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`numer`

Numerator of a rational expression

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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`