https://github.com/junjihashimoto/th-cas

Compile time CAS(Computer Algebra System) for Haskell
https://github.com/junjihashimoto/th-cas

algebra cas computer-algebra haskell

Last synced: 2 months ago
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Compile time CAS(Computer Algebra System) for Haskell

• Host: GitHub
• URL: https://github.com/junjihashimoto/th-cas
• Owner: junjihashimoto
• License: mit
• Created: 2015-04-10T01:54:39.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2019-11-27T17:30:11.000Z (about 5 years ago)
• Last Synced: 2024-07-30T17:49:52.854Z (5 months ago)
• Topics: algebra, cas, computer-algebra, haskell
• Language: Haskell
• Homepage:
• Size: 170 KB
• Stars: 17
• Watchers: 5
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Changelog: ChangeLog.md
  • License: LICENSE

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README

        
# th-cas : Compile-time CAS(Computer Algebra System)

[![Hackage version](https://img.shields.io/hackage/v/th-cas.svg?style=flat)](https://hackage.haskell.org/package/th-cas)  [![Build Status](https://travis-ci.org/junjihashimoto/th-cas.png?branch=master)](https://travis-ci.org/junjihashimoto/th-cas)

CAS(Computer Algebra System) operations like diff are done at compile-time.

Compile time operations is done in TemplateHaskell.

## Interactive Usage

```th-cas``` supports interactive usage like mathematica.

To start repl, type "stack ghci".

Variables are defined by ```V``` of data-constructor.

A example of intertative usage is below.

```

$ stack ghci

...

*Algebra.CAS> 

*Algebra.CAS> let x = V "x" 

*Algebra.CAS> let y = V "y" 

*Algebra.CAS> x^2 + 2*x + x^2

2*x + 2*(x^2)

*Algebra.CAS> diff (x^2 + 2*x + x^2) x

2 + 4*x

*Algebra.CAS> linsolve [x+y=:2,x-y=:3]

Just [(x,5/2),(y,-1/2)]

*Algebra.CAS> subst [(x,1)] $ diff (x^2 + 2*x + x^2) x

6

```

## Usage at compile time

Write ```diff function var``` with Quotes of TemplateHaskell.

```diff``` makes a diffirential of the function at compile-time.

So there is no overhead at execution-time.

A example is below.

Write following code with quotes.

```

import Algebra.CAS.TH

myfunc :: Int -> Int

myfunc x = $(diff [|x*x+2*x+1|] [|x|])

```

At compile time, the quotes is translated to ```2*x+2```.

```

import Algebra.CAS.TH

myfunc :: Int -> Int

myfunc x = 2*x+2

```