initial commit

.gitignore

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+#### joe made this: http://goel.io/joe
+#### haskell ####
+dist
+dist-*
+cabal-dev
+*.o
+*.hi
+*.chi
+*.chs.h
+*.dyn_o
+*.dyn_hi
+.hpc
+.hsenv
+.cabal-sandbox/
+cabal.sandbox.config
+*.prof
+*.aux
+*.hp
+*.eventlog
+.stack-work/
+cabal.project.local
+.HTF/
+

LICENSE

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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+the GNU General Public License is intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.  We, the Free Software Foundation, use the
+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors.  You can apply it to
+your programs, too.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights.  Therefore, you have
+certain responsibilities if you distribute copies of the software, or if
+you modify it: responsibilities to respect the freedom of others.
+
+  For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must pass on to the recipients the same
+freedoms that you received.  You must make sure that they, too, receive
+or can get the source code.  And you must show them these terms so they
+know their rights.
+
+  Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+  For the developers' and authors' protection, the GPL clearly explains
+that there is no warranty for this free software.  For both users' and
+authors' sake, the GPL requires that modified versions be marked as
+changed, so that their problems will not be attributed erroneously to
+authors of previous versions.
+
+  Some devices are designed to deny users access to install or run
+modified versions of the software inside them, although the manufacturer
+can do so.  This is fundamentally incompatible with the aim of
+protecting users' freedom to change the software.  The systematic
+pattern of such abuse occurs in the area of products for individuals to
+use, which is precisely where it is most unacceptable.  Therefore, we
+have designed this version of the GPL to prohibit the practice for those
+products.  If such problems arise substantially in other domains, we
+stand ready to extend this provision to those domains in future versions
+of the GPL, as needed to protect the freedom of users.
+
+  Finally, every program is threatened constantly by software patents.
+States should not allow patents to restrict development and use of
+software on general-purpose computers, but in those that do, we wish to
+avoid the special danger that patents applied to a free program could
+make it effectively proprietary.  To prevent this, the GPL assures that
+patents cannot be used to render the program non-free.
+
+  The precise terms and conditions for copying, distribution and
+modification follow.
+
+                       TERMS AND CONDITIONS
+
+  0. Definitions.
+
+  "This License" refers to version 3 of the GNU General Public License.
+
+  "Copyright" also means copyright-like laws that apply to other kinds of
+works, such as semiconductor masks.
+
+  "The Program" refers to any copyrightable work licensed under this
+License.  Each licensee is addressed as "you".  "Licensees" and
+"recipients" may be individuals or organizations.
+
+  To "modify" a work means to copy from or adapt all or part of the work
+in a fashion requiring copyright permission, other than the making of an
+exact copy.  The resulting work is called a "modified version" of the
+earlier work or a work "based on" the earlier work.
+
+  A "covered work" means either the unmodified Program or a work based
+on the Program.
+
+  To "propagate" a work means to do anything with it that, without
+permission, would make you directly or secondarily liable for
+infringement under applicable copyright law, except executing it on a
+computer or modifying a private copy.  Propagation includes copying,
+distribution (with or without modification), making available to the
+public, and in some countries other activities as well.
+
+  To "convey" a work means any kind of propagation that enables other
+parties to make or receive copies.  Mere interaction with a user through
+a computer network, with no transfer of a copy, 

README.md

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+slope-field
+===========
+
+I was studying [this course on Integration](https://www.edx.org/course/calculus-1b-integration-mitx-18-01-2x) when I encountered
+slope fields and I found them interesting!
+
+So I thought I would give it a shot and try to write a program to draw slope fields myself!
+In order to read a mathematical function definition from input, I wrote [mathexpr](/mdibaiee/mathexpr).
+
+Get Started
+-----------
+If you don't already, install [Haskell Platform](https://www.haskell.org/platform/).
+
+```
+git clone https://github.com/mdibaiee/slope-field
+cd slope-field
+stack install
+slope-field
+```
+Examples
+--------
+Parameters:
+  - dy/dx: derivative of the function you are trying to visualize
+  - range: range of numbers to draw
+  - estimation size: size of `deltax` which is used to draw the slope corresponding to a small point, `0.03` is usually a good number, but you might want to try out larger numbers to get a more detailed picture on some examples
+```
+dy/dx = 
+x + y
+range - format: (lower, upper): 
+(-10, 10)
+estimation size: 
+0.03
+```
+
+![x plus y](https://github.com/mdibaiee/slope-field/blob/master/xpy.png?raw=true)
+
+```
+dy/dx = 
+x * y
+range - format: (lower, upper): 
+(-10, 10)
+estimation size: 
+0.03
+```
+
+![x times y](https://github.com/mdibaiee/slope-field/blob/master/xty.png?raw=true)
+
+```
+dy/dx = 
+-y
+range - format: (lower, upper): 
+(-10, 10)
+estimation size: 
+0.03
+```
+
+![minus y](https://github.com/mdibaiee/slope-field/blob/master/minusy.png?raw=true)
+
+```
+dy/dx = 
+y/x
+range - format: (lower, upper): 
+(-10, 10)
+estimation size: 
+0.1
+```
+
+![y divided by x](https://github.com/mdibaiee/slope-field/blob/master/ydx.png?raw=true)

