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SlackIdeals :: getFacetBases

getFacetBases -- given a slack matrix or a list of vertices of d-polytope or a rank d+1 matroid, or (d+1)-cone generators, creates a sorted list of vertices (empty if a matrix is given as input) in the order corresponding to B, and B the list of d spanning elements for each facet

Synopsis

Description

This function produces a list B of d spanning elements for each facet a given d-polytope or rank d+1 matroid, or (d+1)-cone generators. If a list of vertices is given as input, it also creates a sorted list of vertices from which B is computed

i1 : V = {{0, 0}, {1, 0}, {2, 1}, {1, 2}, {0, 1}};
i2 : (newV, B) = getFacetBases V

o2 = ({{0, 0}, {1, 0}, {0, 1}, {2, 1}, {1, 2}}, {{0, 2}, {0, 1}, {1, 3}, {2,
     ------------------------------------------------------------------------
     4}, {3, 4}})

o2 : Sequence
i3 : V = {{0, 0}, {1, 0}, {1, 1}, {0, 1}};
i4 : S = slackMatrix V;

Order of vertices is 
{{0, 0}, {1, 0}, {0, 1}, {1, 1}}

              4        4
o4 : Matrix QQ  <--- QQ
i5 : (newV, B) = getFacetBases S

o5 = ({}, {{0, 2}, {1, 3}, {0, 1}, {2, 3}})

o5 : Sequence

See also

Ways to use getFacetBases :