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SlackIdeals :: slackFromPlucker

slackFromPlucker -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, it fills the corresponding slack matrix with Plucker coordinates

Synopsis

Description

It fills the slack matrix of a given polytope, cone or matroid with Plucker coordinates

i1 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}};
i2 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}};
i3 : fillPl = slackFromPlucker(V, B)

o3 = | -1 0 0  -1 0 |
     | 0  1 0  -1 0 |
     | 0  0 -1 0  0 |
     | -1 0 0  0  1 |
     | 0  1 0  0  1 |
     | 1  1 -1 0  0 |

              6        5
o3 : Matrix ZZ  <--- ZZ
i4 : V = {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {1, 1, 0}};
i5 : fillPl = slackFromPlucker V

Input has been reorderd to
{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}, {0, 0, 1}, {1, 0, 1}}

o5 = | 0 -1 0  0 1 |
     | 1 0  0  0 1 |
     | 0 -1 -1 0 0 |
     | 1 0  -1 0 0 |
     | 0 -1 0  1 0 |
     | 1 0  0  1 0 |

              6        5
o5 : Matrix QQ  <--- QQ

Caveat

Does not check if B actually spans for given V, does not check orientation of simplices in B, so that the resulting slack matrix may differ by signs of each column.

See also

Ways to use slackFromPlucker :