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>)
Parameterssfa | - | a linear combination of products of symmetric functions |
b | - | a basis |
blist | - | a list of bases |
IntroductionThe 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 FunctionsSYMF::SfCollect, SfAExpand, ToeA, TohA, TopA, TomA, TosA
MuPAD Combinat, an open source algebraic combinatorics package