"Source: Text/Commut/PMod.text";
"Line: 1981";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Commut/PMod.text, line: 1981
// Example: H119E6 ()
print "Example: H119E6";
ei := GetEchoInput();
SetEchoInput(true);
R<x,y,z> := PolynomialRing(RationalField(), 3);
F := GradedModule(R, 3);
M := quo<F | [x,0,0], [0,y^2,0]>;
M;
HilbertSeries(M);
HilbertSeries(M, 10);
HilbertNumerator(M);
HilbertDenominator(M);
HilbertPolynomial(M);
[Evaluate(HilbertPolynomial(F), i): i in [0..10]]; 
F := GradedModule(R, [-1]);
F;
HilbertSeries(F);    
HilbertSeries(F, 10);
HilbertNumerator(F);
assert $1 eq 1;
HilbertDenominator(F);
HilbertPolynomial(F);
[Evaluate(HilbertPolynomial(F), i): i in [-1..10]];
SetEchoInput(ei);
