| Copyright | (c) Eric Bailey 2024-2025 |
|---|---|
| License | MIT |
| Maintainer | eric@ericb.me |
| Stability | experimental |
| Portability | POSIX |
| Safe Haskell | Safe-Inferred |
| Language | GHC2021 |
Data.Rhythm.ContinuedFractions
Description
Simple continued fractions represented by nonempty lists of terms.
\[ \begin{align*} [b_0; b_1, b_2, b_3, \dotsc] &= b_0 + \cfrac{1}{b_1 + \cfrac{1}{b_2 + \cfrac{1}{b_3 + \dotsm}}} \\ &= b_0 + \mathop{\vcenter{\Huge\mathcal{K}}}_{n=1}^{\infty} \frac{1}{b_n} \end{align*} \]
Synopsis
- newtype ContinuedFraction = ContinuedFraction {}
- collapseFraction :: ContinuedFraction -> Rational
- continuedFractionSqrt :: Integral a => a -> ContinuedFraction
Documentation
newtype ContinuedFraction Source #
A ContinuedFraction is a NonEmpty, potentially infinite, list of
integer terms.
>>>ContinuedFraction (1 :| [2,3,4])[1;2,3,4]
Constructors
| ContinuedFraction | |
Instances
| Show ContinuedFraction Source # | |
Defined in Data.Rhythm.ContinuedFractions Methods showsPrec :: Int -> ContinuedFraction -> ShowS # show :: ContinuedFraction -> String # showList :: [ContinuedFraction] -> ShowS # | |
| Eq ContinuedFraction Source # | |
Defined in Data.Rhythm.ContinuedFractions Methods (==) :: ContinuedFraction -> ContinuedFraction -> Bool # (/=) :: ContinuedFraction -> ContinuedFraction -> Bool # | |
| Ord ContinuedFraction Source # | |
Defined in Data.Rhythm.ContinuedFractions Methods compare :: ContinuedFraction -> ContinuedFraction -> Ordering # (<) :: ContinuedFraction -> ContinuedFraction -> Bool # (<=) :: ContinuedFraction -> ContinuedFraction -> Bool # (>) :: ContinuedFraction -> ContinuedFraction -> Bool # (>=) :: ContinuedFraction -> ContinuedFraction -> Bool # max :: ContinuedFraction -> ContinuedFraction -> ContinuedFraction # min :: ContinuedFraction -> ContinuedFraction -> ContinuedFraction # | |
collapseFraction :: ContinuedFraction -> Rational Source #
Evaluate a finite ContinuedFraction.
>>>collapseFraction (ContinuedFraction (1 :| [2,3,4]))43 % 30
continuedFractionSqrt :: Integral a => a -> ContinuedFraction Source #
Calculate the ContinuedFraction representation of the square root of a
given number.
>>>continuedFractionSqrt 7[2;1,1,1,4]