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