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GCExpression

Description

A general data type for representing elements of bracket rings and Grassmann-Cayley algebras. GC expressions can be assembled into matrices, and they support a number of the usual arithmetic operations: addition, multiplication, and scalar multiplication.

Multiplication on the Grassmann-Cayley algebra is the usual exterior product. This represents the span, or join, of linear subspaces in a given vector space.

The Grassmann-Cayley algebra is also endowed with a "shuffle product", representing the intersection or meet of linear subspaces. This is implemented in GCExpression ^ GCExpression.

Types of GCExpression:

Methods that use an object of class GCExpression:

  • bracketRing(GCExpression) -- see bracketRing -- Constructor for bracket rings
  • coefficients(GCExpression) (missing documentation)
  • commonRing(GCExpression,GCExpression) (missing documentation)
  • degree(GCExpression) (missing documentation)
  • factor(GCExpression) (missing documentation)
  • GCExpression * GCExpression (missing documentation)
  • GCExpression * Number (missing documentation)
  • GCExpression * RingElement (missing documentation)
  • GCExpression + GCExpression (missing documentation)
  • GCExpression - GCExpression (missing documentation)
  • GCExpression ^ GCExpression -- Shuffle product in the Grassmann-Cayley Algebra
  • GCExpression ^ RingElement (missing documentation)
  • GCExpression ^ ZZ (missing documentation)
  • GCExpression _ BracketRing -- Substituting top-degree Grassmann-Cayley elements into the bracket ring
  • GCExpression _ GCAlgebra (missing documentation)
  • net(GCExpression) (missing documentation)
  • normalForm(GCExpression) -- see normalForm -- Represent a bracket polynomial in a normal form with respect to a Groebner basis
  • Number * GCExpression (missing documentation)
  • ring(GCExpression) (missing documentation)
  • RingElement * GCExpression (missing documentation)
  • RingElement ^ GCExpression (missing documentation)
  • terms(GCExpression) (missing documentation)

For the programmer

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


The source of this document is in Brackets.m2:579:0.