# Documentation

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# `polylib`::`Poly`

Domain of polynomials

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## Syntax

### Domain Creation

`polylib::Poly(`[x1, …]`, <`R`>)`

## Description

`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.

`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.

## Examples

### 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]))```

## Parameters

 `x1` Unknown `R` Admissible coefficient ring for polynomials. See `poly`.

## Entries

 "zero" the zero polynomial "one" the constant polynomial one "indets" list of unknowns "coeffRing" the coefficient ring `R`