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src/Data/Number/Functions.hs

@@ -40,26 +40,26 @@ toList (x:|xs) = x : toList xs
 
 -- | The infinite continued fraction whose terms are naturals numbers
 --
--- \[0, 1, 2, 3, 4,...\] = 0.6977746...
+-- <<https://i.imgur.com/wYz0tig.png>>
 σ :: Number
 σ = σ' 0 where
   σ' n = n :| σ' (succ n)
 
 -- | The golden ratio
 --
--- φ = (1 + √5)/2 = 1.6180339...
+-- <<https://i.imgur.com/3Yb5bWc.png>>
 φ :: Number
 φ = 1 :| φ
 
 -- | Pi: the ratio of a circle's circumference to its diameter
 --
---  π = 3.1415926...
+--  <<https://i.imgur.com/S1F6UoI.png>>
 π :: Number
 π = toNumber pi
 
 -- | Euler's number: the base of the natural logarithm
 --
--- e = 2.7182818...
+-- <<https://i.imgur.com/q1SwKoy.png>>
 e :: Number
 e = fmap a σ where 
   a n | p == 0    = 2*q

src/Data/Number/Internal.hs

@@ -1,6 +1,7 @@
 -- | Data.Number internals
 module Data.Number.Internal
-( operator
+( Matrix
+, operator
 , cut
 , first
 , rest
@@ -18,8 +19,12 @@ type Matrix = (Whole, Whole, Whole, Whole, Whole, Whole, Whole, Whole)
 -- | Continued fraction operator (implements Gosper's arithmetics)
 --
 -- Given two 'Number' @x@, @y@ and the operator matrix
--- @\<a, b, c, d, e, f, g, h\>@
+--
--- calculates @z = (a + bx + cy + dxy) / (e + fx + gy + hxy)@
+-- <<https://i.imgur.com/Hm7TiIH.png>>
+--
+-- calculates 
+--
+-- <<https://i.imgur.com/IZvQmy9.png>>
 --
 -- See <http://perl.plover.com/yak/cftalk/INFO/gosper.txt> for a complete
 -- explanation.

src/Data/Number/Types.hs

@@ -5,11 +5,21 @@ import Data.Number.Peano
 
 infixr 5 :| 
 -- | ==Continued fraction type
--- represents a simple continued fraction of the form:
+-- Represents a simple continued fraction of the form:
--- @[a0, a1, a2,...] = a0 + 1\/(a1 + 1\/(a2 + 1\/...))@
 --
--- == /Cons/ operator
+-- <<https://i.imgur.com/RgNIDHQ.png>>
+--
+-- Supports Haskell arithmetic operators though the use of the 'operator'
+-- function is to be preferred since provide shortcuts to calculations.
+--
+-- It can be an infinite sequence. Be careful with functions like @show@
+-- and @precision@: they may not terminate.
+--
+-- === Cons operator
 -- @n :| x @ equivalent to @n@ + 1/@x@
+--
+-- === Negate operator
+-- @M x @ equivalent to @-x@
 data Continued a =
   M (Continued a)      -- ^Negative number
   | a :| (Continued a) -- ^Positive number