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isCoherent -- Is the matching field coherent

Synopsis

Description

We say that a matching field $\Lambda$ is coherent if it is induced by a weight matrix. Note that we use the minimum convention for weight matrices however for polynomial rings, the Weights option for MonomialOrder uses the maximum convention.

i1 : L1 = grMatchingField(2, 4, {{1,2}, {1,3}, {2,3}, {1,4}, {2,4}, {4,3}})

o1 = Grassmannian Matching Field for Gr(2, 4)

o1 : GrMatchingField
 
i2 : isCoherent L1

o2 = true
 
i3 : getWeightMatrix L1

o3 = | 0 0  0  0  |
     | 0 -1 -3 -2 |

              2       4
o3 : Matrix ZZ  <-- ZZ
 
i4 : L2 = grMatchingField(2, 3, {{1,2}, {2,3}, {3,1}})

o4 = Grassmannian Matching Field for Gr(2, 3)

o4 : GrMatchingField
 
i5 : isCoherent L2

o5 = false

In the examples above, the matching fields are defined in terms of their tuples. To check whether the matching fields are coherent, the weight matrix cone is constructed, see the function weightMatrixCone. The matching field is coherent if and only if the weight matrix cone is full dimensional. If the matching field happens to be coherent, then an interior point is used for any further computations that require a weight matrix.

See also

Ways to use isCoherent :

For the programmer

The object isCoherent is a method function.

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