# rational

From MASS v7.3-20
by Brian Ripley

##### 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

```
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 7.3-20, License: GPL-2 | GPL-3*

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