Documentation

# `tcoeff`

Trailing coefficient of a polynomial

MuPAD® notebooks will be removed in a future release. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```tcoeff(`p`, <`order`>)
tcoeff(`f`, <`vars`>, <`order`>)
```

## Description

`tcoeff(p)` returns the trailing coefficient of the polynomial `p`.

The returned coefficient is “trailing” with respect to the lexicographical ordering, unless a different ordering is specified via the argument `order`. Cf. Example 1.

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. Cf. Example 3.

The result of `tcoeff` is not fully evaluated. Evaluation can be enforced by the function `eval`. Cf. Example 2.

## Examples

### Example 1

We demonstrate how various orderings influence the result:

```p := poly(5*x^2*y^3 + 4*x^3*y*z + 3*x*y^4*z, [x, y, z]): tcoeff(p), tcoeff(p, DegreeOrder), tcoeff(p, DegInvLexOrder)```
` `

The following call uses the reverse lexicographical order on 3 indeterminates:

`tcoeff(p, Dom::MonomOrdering(RevLex(3)))`
` `
`delete p:`

### Example 2

The result of `tcoeff` is not fully evaluated:

```p := poly(27*x^2 + a*x, [x]): a := 5: tcoeff(p), eval(tcoeff(p))```
` `
`delete p, a:`

### Example 3

The expression `1/x` may not be regarded as polynomial:

`lterm(1/x)`
` `

## Parameters

 `p` A polynomial of type `DOM_POLY` `f` `vars` A list of indeterminates of the polynomial: typically, identifiers or indexed identifiers `order` The term ordering: either `LexOrder`, or `DegreeOrder`, or `DegInvLexOrder`, or a user-defined term ordering of type `Dom::MonomOrdering`. The default is the lexicographical ordering `LexOrder`.

## Return Values

Element of the coefficient domain of the polynomial or `FAIL`.

`p`