Faulhaber's formula: Difference between revisions

<lang Haskell>import Data.Ratio ((%), numerator, denominator)

import Data.List (intercalate, transpose)

import Data.Char (isSpace)

import Data.Monoid ((<>))

import Data.Bool (bool)

faulhaber :: [[Rational]]

faulhaber =

[]

[0 ..]

-- Rows of (Power string, Ratio string) tuples -> Printable lines

zipWith

(\(lw, rw) col ->

(colWidths cols)

cols)

-- Value pair -> String pair (lifted into list for use with >>=)

ratioPower :: (Rational, Integer) -> [(String, String)]

ratioPower (nd, j) =

sn

| num == 0 = []

s = sr <> sn

in bool [(sn, sr)] [] (null s)

-- Rows of uneven length -> All rows padded to length of longest

fullTable :: [[(String, String)]] -> [[(String, String)]]

let lng = maximum $ length <$> xs

in (<>) <*> (flip replicate ([], []) . (-) lng . length) <$> xs

justifyLeft :: Int -> Char -> String -> String

justifyLeft n c s = take n (s <> replicate n c)

-- (Row index, Expression pairs) -> String joined by conjunctions

expressionRow :: (Int, [(String, String)]) -> String

(polyTerm <$> row)

]

-- (Power string, Ratio String) -> Combined string with possible '*'

polyTerm :: (String, String) -> String

| head r == '-' = concat ["- ", l, " * ", tail r]

| otherwise = intercalate " * " [l, r]

blank :: String -> Bool

blank = all isSpace

-- Maximum widths of power and ratio elements in each column

colWidths :: [[(String, String)]] -> [(Int, Int)]

(\(ls, rs) (lMax, rMax) -> (max (length ls) lMax, max (length rs) rMax))

(0, 0))

-- Length of string excluding any leading '-'

unsignedLength :: String -> Int

unsignedLength xs =

let l = length xs

{{Out}}

<pre>0 -> n