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SP::ToY -- converts any expression to the Y Schubert basis

Call(s)


SP::ToY(expr)

Parameters

expr- any expression
b- any name of a known basis

Introduction

The SP::ToY function converts any expression expr to the Y Schubert basis. 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).

The call SP::ToY(expr, Y) 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 ToY(expr, b, Collect). For instance, SP::ToY(expr, Y, Collect) may be used to collect the argument expr.

Example 1

>> 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]

Related Functions

Tox, ToX

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MuPAD Combinat, an open source algebraic combinatorics package