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## `SP::ToXX` -- converts any expression to the XX Schubert basis

#### Call(s)

`SP::ToXX(expr)`

#### Parameters

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

#### Introduction

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 ``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, ``SP::ToXX`(expr, XX, Collect)` may be used to collect the argument `expr`.

#### Example 1

    >> 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]

#### Related Functions

`ToYY`

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MuPAD Combinat, an open source algebraic combinatorics package