# `lterm`

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## Syntax

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

## Description

`lterm(p)` returns the leading term of the polynomial `p`.

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

The identity `lterm(p)*lcoeff(p) = lmonomial(p)` holds.

The leading term of the zero polynomial is the zero polynomial.

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.

## Examples

### Example 1

We demonstrate how various orderings influence the result:

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

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

`lterm(p, Dom::MonomOrdering(RevLex(3)))`

`delete p:`

### Example 2

```p := poly(2*x^2*y + 3*x*y^2 + 6, [x, y]): mapcoeffs(lterm(p),lcoeff(p)) = lmonomial(p)```

`delete p:`

### 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

Polynomial of the same type as `p`. An expression is returned if an expression is given as input. `FAIL` is returned if the input cannot be converted to a polynomial.

`p`