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D.15.18.12 computeAfaceOrbits
Procedure from library gitfan.lib (see gitfan_lib).
- Usage:
- computeAfaceOrbits(AF,G); AF list of intvecs, G: list of permutations
- Purpose:
- Computes the orbits of the afaces in the list AF under the group action in G, where G is a list of permutations. We assume that the elements of G form a group and the first entry corresponds to the neutral element.
- Return:
- a list of lists of intvecs
Example:
| | 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);
==> (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(6),T(9),T(10))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(6)
==> [4]:
==> T(9)
==> [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(4),T(5),T(6))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(4)
==> [5]:
==> T(5)
==> [6]:
==> T(6)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 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(10))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(4)
==> [5]:
==> T(5)
==> [6]:
==> T(10)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 1,1,1,1,1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> (T(1),T(2),T(3),T(5),T(6),T(8))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(5)
==> [5]:
==> T(6)
==> [6]:
==> T(8)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 1,1,1,1,1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> (T(1),T(2),T(3),T(5),T(6),T(9))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(5)
==> [5]:
==> T(6)
==> [6]:
==> T(9)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 1,1,1,1,1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> (T(1),T(2),T(3),T(5),T(7),T(10))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(5)
==> [5]:
==> T(7)
==> [6]:
==> T(10)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 1,1,1,1,1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> (T(1),T(2),T(3),T(7),T(9),T(10))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(7)
==> [5]:
==> T(9)
==> [6]:
==> T(10)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 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))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(4)
==> [5]:
==> T(5)
==> [6]:
==> T(6)
==> [7]:
==> T(7)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 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(8))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(4)
==> [5]:
==> T(5)
==> [6]:
==> T(6)
==> [7]:
==> T(8)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 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(9))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(4)
==> [5]:
==> T(5)
==> [6]:
==> T(6)
==> [7]:
==> T(9)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 1,1,1,1,1,1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> (T(1),T(2),T(3),T(5),T(6),T(9),T(10))
==> [1]:
==> 0
==> [2]:
==> [1]:
==> T(1)
==> [2]:
==> T(2)
==> [3]:
==> T(3)
==> [4]:
==> T(5)
==> [5]:
==> T(6)
==> [6]:
==> T(9)
==> [7]:
==> T(10)
==> [3]:
==> [1]:
==> [1]:
==> wp
==> [2]:
==> 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))
==> [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)
==> [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(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 fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
apply(afaceOrbits,size);
==> 10 15 10 1
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