Num.ContinuedFraction

Conversion between numbers and continued fractions

continuedFraction :: (RealFrac a, Integral b) => a -> [b]

This take a number and returns its continued fraction expansion as a list of integers.

>>> continuedFraction 2
[2]

collapseFraction :: (Integral a, Integral b) => NonEmpty b -> Ratio a

Take a non-empty list of integers and return the corresponding rational number.

>>> collapseFraction (1 :| [2,2,2])
17 % 12

Rational approximations using continued fractions

approximate :: (RealFrac a, Integral b) => a -> b -> Ratio b

Find the best rational approximation to a number such that the denominator is bounded by a given value.

>>> approximate pi 100
22 % 7

convergent :: (RealFrac a, Integral b) => Int -> a -> Ratio b

Find a given convergent of the continued fraction expansion of a number

>>> convergent 4 $ sqrt 2
17 % 12

Pretty-printer for continued fractions

prettyFrac :: Show a => NonEmpty a -> String

prettyFracM :: Show a => [a] -> Maybe String

Print a list as a continued fraction.

>>> prettyFracM (take 5 $ continuedFraction (sqrt 2))
Just "[1; 2, 2, 2, 2]"