muEC::SP::ToXX – converts any expression to the XX Schubert basis
The muEC::SP::ToXX function converts any expression expr to the XX Schubert basis. expr may involve some xi's, simple Schubert polynomials (X[perm], Y[code]), double Schubert polynomials (XX[perm], YY[code], the second alphabet being the yi'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 muEC::SP::ToXX(expr, XX) does not affect the argument 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, muEC::SP::ToXX(expr, XX, Collect) may be used to collect the argument expr.
Calls:
muEC::SP::ToXX(expr)
muEC::SP::ToXX(expr, b)
Parameters:
|
expr: |
any expression |
|
b: |
any name of a known basis |
Related Functions:
muEC::SP::ToXX((1+q)^5*x3*x4, NoExpand);
muEC::SP::ToXX(q^2*x3*X[3,1,2], Collect); // BROKEN EXAMPLE
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]