Singular

LIB "gitfan.lib";
// Note that simplexOrbitRepresentatives and simplexSymmetryGroup are subsets of the actual sets for G25. For the full example see the examples in the documentation
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 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, 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);
==> (T(1),T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5),T(6))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==>    [5]:
==>       T(6)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5),T(7))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==>    [5]:
==>       T(7)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5),T(10))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==>    [5]:
==>       T(10)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(7),T(9))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(7)
==>    [5]:
==>       T(9)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5),T(6),T(9),T(10))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==>    [6]:
==>       T(6)
==>    [7]:
==>       T(9)
==>    [8]:
==>       T(10)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8),T(9))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==>    [6]:
==>       T(6)
==>    [7]:
==>       T(7)
==>    [8]:
==>       T(8)
==>    [9]:
==>       T(9)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5),T(6),T(7),T(8),T(9),T(10))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==>    [6]:
==>       T(6)
==>    [7]:
==>       T(7)
==>    [8]:
==>       T(8)
==>    [9]:
==>       T(9)
==>    [10]:
==>       T(10)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1,1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
list simplexSymmetryGroup = permutationFromIntvec(intvec( 1 .. 10 )),
permutationFromIntvec(intvec( 1, 2, 4, 3, 5, 7, 6, 9, 8, 10 )),
permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )),
permutationFromIntvec(intvec( 1, 3, 4, 2, 6, 7, 5, 10, 8, 9 )),
permutationFromIntvec(intvec( 1, 4, 2, 3, 7, 5, 6, 9, 10, 8 )),
permutationFromIntvec(intvec( 1, 4, 3, 2, 7, 6, 5, 10, 9, 8 ));
list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
apply(afaceOrbits,size);
==> 3 3 1
list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits);
apply(minAfaceOrbits,size);
==> 3
list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q);