"Source: Text/Geometry/Sheaf.text";
"Line: 1591";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Sheaf.text, line: 1591
// Example: H123E7 ()
print "Example: H123E7";
ei := GetEchoInput();
SetEchoInput(true);
P<x,y,z,t> := ProjectiveSpace(Rationals(),3);
C := Curve(P,[ x^2*y^2 - 23/59*x*y^3 + 9/59*y^4 + 27/59*x^3*z - 23/59*x^2*y*
z - 6/59*x*y^2*z + 6/59*y^3*z - 10/59*x^2*z^2 + 5/59*x*y*z^2 - 3/59*y^2*z^2 +
1/59*x*z^3 - 74/59*x^3*t + 115/59*x^2*y*t - 83/59*x*y^2*t + 3/59*y^3*t -
105/59*x^2*z*t + 1/59*x*y*z*t - 2/59*y^2*z*t + 36/59*x*z^2*t + 4/59*y*z^2*t -
3/59*z^3*t + 297/59*x^2*t^2 - 135/59*x*y*t^2 + 52/59*y^2*t^2 + 68/59*x*z*t^2 -
11/59*y*z*t^2 - 18/59*z^2*t^2 - 315/59*x*t^3 + 42/59*y*t^3 + 96/59*t^4,
x^3*y - 833/354*x*y^3 - 11/236*y^4 - 1633/708*x^3*z - 4675/708*x^2*y*z -
2633/708*x*y^2*z - 27/236*y^3*z + 805/354*x^2*z^2 + 223/59*x*y*z^2 -
4/59*y^2*z^2 - 38/59*x*z^3 + 3359/708*x^3*t + 3811/354*x^2*y*t +
1445/708*x*y^2*t + 303/118*y^3*t - 715/177*x^2*z*t - 527/177*x*y*z*t +
211/118*y^2*z*t + 347/354*x*z^2*t - 195/236*y*z^2*t - 4/59*z^3*t -
127/236*x^2*t^2 - 8237/708*x*y*t^2 + 65/708*y^2*t^2 + 1973/708*x*z*t^2 +
123/59*y*z*t^2 - 24/59*z^2*t^2 - 1753/354*x*t^3 + 873/236*y*t^3 + 128/59*t^4,
x^4 + 269/354*x*y^3 + 35/236*y^4 + 1849/708*x^3*z + 4255/708*x^2*y*z -
247/708*x*y^2*z + 43/236*y^3*z - 727/354*x^2*z^2 - 82/59*x*y*z^2 +
2/59*y^2*z^2 + 19/59*x*z^3 - 5603/708*x^3*t - 3469/354*x^2*y*t -
1637/708*x*y^2*t - 63/118*y^3*t + 328/177*x^2*z*t - 769/177*x*y*z*t -
17/118*y^2*z*t + 151/354*x*z^2*t + 127/236*y*z^2*t + 2/59*z^3*t +
1391/236*x^2*t^2 + 7865/708*x*y*t^2 + 823/708*y^2*t^2 - 1901/708*x*z*t^2 +
86/59*y*z*t^2 + 12/59*z^2*t^2 + 493/354*x*t^3 - 761/236*y*t^3 - 64/59*t^4]);
OC1 := StructureSheaf(C,1);
DimensionOfGlobalSections(OC1);
assert $1 eq 8;
norm_mp, X := DivisorMap(OC1);
ArithmeticGenus(X);
assert $1 eq 1;
B := MinimalBasis(Ideal(X));
#B;
assert $1 eq 20;
[TotalDegree(f) : f in B];
SetEchoInput(ei);
