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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 `x`i'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