HELP FOR: A package to compute in the polynomial ring in several variables.

CALLING SEQUENCE:

FM[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to compute in the polynomial ring in several, say n, variables, seen as a free module of rank n! over the ring of symmetric polynomials in n variables. We choose as basis of this module Schubert polynomials indexed by permutations in the symmetric group of degree n.

• By default, one computes in the polynomial ring in 4 variables x1, x2, x3 and x4. In this case, x5, x6, etc. are considered as scalars.

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

• The available functions are:

  FM_n	ToXfix	ToXfixScal	x2Xfix
  x2XfixScal	X2Xfix	Xfix2x	Xfix2X

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

EXAMPLES:

> with(FM):
> FM_n(3);
 
                                      3
 
> x2XfixScal(q*x2*x3);
 
           q s[1, 1] X[1, 2, 3] - q s[1] X[2, 1, 3] + q X[3, 1, 2]