Documentation

# `numer`

Numerator of a rational expression

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

```numer(`f`)
```

## Description

`numer(f)` returns the numerator of the expression `f`.

`numer` regards the input as a rational expression: non-rational subexpressions such as `sin(x)`, `x^(1/2)` etc. are internally replaced by “temporary variables”. The numerator of this rationalized expression is computed, the temporary variables are finally replaced by the original subexpressions.

### Note

Numerator and denominator are not necessarily cancelled: the numerator returned by `numer` may have a non-trivial `gcd` with the denominator returned by `denom`. Preprocess the expression by `normal` to enforce cancellation of common factors. Cf. Example 2.

## Examples

### Example 1

We compute the numerators of some expressions:

`numer(-3/4)`

`numer(x + 1/(2/3*x -2/x))`

`numer((cos(x)^2 -1)/(cos(x) -1))`

### Example 2

`numer` performs no cancellations if the rational expression is of the form “numerator/denominator”:

`r := (x^2 - 1)/(x^3 - x^2 + x - 1): numer(r)`

This numerator has a common factor with the denominator of `r`; `normal` enforces cancellation of common factors:

`numer(normal(r))`

However, automatic normalization occurs if the input expression is a sum:

`numer(r + x/(x + 1) + 1/(x + 1) - 1)`

`delete r:`

## Parameters

 `f`

## Return Values

Arithmetical expression.

`f`