SYMF::SfCollect
--
collects products that are on algebraic bases (e, h, p
)
and expands products on linear bases (m, s
)
SYMF::SfCollect(sf <,b> <,blist>)
sf | - | a linear combination of products of symmetric functions |
b | - | a basis |
blist | - | a list of bases |
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.
>> 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]
SFA::SfACollect
, Toe
, Toh
, Top
, Tom
, Tos
MuPAD Combinat, an open source algebraic combinatorics package