fractions | R Documentation |

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

```
fractions(x, cycles = 10, max.denominator = 2000, ...)
as.fractions(x)
is.fractions(f)
```

`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. |

`f` |
an |

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.

`rational`

```
X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
fractions(solve(X, X/5))
fractions(solve(X, X/5)) + 1
```

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