FUNCTION: Table2Sf - convert a table into a symmetric function

CALLING SEQUENCE:

Table2Sf(t, b)

SYMF[Table2Sf](t, b)

PARAMETERS:

t = any table representing a symmetric function

b = any name of a known basis

SYNOPSIS:

• The Table2Sf function converts a table into a symmetric function. The table should be indexed by partitions and each entry corresponding to a partition (possibly empty) part is interpreted as the coefficient of b[part] in the expression of the symmetric function in the basis b.

• Note that for instance if b='s' then [3,1,1] stands for s[3,1,1] and if b='h' then [3,1,1] denotes the element h3*h1^2.

• Whenever there is a conflict between the function name Table2Sf and another name used in the same session, use the long form SYMF['Table2Sf'].

EXAMPLES:

> with(SYMF):
> t:=table([[]=q, [3,1,1]=q^2, [4,2]=q+1]);
 
                          t := table([
                                                2
                                   [3, 1, 1] = q
                                   [4, 2] = q + 1
                                   [] = q
                               ])
 
> Table2Sf(t, 's');
 
                   2
                  q  s[3, 1, 1] + (q + 1) s[4, 2] + q s[]
 
> Table2Sf(t, 'e');
 
                        2      2
                       q  e3 e1  + (q + 1) e4 e2 + q