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## `SP::Sp2TableVar` -- variable set for the SP package

#### Call(s)

`SP::Sp2TableVar(expr)`

#### Parameters

`expr` | - | any expression

#### Introduction

The `SP::Sp2TableVar` function returns a table whose entries describe the set of all Schubert polynomials and variables that appear in a given expression `expr`. The indices of the table are taken into the global variable `SP::SPBases`.

For all bases of type `_index` (`SP::SPBasesIndexed`), the entry consists of the set of all permutations that index the corresponding Schubert polynomials in `expr`.

For all bases of type `DOM_IDENT` (`SP::SPBasesString`), the entry consists of the set of all integers that index the corresponding variable in `expr`.

An entry equal to an empty set means that the element does not appear in `expr`.

One can add a second argument to select some elements among those in `SP::SPBases`. If the second argument is a set of names, then the restriction to this set of indices of the table is returned. In case the second argument is a single name, then the corresponding entry in the table is returned instead of the table.

#### Example 1

    >> muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1]);

                         table(
                           Pe = {},
                           YY = {},
                           Y = {},
                           XX = {},
                           X = {[2, 3, 1], [4, 1, 3, 2]},
                           y = {4, 6},
                           x = {1, 4}
                         )

    >> muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], {X, x});

                         table(
                           X = {[2, 3, 1], [4, 1, 3, 2]},
                           x = {1, 4}
                         )

    >> muEC::SP::Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], y);

                                      {4, 6}

#### Related Functions

``

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MuPAD Combinat, an open source algebraic combinatorics package