"Source: Text/Geometry/GrdRng.text";
"Line: 468";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/GrdRng.text, line: 468
// Example: H128E1 ()
print "Example: H128E1";
ei := GetEchoInput();
SetEchoInput(true);
T<t> := PolynomialRing(Rationals());
p := 2*t - 3;
V := [ 1, 2, 3, 4 ];                          
h_fun := HilbertFunction(p,V);
[ h_fun(n) : n in [0..7]];        
h := HilbertSeries(p,V);
h;
S<s> := PowerSeriesRing(Rationals(),8);
S ! h;                                  
HilbertSeriesMultipliedByMinimalDenominator(p,V);
HilbertNumerator(h,[1,1,4]);
HilbertNumerator(h,[1,1,5]);
h1 := HilbertSeries(p,[1,1,2,4]);
S ! h1;
HilbertNumerator(h1,[1,1,5]);
HilbertNumerator(h1,[1,5]);     
HilbertNumerator(h1,[1,2,3,3,5]);     
HilbertNumerator(h1,[1,2,3,3]);
SetEchoInput(ei);
