# fractions {MASS}

### Description

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

### Usage

fractions(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.

The numerators and denominators are then combined into a character vector that becomes the `"fracs"`

attribute and used in printed representations.

Arithmetic operations on `"fractions"`

objects have full floating point accuracy, but the character representation printed out may not.

### Values

An object of class `"fractions"`

. A structure with `.Data`

component the same as the input numeric `x`

, but with the rational approximations held as a character vector attribute, `"fracs"`

. Arithmetic operations on `"fractions"`

objects are possible.

### References

Venables, W. N. and Ripley, B. D. (2002) *Modern Applied Statistics with S.* Fourth Edition. Springer.

### See Also

### Examples

Documentation reproduced from package MASS, version 7.3-45. License: GPL-2 | GPL-3