Documentation

# `degree`

Degree of a polynomial

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## Syntax

```degree(`p`)
degree(`p`, `x`)
degree(`f`, <`vars`>)
degree(`f`, <`vars`>, `x`)
```

## Description

`degree(p)` returns the total degree of the polynomial `p`.

`degree(p, x)` returns the degree of `p` with respect to the variable `x`.

If the first argument `f` is not element of a polynomial domain, then `degree` converts the expression internally to a polynomial of type `DOM_POLY` via `poly``(f)`. If a list of indeterminates is specified, the polynomial `poly``(f, vars)` is considered.

`degree(f, vars, x)` returns 0 if `x` is not an element of the list `vars`.

The degree of the zero polynomial is defined as 0.

## Examples

### Example 1

The total degree of the terms in the following polynomial expression is computed:

`degree(x^3 + x^2*y^2 + 2)`
` `

### Example 2

`degree` may be applied to polynomials of type `DOM_POLY`:

`degree(poly(x^2*z + x*z^3 + 1, [x, z]))`
` `

### Example 3

The next expression is regarded as a bi-variate polynomial in `x` and `z`. The degree with respect to `z` is computed:

`degree(x^2*z + x*z^3 + 1, [x, z], z)`
` `

### Example 4

The degree of the zero polynomial is defined as 0:

`degree(0, [x, y])`
` `

## Parameters

 `p` A polynomial of type `DOM_POLY` `f` `vars` A list of indeterminates of the polynomial: typically, identifiers or indexed identifiers `x` An indeterminate

## Return Values

Nonnegative number. `FAIL` is returned if the input cannot be converted to a polynomial.

` f`, `p`