## `polylib::Poly` -- domain of polynomials

#### Introduction

`polylib::Poly``([x1,...,xn], R)` creates the ring of polynomials in the unknowns `x1` through `xn` over the coefficient ring `R`. If the argument `R` is missing, `Expr` is used.

#### Domain

`polylib::Poly([x1...] <, R>)`

#### Parameters

`x1` | - | unknown
`R` | - | admissible coefficient ring for polynomials. See `poly`.

#### Details

- `polylib::Poly` is a facade domain; it has no domain elements. It serves only as a coefficient ring for polynomials.
- The attempt to create an element of `polylib::Poly` results in a `DOM_POLY`.
- The arithmetical operations of the domain are realized by the corresponding kernel methods.

#### Related Domains

`Dom::DistributedPolynomial`

#### Entries

zero

  the zero polynomial

one

  the constant polynomial one

indets

  list of unknowns

coeffRing

  the coefficient ring `R`

#### Example 1

`polylib::Poly` can be used for defining polynomials in `x` whose coefficients are polynomials in `y`. Such polynomials must not be confused with bivariate polynomials in `x` and `y`.

    >> delete x,y: e:= x*(y^2*2 + y) + 3*y:
       poly(e, [x, y]);  poly(e, [x], polylib::Poly([y]))

                                   2
                         poly(2 x y  + x y + 3 y, [x, y])

                           2
              poly((y + 2 y ) x + 3 y, [x], polylib::Poly([y], Expr))

#### Changes

- used to be called `Poly`

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