number-wall 0.1.0.1 → 0.1.0.2

raw patch · 3 files changed

+15/−31 lines, 3 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• CHANGELOG.md +6/−0
• number-wall.cabal +1/−28
• src/NumberWall.hs +8/−3

@@ -8,3 +8,9 @@  * Added example usage to documentation. * Fixed image and math in description.++## 0.1.0.2 -- 2022-9-3++* Removed formal definition.+* Added section headings in documentation.+* Removed unnecessary `Show` constraint.

@@ -1,6 +1,6 @@ cabal-version: 2.4 name:          number-wall-version:       0.1.0.1+version:       0.1.0.2 author:        Owen Bechtel maintainer:    ombspring@gmail.com @@ -12,33 +12,6 @@   The "numbers" in the grid are usually either integers, or integers modulo some prime.   Number walls can be defined in terms of determinants, but can also be calculated   using a recursive algorithm.-  .-  Formally, let \( R \) be an integral domain. The number wall of a-  sequence \( S : \mathbb{Z} \to R \) is an infinite grid of-  numbers \( W \), defined as follows:-  .-  \[-  W(x, y) = \begin{cases}-    0 & y < -1 \\-    1 & y = -1 \\-    S(x) & y = 0 \\-    D(x, y) & y > 0-  \end{cases}-  \]-  .-  \[-  D(x, y) = \begin{vmatrix}-    S(x) & S(x + 1) & \ldots & S(x + y) \\-    S(x - 1) & S(x) & \ldots & S(x + y - 1) \\-    \vdots & \vdots & \ddots & \vdots \\-    S(x - y) & S(x - y + 1) & \ldots & S(x)-  \end{vmatrix}-  \]-  .-  The values in any number wall satisfy the-  relation \( W(x, y - 1) W(x, y + 1) + W(x - 1, y) W(x + 1, y) = W(x, y)^2 \),-  and some other more complicated relations. You can use these to define a-  recursive algorithm for generating number walls.   .   Here are some cool images created using the functions in this package:   .

@@ -17,7 +17,13 @@ {-# LANGUAGE BlockArguments #-} {-# LANGUAGE ConstraintKinds #-} module NumberWall-  ( NumberWall, Col, Row, numberWall, pagoda, rueppel, ternary, saveImage, showSection, printSection+  ( -- * Creating number walls+    Col, Row, numberWall, NumberWall+    -- * Special sequences+  , pagoda, rueppel, ternary+    -- * Displaying number walls+  , saveImage, showSection, printSection+    -- * Modular arithmetic   , module Data.Mod.Word   ) where @@ -39,7 +45,6 @@ are not actually Euclidean domains, and using 'numberWall' with them often causes divide-by-zero errors. -}- type NumberWall a = (Eq a, Ring a, Euclidean a)  type Col = Int@@ -51,7 +56,7 @@ {-| Generate the number wall for a sequence. -}-numberWall :: (NumberWall a, Show a) => (Int -> a) -> Col -> Row -> a+numberWall :: NumberWall a => (Int -> a) -> Col -> Row -> a numberWall s = memoFix2 \recurse col row ->   let f a b = recurse (col + a) (row - b) in   case row of