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ThinSincereQuivers :: basisForFlowPolytope

basisForFlowPolytope -- compute the necessary basis vectors for the hyperplane of a flow polytope

Synopsis

Description

The polytope associated to a toric quiver is defined in terms of the stable spanning trees for that given quiver, and hence its vertices are in a lower dimensional subspace of the space with dimension $|Q_1|$. Thus a lower dimensional basis is useful for viewing polytopes in the appropriate dimension.

i1 : basisForFlowPolytope bipartiteQuiver(2,3)

o1 = | -1 0  |
     | 0  -1 |
     | 1  1  |
     | 1  0  |
     | 0  1  |
     | -1 -1 |

              6        2
o1 : Matrix ZZ  <--- ZZ
 
i2 : basisForFlowPolytope ({0,1,4,5},  bipartiteQuiver(2,3))

o2 = | 0  1  |
     | 1  -1 |
     | -1 0  |
     | 0  -1 |
     | -1 1  |
     | 1  0  |

              6        2
o2 : Matrix ZZ  <--- ZZ

Ways to use basisForFlowPolytope :

For the programmer

The object basisForFlowPolytope is a method function.