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FlMatchingField -- the class of matching fields for partial flag varieties

Description

Common ways to define flag matching fields:

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

  • kList of type ZZ
  • n of type ZZ
  • grMatchingFieldList of type List, the list of Grassmannian matching fields contained within, accessible with the functiongetGrMatchingFields
  • 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 kList or n. If you wish to directly address the contents of the FlMatchingField, then use "debug MatchingFields".

See also

Menu

Functions and methods returning an object of class FlMatchingField:

Methods that use an object of class FlMatchingField:

  • FlMatchingField == FlMatchingField -- equality of flag matching fields
  • getGrMatchingFields(FlMatchingField) -- see getGrMatchingFields -- The Grassmannian matching fields of a Flag matching field
  • getTuples(FlMatchingField) -- see getTuples -- The tuples of a matching field
  • getWeightMatrix(FlMatchingField) -- see getWeightMatrix -- weight matrix that induces the matching field
  • getWeightPluecker(FlMatchingField) -- see getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
  • isCoherent(FlMatchingField) -- see isCoherent -- Is the matching field coherent
  • isToricDegeneration(FlMatchingField) -- see isToricDegeneration -- Does the matching field give rise to a toric degeneration
  • matchingFieldIdeal(FlMatchingField) -- see matchingFieldIdeal -- The toric ideal of a matching field
  • matchingFieldPolytope(FlMatchingField) -- see matchingFieldPolytope -- The polytope of a matching field
  • matchingFieldRingMap(FlMatchingField) -- see matchingFieldRingMap -- monomial map of the matching field
  • net(FlMatchingField) -- see net(GrMatchingField) -- display a matching field
  • NOBody(FlMatchingField) -- see NOBody -- Newton-Okounkov body of the matching field
  • plueckerAlgebra(FlMatchingField) -- see plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
  • plueckerIdeal(FlMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
  • plueckerMap(FlMatchingField) -- see plueckerMap -- The ring map of the Pluecker embedding
  • weightMatrixCone(FlMatchingField) -- see weightMatrixCone -- The cone of weight matrices that induce the matching field

For the programmer

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


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/MatchingFields.m2:2376:0.