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SlackIdeals :: graphicIdeal

graphicIdeal -- creates the toric ideal of the non-incidence graph of a polytope

Synopsis

Description

The graphic ideal associated to a polytope is the toric ideal of the vector configuration consisting of the columns of the vertex-edge incidence matrix of the non-incidence (of vertices and facets) graph of the polytope.

i1 : P = convexHull(matrix{{0, 0, 1, 1}, {0, 1, 0, 1}});
i2 : T = graphicIdeal P

Order of vertices is 
{{0, 0}, {1, 0}, {0, 1}, {1, 1}}
Graph computed from symbolic adjacency matrix: | 0   y_1 0   y_2 |
                                               | y_3 0   0   y_4 |
                                               | 0   y_5 y_6 0   |
                                               | y_7 0   y_8 0   |

o2 = ideal(y y y y  - y y y y )
            0 3 5 6    1 2 4 7

o2 : Ideal of QQ[y , y , y , y , y , y , y , y ]
                  0   1   2   3   4   5   6   7

Caveat

If S is not a symbolic slack matrix, the ideal will have variables indexed as in symbolicSlackMatrix (from left to right in order by rows of S).

See also

Ways to use graphicIdeal :