Find rational approximations to the components of a real numeric object using a standard continued fraction method.
fractions(x, cycles = 10, max.denominator = 2000, ...)
- Any object of mode numeric. Missing values are now allowed.
- The maximum number of steps to be used in the continued fraction approximation process.
- An early termination criterion. If any partial denominator
max.denominatorthe continued fraction stops at that point.
- 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 + ...)))
p2, ...are positive integers, terminating either
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
Arithmetic operations on
"fractions" objects have full floating
point accuracy, but the character representation printed out may
- An object of class
"fractions". A structure with
.Datacomponent 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.
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