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GrMatchingField -- the class of Grassmannian matching fields

Description

Common ways to define Grassmannian matching fields:

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 MatchingField. All Grassmannian matching fields have 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 all 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

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
  • isLinkage(GrMatchingField) -- see isLinkage -- Test if a tope field is linkage
  • linearSpanTropCone(GrMatchingField) -- see linearSpanTropCone -- linear span of the tropical cone associated to the matching field
  • matchingFieldPolytope(GrMatchingField) -- see matchingFieldPolytope -- The polytope of a matching field
  • matroidSubdivision(GrMatchingField) -- see matroidSubdivision -- The matroid subdivision induced by the Pluecker weight of a coherent matching field
  • html(GrMatchingField) -- see net(GrMatchingField) -- display a matching field
  • net(GrMatchingField) -- display a matching field
  • NOBody(GrMatchingField) -- see NOBody -- Newton-Okounkov body of the matching field
  • Grassmannian(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
  • plueckerIdeal(GrMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
  • 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 MatchingField < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/MatchingFields.m2:2174:0.