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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