ContinAbsvalParametrisation.hs

contin-absval-parametrisation.cabal

cabal-version:       >=1.10
-- Initial package description 'contin-absval-parametrisation.cabal'
-- generated by 'cabal init'.  For further documentation, see
-- http://haskell.org/cabal/users-guide/

name:                contin-absval-parametrisation
version:             0.1.0.0
synopsis:            https://math.stackexchange.com/questions/3792238/idea-behind-reparameterization-hiding-a-corner-in-single-variable-calculus/3792259?noredirect=1#comment7813010_3792259
-- description:
homepage:            https://gist.github.com/leftaroundabout/2a19aea0e8dcb7b63d919406ecdb8c4a
-- bug-reports:
license:             PublicDomain
author:              Justus Sagemüller
maintainer:          (@) jsag $ hvl.no
category:            Math
build-type:          Simple
extra-source-files:  CHANGELOG.md

executable contin-absval-parametrisation
  main-is:             Main.hs
  -- other-modules:
  -- other-extensions:
  build-depends:       base >=4.10 && <4.15, dynamic-plot >=0.4 && <0.5
  -- hs-source-dirs:
  default-language:    Haskell2010

Main.hs

import Graphics.Dynamic.Plot.R2
import Data.Semigroup
import Control.Monad (join)

f, g :: Double -> Double
g t = t^2
f t
 | t<0        = -t^2
 | otherwise  = t^2

main :: IO ()
main = do
 plotWindow
  [plotLatest
    $ (plotDelay 1 $ mempty)
    : [ plotMultiple
         [ lineSegPlot [(f t,t),(f t,g t),(t, g t)]
         , lineSegPlot [(t, g t) | t<-post]
                 <> lineSegPlot [(t,-4),(t,4)]
         , lineSegPlot [(f t, t) | t<-post]
                 <> lineSegPlot [(-6,t),(6,t)]
         , lineSegPlot [(f t, g t) | t<-pre]
         ]
      | (pre,post@(t:_))<-join $ cycle
          [ [splitAt i [-5,1/20-5 .. 5]|i<-[0..190]]
          , [splitAt i [5,5-1/20 .. -5]|i<-[190,189..0]] ]
      ]
  , unitAspect, xInterval (-4,4), yInterval (-3,3), dynamicAxes
  ]
 return ()

This Haskell script shows an animation of the continuous parametrization of the absolute-value function, as discussed in https://math.stackexchange.com/questions/3792238/idea-behind-reparameterization-hiding-a-corner-in-single-variable-calculus/3792259?noredirect=1#comment7813010_3792259

To run the script, you need a GHC setup with either Cabal or Stack (see https://www.haskell.org/ for instructions).

Running with Cabal: put both files in a directory and execute cabal run. (It will take a while to install the dynamic-plot library with all its dependencies.)