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SFA::SfACollect -- collects products that are on algebraic bases (e, h, p) and expands products on linear bases (m, s)

Call(s)


SFA::SfACollect(sfa <,b> <,blist>)

Parameters

sfa- a linear combination of products of symmetric functions
b- a basis
blist- a list of bases

Introduction

The SFA::SfACollect function transforms products of power sums, elementary and complete functions into a valid SFA expression.

Special algorithms are used for products of monomial symmetric functions and products of Schur functions.

The SFA::SfACollect function also normalizes indexing vectors of each symmetric function.

Valid bases are SFA::SFABases. They all are considered by default.

One may specify to collect products (and / or normalize indexing vectors) expressed only on specified bases by adding a second argument which is either a single basis or a list of bases.

Example 1

>> muEC::SFA::SfACollect( p[3](A1)^4 * e[2](A2) * e[1](A2)
             - q*s[2](A3)^2 );
      e[2, 1](A2) p[3, 3, 3, 3](A1) -
      
         q (s[4](A3) + s[2, 2](A3) + s[3, 1](A3))
>> muEC::SFA::SfACollect( p[1,2](A1)^2 - q*m[1,0,0](A2)^2*s[1,3](A3)^2,
               [ s, m ] );
                 2
      p[1, 2](A1)  - q (m[2](A2) + 2 m[1, 1](A2))
      
         (s[4, 4](A3) + s[4, 2, 2](A3) + s[4, 3, 1](A3) +
      
         s[2, 2, 2, 2](A3) + s[3, 2, 2, 1](A3) + s[3, 3, 1, 1](A3))
>> muEC::SFA::SfACollect( p[1,2](A1)^2 - q*m[1,0,0](A2)^2*s[1,3](A3)^2,
               p );
                                             2               2
             p[2, 2, 1, 1](A1) - q s[1, 3](A3)  m[1, 0, 0](A2)

Related Functions

SYMF::SfCollect, SfAExpand, ToeA, TohA, TopA, TomA, TosA

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MuPAD Combinat, an open source algebraic combinatorics package