GrMatchingField -- the class of Grassmannian matching fields

Description

Common ways to define Grassmannian matching fields:

grMatchingField-- defined in terms of tuples or a weight matrix
diagonalMatchingField-- the diagonal matching field
matchingFieldFromPermutation-- family of matching fields indexed by permutations

Two Grassmannian matching fields are said to be equal if and only if their tuples are the same.

Technical details. A Grassmannian matching field is derived from the class HashTable. All Grassmannian matching fields have the following fields:

k of type ZZ
n of type ZZ
tuples of type List, accessible withgetTuples
cache

Everything else, including: weight matrices; polynomial rings, maps and ideals; polyhedra such as the weight matrix cone and matching field polytope, are all stored inside the cache. Note that the package does not export the keys, such as k or n. If you wish to directly address the contents of the GrMatchingField, then use "debug MatchingFields".

Functions and methods returning an object of class GrMatchingField :

grMatchingField -- Construct a matching field for the Grassmannian variety

Methods that use an object of class GrMatchingField :

algebraicMatroid(GrMatchingField) -- see algebraicMatroid -- The algebraic matroid of the tropical cone that induces the matroid
algebraicMatroidBases(GrMatchingField) -- see algebraicMatroidBases -- The bases of the algebraic matroid
algebraicMatroidCircuits(GrMatchingField) -- see algebraicMatroidCircuits -- The bases of the algebraic matroid
amalgamation(ZZ,GrMatchingField) -- see amalgamation -- The $i$th amalgamation of a tope field
getTuples(GrMatchingField) -- see getTuples -- The tuples of a matching field
getWeightMatrix(GrMatchingField) -- see getWeightMatrix -- weight matrix that induces the matching field
getWeightPluecker(GrMatchingField) -- see getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
GrMatchingField == GrMatchingField -- equality of Grassmannian matching fields
isCoherent(GrMatchingField) -- see isCoherent -- Is the matching field coherent
isLinkage(GrMatchingField) -- see isLinkage -- Test if a tope field is linkage
isToricDegeneration(GrMatchingField) -- see isToricDegeneration -- Does the matching field give rise to a toric degeneration
linearSpanTropCone(GrMatchingField) -- see linearSpanTropCone -- linear span of the tropical cone associated to the matching field
matchingFieldIdeal(GrMatchingField) -- see matchingFieldIdeal -- The toric ideal of a matching field
matchingFieldPolytope(GrMatchingField) -- see matchingFieldPolytope -- The polytope of a matching field
matchingFieldRingMap(GrMatchingField) -- see matchingFieldRingMap -- monomial map of the matching field
matroidSubdivision(GrMatchingField) -- see matroidSubdivision -- The matroid subdivision induced by the Pluecker weight of a coherent matching field
net(GrMatchingField) -- display a matching field
NOBody(GrMatchingField) -- see NOBody -- Newton-Okounkov body of the matching field
plueckerAlgebra(GrMatchingField) -- see plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
Grassmannian(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
plueckerIdeal(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
plueckerMap(GrMatchingField) -- see plueckerMap -- The ring map of the Pluecker embedding
topeField(GrMatchingField) -- see topeField -- Constructor of a tope field
topeField(GrMatchingField,List) -- see topeField -- Constructor of a tope field
weightMatrixCone(GrMatchingField) -- see weightMatrixCone -- The cone of weight matrices that induce the matching field

For the programmer

The object GrMatchingField is a type, with ancestor classes HashTable < Thing.

GrMatchingField -- the class of Grassmannian matching fields

Description

See also

Functions and methods returning an object of class GrMatchingField :

Methods that use an object of class GrMatchingField :

For the programmer

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