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bracketRing -- Constructor for bracket rings

Description

To construct the bracket ring $B_{n,d}$ it is enough to specify two integers. In that case, each bracket will contain $n$ symbols which are integers between $1$ and $d.$

i1 : B = bracketRing(6, 3)

o1 = B
      6,3

o1 : BracketRing
i2 : T = [1 4 5]_B * [1 5 6]_B * [2 3 4]_B

o2 = [234]*[156]*[145]

o2 : GCExpression

One may also provide a visible list of $n$ symbols.

i3 : B2 = bracketRing(a..f, 3)

o3 = B
      6,3

o3 : BracketRing

Additionally, brackets can be interpreted as the top-degree elements of the Grassmann-Cayley algebra.

i4 : G = gc(a..f, 3)

o4 = Grassmann-Cayley Algebra generated by 1-extensors a..f

o4 : GCAlgebra
i5 : B3 = bracketRing G

o5 = B
      6,3

o5 : BracketRing

See also BracketRing.

Ways to use bracketRing:

  • bracketRing(AbstractGCRing)
  • bracketRing(BracketRing)
  • bracketRing(GCAlgebra)
  • bracketRing(GCExpression)
  • bracketRing(VisibleList,ZZ)
  • bracketRing(ZZ,ZZ)

For the programmer

The object bracketRing is a method function with options.


The source of this document is in Brackets.m2:461:0.