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# 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 polynomialp.

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.