MatchingFields : Table of Contents

• MatchingFields -- A package for working with matching fields for Grassmannians and partial flag varieties

  • GrMatchingField -- the class of Grassmannian matching fields
  • FlMatchingField -- the class of matching fields for partial flag varieties
  • grMatchingField -- Construct a matching field for the Grassmannian variety
  • flMatchingField -- Construct a matching field for a partial flag variety
  • diagonalMatchingField -- the diagonal matching field
  • matchingFieldFromPermutation -- matching field parametrised by permutations

    • RowNum -- the row of the diagonal weight matrix to permute
    • UsePrimePowers -- use a diagonal weight matrix with multiples of certain powers
    • ScalingCoefficient -- scale the permuted row of the weight matrix
  • getTuples -- The tuples of a matching field
  • getGrMatchingFields -- The Grassmannian matching fields of a Flag matching field
  • isCoherent -- Is the matching field coherent
  • getWeightMatrix -- weight matrix that induces the matching field
  • getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
  • isToricDegeneration -- Does the matching field give rise to a toric degeneration
  • net(GrMatchingField) -- display a matching field
  • GrMatchingField == GrMatchingField -- equality of Grassmannian matching fields
  • FlMatchingField == FlMatchingField -- equality of flag matching fields
  • plueckerIdeal -- The Pluecker ideal of a matching field
  • matchingFieldIdeal -- The toric ideal of a matching field
  • plueckerMap -- The ring map of the Pluecker embedding
  • matchingFieldRingMap -- monomial map of the matching field
  • plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
  • matchingFieldPolytope -- The polytope of a matching field

    • ExtraZeroRows -- enlarging a matrix with zero rows
  • NOBody -- Newton-Okounkov body of the matching field
  • weightMatrixCone -- The cone of weight matrices that induce the matching field
  • algebraicMatroid -- The algebraic matroid of the tropical cone that induces the matroid
  • algebraicMatroidCircuits -- The bases of the algebraic matroid
  • algebraicMatroidBases -- The bases of the algebraic matroid
  • matroidSubdivision -- The matroid subdivision induced by the Pluecker weight of a coherent matching field
  • linearSpanTropCone -- linear span of the tropical cone associated to the matching field
  • TopeField -- A tope field structure on a matching field
  • topeField -- Constructor of a tope field
  • net(TopeField) -- display a tope field
  • getTuples(TopeField) -- tuples of a tope field
  • isLinkage -- Test if a tope field is linkage
  • amalgamation -- The $i$th amalgamation of a tope field