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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