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SlackIdeals :: slackFromGalePlucker

slackFromGalePlucker -- fill the slack matrix with Plucker coordinates of the Gale transform

Synopsis

Description

Given a set of vectors of a Gale transform or a matrix whose columns form a Gale transform of a polytope, it fills the slack matrix of the polytope with Plucker coordinates of the Gale transform.

i1 : G = {{0, 1}, {1, 0}, {-1, -1}, {0, -1}, {-1, 0}, {1, 1}};
i2 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}};
i3 : slackFromGalePlucker(B, G)

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

              6        5
o3 : Matrix ZZ  <--- ZZ
i4 : MG = matrix(RR, {{0, 1, -1, 0, -1, 1}, {1, 0, -1, -1, 0, 1}});

                2          6
o4 : Matrix RR    <--- RR
              53         53
i5 : B = {{1, 2, 4}, {0, 2, 3}, {0, 1, 4}, {3, 4, 5}, {0, 1, 2}};
i6 : slackFromGalePlucker(B, MG)

o6 = | 1 0  0 1 0  |
     | 0 -1 0 1 0  |
     | 0 0  1 1 0  |
     | 1 0  0 0 -1 |
     | 0 -1 0 0 -1 |
     | 0 0  1 0 -1 |

                6          5
o6 : Matrix RR    <--- RR
              53         53

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 slackFromGalePlucker :

For the programmer

The object slackFromGalePlucker is a method function.