SP::ToXX
--
converts any expression to the XX Schubert basis
SP::ToXX(expr)
expr | - | any expression |
b | - | any name of a known basis |
The SP::ToXX
function converts any expression expr to the XX Schubert basis.
expr may involve some x
i's, simple Schubert polynomials
(X[perm]
, Y[code]
), double Schubert polynomials
(XX[perm]
, YY[code]
, the second alphabet being the y
i's),
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::ToXX
(expr, XX)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
ToXX(expr, b, Collect)
.
For instance,
may be used to collect the
argument SP::ToXX
(expr, XX, Collect)expr
.
>> muEC::SP::ToXX((1+q)^5*x3*x4, NoExpand);
5 (q + 1) (y3 XX[1, 2, 4, 3] - y4 XX[1, 3, 2] + y3 (y4 XX[1] - XX[1, 2, 4, 3] + XX[1, 2, 3, 5, 4]) + XX[1, 4, 2, 3] + XX[1, 2, 4, 5, 3] - XX[1, 3, 2, 5, 4])
>> muEC::SP::ToXX(q^2*x3*X[3,1,2], Collect);
2 2 2 2 (q y1 + q y2) XX[2, 1, 4, 3] - (q y1 + q y2) XX[2, 3, 1] + 2 2 2 (q y1 y3 + q y2 y3) XX[2, 1] - q XX[3, 2, 1] + 2 2 2 q XX[3, 1, 4, 2] - q y1 XX[1, 3, 2] + 2 2 2 2 2 q y1 XX[1, 2, 4, 3] - q y1 XX[3, 1, 2] + q y1 y3 XX[1]
MuPAD Combinat, an open source algebraic combinatorics package