HELP FOR: A package for algebras related to hyperoctahedral groups.

CALLING SEQUENCE:

BNA[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to work with several algebras associated to the hyperoctahedral groups Bn, together with their realizations as algebras of operators on the ring of polynomials. It includes the Bn-group algebra together with the Bn-nilCoxeter and Bn-idCoxeter algebra. Bases of these algebras are indexed by codes of Bn.

• A general element is expressed as a linear combination of B[code], where code is a code of B(n), with arbitrary coefficients.

• Whenever there is a conflict between a function name in BNA and another name used in the same session, use the long form BNA[<function>].

• The available functions are:

  BnGaMult	BnGaOnPol	BnGaYang	BnIdcaMult
  BnIdcaOnPol	BnIdcaYang	BnNcaMult	BnNcaOnPol
  BnNcaYang	Bna2Table	BnaAdd	BnaCode2Bar
  BnaCode2Palin	BnaMinus	BnaNormal	BnaPalin2Code
  Rd2BnGa	Rd2BnIdca	Rd2BnNca	Table2Bna

• For help with a particular function do either ?BNA[<function>] or ?BNA,<function> where <function> is one from the above list.

• Instead of BnaAdd, BnaMinus, BnGaMult, BnNcaMult, BnIdcaMult, one can use in short &!!+ &!!- &!!* &!@* &!$*

EXAMPLES:

> with(BNA):
> BnaCode2Palin(q*B[0,1,0,2] - q^2*B[1,1,0,3]);
 
                                         2
          q A[2, 4, 1, 3, 6, 8, 5, 7] - q  A[2, 5, 3, 1, 8, 6, 4, 7]