SP::ToY
--
converts any expression to the Y Schubert basis
SP::ToY(expr)
expr | - | any expression |
b | - | any name of a known basis |
The SP::ToY
function converts any expression expr to the Y Schubert basis.
expr
may involve some x
i's, simple Schubert polynomials
(X[perm]
, Y[code]
), double Schubert polynomials
(XX[perm]
, YY[code]
), product of elementary functions
(Pe[vect]
), other terms being considered as coefficients.
The expression expr
is expanded and the result is not collected.
One may specify by a second argument, say b
, that expr
is
solely expressed in terms of the known basis b
(x
, X
,
Y
, XX
, YY
, Pe
and even y
that is seen as a basis
in the package).
The call
does not affect the argument SP::ToY
(expr, Y)expr
, but
it simplifies Schubert polynomials indices.
One may add NoExpand
just after the argument expr
to choose not to
expand the expression expr before treating it.
One may collect the result by adding a third argument: this is done by
ToY(expr, b, Collect)
.
For instance,
may be used to collect the
argument SP::ToY
(expr, Y, Collect)expr
.
>> muEC::SP::ToY((1+q)^5*x3*x4,NoExpand,x);
5 (q + 1) (Y[0, 0, 1, 0] - Y[0, 1, 0]) (Y[0, 0, 0, 1, 0] - Y[0, 0, 1, 0])
>> muEC::SP::ToY(q^2*x3*XX[3,1,2]*Y[0,0,1], Collect);
2 2 (q y1 + q y2) Y[1, 2, 0, 0] + 2 2 (q y1 + q y2) Y[3, 0, 0, 0] - 2 2 2 (q y1 + q y2) Y[1, 0, 2, 0, 0] - q Y[2, 2, 0, 0] - 2 2 q Y[3, 1, 0, 0] + q Y[2, 0, 2, 0, 0] - 2 2 q y1 y2 Y[0, 2, 0, 0] + q y1 y2 Y[0, 0, 2, 0, 0]
MuPAD Combinat, an open source algebraic combinatorics package