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

The muEC::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 muEC::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.

→ Examples

Call:

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

Parameters:

sf

a linear combination of products of symmetric functions

b

a basis

blist

a list of bases

Related Functions:

muEC::SFA::SfACollect, muEC::SYMF::Toe, muEC::SYMF::Toh, muEC::SYMF::Tom, muEC::SYMF::Top, muEC::SYMF::Tos

Example 1:

muEC::SYMF::SfCollect( p[3]^4 * e[2] * e[1] - q*s[2]^2 );

math

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 );

math