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## `SP::Tox` -- expresses any expression in the basis of monomials

#### Call(s)

`SP::Tox(expr)`

#### Parameters

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

#### Introduction

The `SP::Tox` function expresses any expression `expr` in the basis of monomials. `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::Tox`(expr, x)` does not affect the argument `expr`.

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 `Tox(expr, b, Collect)`. For instance, ``SP::Tox`(expr, x, Collect)` may be used to collect the argument expr.

#### Example 1

    >> muEC::SP::Tox((1+q)^5*X[1,4,3,2], NoExpand);

                      5       2     2                           2
               (q + 1)  (x1 x2  + x1  x2 + x3 (x2 (x1 + x2) + x1 ))

    >> muEC::SP::Tox((1+q)^5*X[3,1,2]*Y[0,1,2], Collect);

            4           5     4           5       3              5
          x1  x2 (q + 1)  + x1  x3 (q + 1)  + 2 x1  x2 x3 (q + 1)  +

               3   2        5     3   2        5     2      2        5
             x1  x2  (q + 1)  + x1  x3  (q + 1)  + x1  x2 x3  (q + 1)  +

               2   2           5
             x1  x2  x3 (q + 1)

#### Related Functions

`ToX`

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MuPAD Combinat, an open source algebraic combinatorics package