# nthterm

N-th term of a polynomial

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```nthterm(`p`, `n`)
nthterm(`f`, <`vars`>, `n`)
```

## Description

`nthterm(p, n)` returns the `n`-th non-zero term of the polynomial`p`.

`nthterm` returns the `n`-th non-zero term with respect to the lexicographical ordering.

The "first" term is the leading term as returned by `lterm`.

A zero polynomial has no terms: `nthterm` returns `FAIL`.

The identity nthterm(p, n) nthcoeff(p, n) = nthmonomial(p, n) holds.

A polynomial expression `f` is first converted to a polynomial with the variables given by `vars`. If no variables are given, they are searched for in `f`. See `poly` about details of the conversion. The result is returned as polynomial expression. `FAIL` is returned if `f` cannot be converted to a polynomial.

## Examples

### Example 1

We give some self explaining examples:

```p := poly(100*x^100 + 49*x^49 + 7*x^7, [x]): nthterm(p, 1), nthterm(p, 2), nthterm(p, 3)```

`nthterm(p, 4)`

`nthterm(poly(0, [x]), 1)`

`delete p:`

### Example 2

The n-th monomial is the product of the n-th coefficient and the n-th term:

```p := poly(2*x^2*y + 3*x*y^2 + 6, [x, y]): mapcoeffs(nthterm(p, 2), nthcoeff(p, 2)) = nthmonomial(p, 2)```

`delete p:`

## Parameters

 `p` A polynomial of type `DOM_POLY` `f` `vars` A list of indeterminates of the polynomial: typically, identifiers or indexed identifiers `n` A positive integer

## Return Values

Polynomial of the same type as `p`. An expression is returned if a polynomial expression is given as input. `FAIL` is returned if `n` is larger than the actual number of terms of the polynomial.

`p`