Degree(f) le D} subset T;
end for;
GroebnerBasis(L, 5);
GroebnerBasis(L, 8);
SetEchoInput(ei);
