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## `SYMF::SfCollect` -- collects products that are on algebraic bases (`e, h, p`) and expands products on linear bases (`m, s`)

#### Call(s)

`SYMF::SfCollect(sf <,b> <,blist>)`

#### Parameters

`sf` | - | a linear combination of products of symmetric functions
`b` | - | a basis
`blist` | - | a list of bases

#### Introduction

The `SYMF::SfCollect` function transforms products of power sums, elementary and complete functions into a valid `SYMF` expression.

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

The `SYMF::SfCollect` function also normalizes indexing vectors of each symmetric function.

Valid bases are `SYMF::SYMFBases`. 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::SYMF::SfCollect( p[3]^4 * e[2] * e[1] - q*s[2]^2 );

               e[2, 1] p[3, 3, 3, 3] - q (s[4] + s[2, 2] + s[3, 1])

    >> muEC::SYMF::SfCollect( p[1,2]^2 - q*m[1,0,0]^2*s[1,3]^2, [ s, m ] );

                 2
          p[1, 2]  - 2 q (m[2] + 2 m[1, 1])

             (s[4, 4] + s[4, 2, 2] + s[4, 3, 1] + s[2, 2, 2, 2] +

             s[3, 2, 2, 1] + s[3, 3, 1, 1])

    >> muEC::SYMF::SfCollect( p[1,2]^2 - q*m[1,0,0]^2*s[1,3]^2, p );

                                               2           2
                      p[2, 2, 1, 1] - q s[1, 3]  m[1, 0, 0]

#### Related Functions

`SFA::SfACollect`, `Toe`, `Toh`, `Top`, `Tom`, `Tos`

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MuPAD Combinat, an open source algebraic combinatorics package