HELP FOR: A package for the nilCoxeter algebra.

CALLING SEQUENCE:

NCA[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to work with the nilCoxeter algebra corresponding to the symmetric group. This algebra is realized as the algebra of divided differences acting on polynomials.

• This algebra is generated by simple divided differences Di satisfying the braid relations, together with Di^2 = 0 for all i.

• A general element is expressed as a linear combination of A[perm], where perm is a permutation, with arbitrary coefficients.

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

• The available functions are:

  Nca2Table	NcaAdd	NcaMinus	NcaMult
  NcaNormal	NcaOnPol	NcaOnX	NcaOnXfix
  NcaOnXX	NcaOnY	NcaOnYY	NcaYang
  Rd2Nca	Table2Nca

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

• Instead of NcaAdd, NcaMinus, NcaMult, one can use in short &@+ &@- &@*

EXAMPLES:

> with(NCA):
> a:=q + u/t*A[3,1,2]:
> b:=t*A[2,1,3] - A[1,3,2]:
> NcaMult(a, b);
 
                                                 u A[3, 2, 1]
                 q t A[2, 1, 3] - q A[1, 3, 2] - ------------
                                                       t