SP::ToYY --
converts any expression to the YY Schubert basis
Call(s)
SP::ToYY(expr)
Parametersexpr | - | any expression |
b | - | any name of a known basis |
Introduction
The SP::ToYY function converts any expression expr to the YY 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 does not affect the argument SP::ToYY(expr, YY)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
ToYY(expr, b, Collect).
For instance, may be used to collect the
argument SP::ToYY(expr, YY, Collect)expr.
Example 1>> muEC::SP::ToYY((1+q)^5*x3*x4, NoExpand);
5
(q + 1) (YY[0, 2, 0, 0] - y4 YY[0, 1, 0] +
y3 YY[0, 0, 1, 0] + YY[0, 0, 1, 1, 0] - YY[0, 1, 0, 1, 0] +
y3 (y4 YY[0] - YY[0, 0, 1, 0] + YY[0, 0, 0, 1, 0]))
>> muEC::SP::ToYY(q^2*x3*X[3,1,2], Collect);
2 2 2 2
q y1 y3 YY[0] - q YY[2, 1, 0] - q y1 YY[2, 0, 0] +
2 2 2
YY[1, 0] (q y1 y3 + q y2 y3) + q YY[2, 0, 1, 0] -
2 2 2 2
q y1 YY[0, 1, 0] + q y1 YY[0, 0, 1, 0] +
2 2
(q y1 + q y2) YY[1, 0, 1, 0] +
2 2
YY[1, 1, 0] (- q y1 - q y2)
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package