# rational

##### Rational Approximation

Find rational approximations to the components of a real numeric object using a standard continued fraction method.

- Keywords
- math

##### Usage

`rational(x, cycles = 10, max.denominator = 2000, …)`

##### Arguments

- x
Any object of mode numeric. Missing values are now allowed.

- cycles
The maximum number of steps to be used in the continued fraction approximation process.

- max.denominator
An early termination criterion. If any partial denominator exceeds

`max.denominator`

the continued fraction stops at that point.- …
arguments passed to or from other methods.

##### Details

Each component is first expanded in a continued fraction of the form

`x = floor(x) + 1/(p1 + 1/(p2 + …)))`

where `p1`

, `p2`

, … are positive integers, terminating either
at `cycles`

terms or when a `pj > max.denominator`

. The
continued fraction is then re-arranged to retrieve the numerator
and denominator as integers and the ratio returned as the value.

##### Value

A numeric object with the same attributes as `x`

but with entries
rational approximations to the values. This effectively rounds
relative to the size of the object and replaces very small
entries by zero.

##### See Also

##### Examples

```
# NOT RUN {
X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
rational(solve(X, X/5))
# }
```

*Documentation reproduced from package MASS, version 7.3-51.1, License: GPL-2 | GPL-3*