Given the number of polytope vertices, cone generators, or matroid vectors, or a set of polytope vertices, cone generators, or matroid vectors, or a slack matrix and a set of set of hyperplane spanning set indices, it fills the slack matrix with Plucker variables.
i1 : v = 6; |
i2 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}}; |
i3 : fillPl = symbolicSlackOfPlucker(v, B) o3 = | -p_(0,1,2,4) 0 0 -p_(0,3,4,5) 0 | | 0 p_(0,1,2,3) 0 -p_(1,3,4,5) 0 | | 0 0 -p_(0,1,2,4) -p_(2,3,4,5) 0 | | -p_(1,2,3,4) 0 -p_(0,1,3,4) 0 p_(0,1,2,3) | | 0 p_(0,2,3,4) 0 0 p_(0,1,2,4) | | p_(1,2,4,5) p_(0,2,3,5) p_(0,1,4,5) 0 p_(0,1,2,5) | 6 5 o3 : Matrix (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) <--- (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 |
i4 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}}; |
i5 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}}; |
i6 : fillPl = symbolicSlackOfPlucker(V, B) o6 = | -p_(0,1,2,4) 0 0 -p_(0,3,4,5) 0 | | 0 p_(0,1,2,3) 0 -p_(1,3,4,5) 0 | | 0 0 -p_(0,1,2,4) -p_(2,3,4,5) 0 | | -p_(1,2,3,4) 0 -p_(0,1,3,4) 0 p_(0,1,2,3) | | 0 p_(0,2,3,4) 0 0 p_(0,1,2,4) | | p_(1,2,4,5) p_(0,2,3,5) p_(0,1,4,5) 0 p_(0,1,2,5) | 6 5 o6 : Matrix (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) <--- (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 |
i7 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}}; |
i8 : fillPl = symbolicSlackOfPlucker V Input has been reorderd to {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}} o8 = | 0 -p_(0,1,3,5) 0 0 -p_(0,2,3,4) | | p_(0,1,2,4) 0 0 0 -p_(1,2,3,4) | | 0 p_(1,2,3,5) -p_(0,1,2,4) 0 0 | | -p_(0,2,3,4) 0 -p_(0,1,3,4) p_(0,1,2,3) 0 | | 0 -p_(1,3,4,5) 0 p_(0,1,2,4) 0 | | p_(0,2,4,5) 0 p_(0,1,4,5) p_(0,1,2,5) p_(2,3,4,5) | 6 5 o8 : Matrix (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) <--- (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 |
i9 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}}; |
i10 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}}; |
i11 : fillPl = symbolicSlackOfPlucker(slackMatrix V, B) Order of vertices is {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}} o11 = | -p_(0,1,2,4) 0 0 -p_(0,3,4,5) 0 | | 0 p_(0,1,2,3) 0 -p_(1,3,4,5) 0 | | 0 0 -p_(0,1,2,4) -p_(2,3,4,5) 0 | | -p_(1,2,3,4) 0 -p_(0,1,3,4) 0 p_(0,1,2,3) | | 0 p_(0,2,3,4) 0 0 p_(0,1,2,4) | | p_(1,2,4,5) p_(0,2,3,5) p_(0,1,4,5) 0 p_(0,1,2,5) | 6 5 o11 : Matrix (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) <--- (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 |
i12 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}}; |
i13 : fillPl = symbolicSlackOfPlucker(slackMatrix V) Order of vertices is {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}} o13 = | 0 -p_(0,1,3,5) 0 0 -p_(0,2,3,4) | | p_(0,1,2,4) 0 0 0 -p_(1,2,3,4) | | 0 p_(1,2,3,5) -p_(0,1,2,4) 0 0 | | -p_(0,2,3,4) 0 -p_(0,1,3,4) p_(0,1,2,3) 0 | | 0 -p_(1,3,4,5) 0 p_(0,1,2,4) 0 | | p_(0,2,4,5) 0 p_(0,1,4,5) p_(0,1,2,5) p_(2,3,4,5) | 6 5 o13 : Matrix (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) <--- (QQ[p ..p , p , p , p , p , p , p , p , p , p , p , p , p , p ]) 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 0,1,2,3 0,1,2,4 0,1,3,4 0,2,3,4 1,2,3,4 0,1,2,5 0,1,3,5 0,2,3,5 1,2,3,5 0,1,4,5 0,2,4,5 1,2,4,5 0,3,4,5 1,3,4,5 2,3,4,5 |
The object symbolicSlackOfPlucker is a method function with options.