Macaulay2 » Documentation
Packages » MatchingFields » MatchingField
next | previous | forward | backward | up | index | toc

MatchingField -- The class of Matching Fields

Description

A MatchingField is the common ancestor of Grassmannian Matching Fields GrMatchingField and partial flag Matching Fields FlMatchingField. A MatchingField is constructed with the function matchingField.

Two MatchingFields are equal if and only if their tuples are the same.

Technical details. A MatchingField is derived from the class HashTable. Each MatchingField has the following fields:

  • tupleMaxSize of type ZZ
  • tupleSizeList of type List
  • tupleMaxValue of type ZZ
  • tuples of type List, accessible with getTuples
  • cache

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

See also

Menu

Types of MatchingField:

Functions and methods returning an object of class MatchingField:

Methods that use an object of class MatchingField:

  • getTuples(MatchingField) -- see getTuples -- The tuples of a matching field
  • getWeightMatrix(MatchingField) -- see getWeightMatrix -- weight matrix that induces the matching field
  • getWeightPluecker(MatchingField) -- see getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
  • isCoherent(MatchingField) -- see isCoherent -- Is the matching field coherent
  • isToricDegeneration(MatchingField) -- see isToricDegeneration -- Does the matching field give rise to a toric degeneration
  • MatchingField == MatchingField -- equality of matching fields
  • matchingFieldIdeal(MatchingField) -- see matchingFieldIdeal -- The toric ideal of a matching field
  • matchingFieldRingMap(MatchingField) -- see matchingFieldRingMap -- monomial map of the matching field
  • html(MatchingField) -- see net(GrMatchingField) -- display a matching field
  • net(MatchingField) -- see net(GrMatchingField) -- display a matching field
  • plueckerAlgebra(MatchingField) -- see plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
  • plueckerMap(MatchingField) -- see plueckerMap -- The ring map of the Pluecker embedding

For the programmer

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

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/MatchingFields.m2:2133:0.