LIB "gitfan.lib";
ring R = 0,T(1..10),wp(1,1,1,1,1,1,1,1,1,1);
ideal J =
T(5)*T(10)-T(6)*T(9)+T(7)*T(8),
T(1)*T(9)-T(2)*T(7)+T(4)*T(5),
T(1)*T(8)-T(2)*T(6)+T(3)*T(5),
T(1)*T(10)-T(3)*T(7)+T(4)*T(6),
T(2)*T(10)-T(3)*T(9)+T(4)*T(8);
intmat Q[5][10] =
1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 1, 1, 1, 0, 0, 0,
0, 1, 1, 0, 0, 0, -1, 1, 0, 0,
0, 1, 0, 1, 0, -1, 0, 0, 1, 0,
0, 0, 1, 1, -1, 0, 0, 0, 0, 1;
list simplexSymmetryGroup = G25Action();
list simplexOrbitRepresentatives = intvec( 1, 2, 3, 4, 5 ),
intvec( 1, 2, 3, 5, 6 ),
intvec( 1, 2, 3, 5, 7 ),
intvec( 1, 2, 3, 5, 10 ),
intvec( 1, 2, 3, 7, 9 ),
intvec( 1, 2, 6, 9, 10 ),
intvec( 1, 2, 3, 4, 5, 6 ),
intvec( 1, 2, 3, 4, 5, 10 ),
intvec( 1, 2, 3, 5, 6, 8 ),
intvec( 1, 2, 3, 5, 6, 9 ),
intvec( 1, 2, 3, 5, 7, 10 ),
intvec( 1, 2, 3, 7, 9, 10 ),
intvec( 1, 2, 3, 4, 5, 6, 7 ),
intvec( 1, 2, 3, 4, 5, 6, 8 ),
intvec( 1, 2, 3, 4, 5, 6, 9 ),
intvec( 1, 2, 3, 5, 6, 9, 10 ),
intvec( 1, 2, 3, 4, 5, 6, 7, 8 ),
intvec( 1, 2, 3, 4, 5, 6, 9, 10 ),
intvec( 1, 2, 3, 4, 5, 6, 7, 8, 9 ),
intvec( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 );
list afaceOrbitRepresentatives=afaces(J,simplexOrbitRepresentatives);
list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
apply(afaceOrbits,size);
==> 10 15 10 1
list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits);
apply(minAfaceOrbits,size);
==> 10 15
list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q);
apply(listOfOrbitConeOrbits,size);
==> 10 15
list listOfMinimalOrbitConeOrbits = minimalOrbitConeOrbits(listOfOrbitConeOrbits);
size(listOfMinimalOrbitConeOrbits);
==> 2