muEC::SP::ToPe((1+q)^5*x3*x4, NoExpand);
muEC::SP::ToPe(q^2*x3*XX[3,1,2]*Y[0,1], Collect);
muEC::SP::ToPe – converts any expression to the Pe-basis
The muEC::SP::ToPe function converts any expression expr to the Pe-basis, which is the dual basis of the basis of monomials less than the “staircase” monomial, i.e. the basis of products of elementary symmetric functions on an alphabet flag. For instance, Pe[1, 2, 0, 1, 0] stands for the product e1(x1,x2,x3,x4)*e2(x1,x2,x3)*e1(x1).
expr may involve some xi'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).
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 ToPe(expr, b, Collect).
Calls:
muEC::SP::ToPe(expr)
muEC::SP::ToPe(expr, b)
Parameters:
|
expr: |
any expression |
|
b: |
any name of a known basis |
Related Functions:
muEC::SP::Tox, muEC::SP::ToX, muEC::SP::ToXX
muEC::SP::ToPe((1+q)^5*x3*x4, NoExpand);
muEC::SP::ToPe(q^2*x3*XX[3,1,2]*Y[0,1], Collect);