Description Usage Arguments Details Value References See Also Examples

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

1 |

`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 |

`...` |
arguments passed to or from other methods. |

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.

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.

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

1 2 3 4 |

```
[,1] [,2] [,3] [,4] [,5]
[1,] 0.2 0.0 0.0 0.0 0.0
[2,] 0.0 0.2 0.0 0.0 0.0
[3,] 0.0 0.0 0.2 0.0 0.0
[4,] 0.0 0.0 0.0 0.2 0.0
[5,] 0.0 0.0 0.0 0.0 0.2
[,1] [,2] [,3] [,4] [,5]
[1,] 1/5 0 0 0 0
[2,] 0 1/5 0 0 0
[3,] 0 0 1/5 0 0
[4,] 0 0 0 1/5 0
[5,] 0 0 0 0 1/5
[,1] [,2] [,3] [,4] [,5]
[1,] 6/5 1 1 1 1
[2,] 1 6/5 1 1 1
[3,] 1 1 6/5 1 1
[4,] 1 1 1 6/5 1
[5,] 1 1 1 1 6/5
```

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