Setup.hs

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+import Distribution.Simple
+main = defaultMain

app/Main.hs

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+{-# LANGUAGE ScopedTypeVariables #-}
+
+module Main where
+  import Lib
+  import System.IO
+  import Graphics.Rendering.Chart
+  import Graphics.Rendering.Chart.Backend.Cairo
+  import Control.Lens
+  import Data.Default.Class
+
+  main :: IO ()
+  main = do
+    putStrLn "dy/dx = "
+    math <- getLine
+    putStrLn "range - format: (lower, upper): "
+    (lower, upper) :: (Int, Int) <- read <$> getLine
+    putStrLn "estimation size: "
+    s <- read <$> getLine
+
+    let pts = points (lower, upper)
+        field = slopeField math pts s
+
+    let chart = toRenderable layout
+          where
+            layout = layout_title .~ "slope field"
+                   $ layout_plots .~ [vectors]
+                   $ def
+
+            vectors = plotVectorField
+                    $ plot_vectors_values .~ field
+                    $ plot_vectors_scale .~ 0
+                    $ plot_vectors_style . vector_head_style . point_radius .~ 0
+                    $ def
+
+    renderableToFile def "slope-field.png" chart
+    putStrLn "created file slope-field.png"
+    return ()

slope-field.cabal

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+name:                slope-field
+version:             0.1.0.0
+synopsis:            Visualize mathematical function's slope fields
+description:         Visualize mathematical function's slope fields
+homepage:            https://github.com/mdibaiee/slope-field
+license:             GPL-3
+license-file:        LICENSE
+author:              Mahdi Dibaiee
+maintainer:          mdibaiee@aol.com
+copyright:           2016 Mahdi Dibaiee
+category:            Web
+build-type:          Simple
+-- extra-source-files:
+cabal-version:       >=1.10
+
+library
+  hs-source-dirs:      src
+  exposed-modules:     Lib
+  build-depends:       base >= 4.7 && < 5
+                     , mathexpr >= 0.3.0.0
+                     , data-default-class
+  default-language:    Haskell2010
+
+executable slope-field
+  hs-source-dirs:      app
+  main-is:             Main.hs
+  ghc-options:         -threaded -rtsopts -with-rtsopts=-N
+  build-depends:       base
+                     , slope-field
+                     , Chart
+                     , Chart-cairo
+                     , lens
+                     , data-default-class
+  default-language:    Haskell2010
+
+source-repository head
+  type:     git
+  location: https://github.com/mdibaiee/slope-field

src/Lib.hs

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+module Lib
+    ( points
+    , slopeField
+    ) where
+      import Numeric.MathExpr
+      import Data.Default.Class
+
+      type Range = (Int, Int)
+
+      points :: Range -> [(Double, Double)]
+      points (lower, upper) =
+        let range = [lower..upper]
+        in [ (fromIntegral x, fromIntegral y) | x <- range, y <- range ]
+
+      slopeField :: String -> [(Double, Double)] -> Double -> [((Double, Double), (Double, Double))]
+      slopeField math pts diff =
+        let d x y = evaluate def math [("x", x), ("y", y)]
+            half = diff / 2
+            res = map (\(x, y) -> ((x - half, y), (half, d x y * diff))) pts
+            inf = 1/0
+        in filter (\((x0, y0), (x, y)) -> x < inf && y < inf && x > -inf && y > -inf) res

stack.yaml

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+# This file was automatically generated by 'stack init'
+# 
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# http://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+# 
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+# resolver: ghcjs-0.1.0_ghc-7.10.2
+# resolver:
+#  name: custom-snapshot
+#  location: "./custom-snapshot.yaml"
+resolver: lts-7.6
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+# 
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+# - location:
+#    git: https://github.com/commercialhaskell/stack.git
+#    commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#   extra-dep: true
+#  subdirs:
+#  - auto-update
+#  - wai
+# 
+# A package marked 'extra-dep: true' will only be built if demanded by a
+# non-dependency (i.e. a user package), and its test suites and benchmarks
+# will not be run. This is useful for tweaking upstream packages.
+packages:
+- '.'
+- '../mathexpr'
+# Dependency packages to be pulled from upstream that are not in the resolver
+# (e.g., acme-missiles-0.3)
+extra-deps:
+  - mathexpr-0.3.0.0
+
+# Override default flag values for local packages and extra-deps
+flags: {}
+
+# Extra package databases containing global packages
+extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+# 
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=1.1"
+# 
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+# 
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+# 
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor

test/Spec.hs

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+main :: IO ()
+main = putStrLn "Test suite not yet implemented"