## `polylib::elemSym` -- elementary symmetric polynomials

#### Introduction

`polylib::elemSym``([x1,...,xn], k)` returns the `k`-th elementary symmetric polynomial in the given variables `x1` through `xn`.

#### Call(s)

`polylib::elemSym(l, k)`

#### Parameters

`l` | - | list of indeterminatess
`k` | - | positive integer

#### Returns

The result is a polynomial over the coefficient ring `Expr`. If `k` is greater than the number of operands of `l`, `undefined` is returned.

#### Related Functions

`polylib::representByElemSym`

#### Details

- A given list `l` is a valid first argument only if its elements can be used as indeterminates of a polynomial .

#### Example 1

The first elementary symmetric polynomial is just the sum of its variables:

    >> polylib::elemSym([x,y,z], 1);

                            poly(x + y + z, [x, y, z])

#### Example 2

Indeterminates may also be e.g. trigonometric functions:

    >> polylib::elemSym([sin(u),cos(u), exp(u)], 2);

          poly(sin(u) cos(u) + sin(u) exp(u) + cos(u) exp(u),

             [sin(u), cos(u), exp(u)])

#### Background

- For more information about elementary symmetric polynomials, see v.d. Waerden, Algebra, vol. 1 .

#### Changes

- new function

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