# Documentation

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# `polylib`::`divisors`

Divisors of a polynomial, polynomial expression, or Factored element

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## Syntax

```polylib::divisors(`p`)
polylib::divisors(`f`)
polylib::divisors(`e`)
```

## Description

`polylib::divisors(p)` computes the set of all monic divisors of the polynomial or polynomial expression `p`.

`polylib::divisors(f)` returns all monic divisors of a pre-factored polynomial. Cf. Example 3.

`polylib::divisors` works on polynomials of category `Cat::Polynomial` as well. Cf. Example 4.

## Examples

### Example 1

If the argument is a polynomial, a set of polynomials is returned:

`polylib::divisors(poly(x^2 - 2*x + 1))`

### Example 2

If the argument is a polynomial expression, a set of polynomial expressions is returned:

`polylib::divisors(x^2 - 1)`

### Example 3

If the argument is of type `Factored` (a `factor` return value) a set of polynomials is returned:

```p := factor(poly(x^2 - 1)); polylib::divisors(p)```

The polynomials in the resulting set have the same type as the polynomials in the `Factored` element:

```p := factor(x^2 - 1); polylib::divisors(p)```

### Example 4

`polylib::divisors` works on polynomials from category `Cat::Polynomial` as well:

```P := Dom::Polynomial(Dom::IntegerMod(7)): polylib::divisors(P(x^3 + 2*x^2 + 1))```

## Parameters

 `p` A polynomial or polynomial expression `f` `Factored` (return value of `factor`) `e` Element of a domain of category `Cat::Polynomial`

## Return Values

`polylib::divisors` returns a set of polynomials. The polynomials are from the same type as the polynomials in the argument.