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README
thcas : Compiletime CAS(Computer Algebra System)
CAS(Computer Algebra System) operations like diff are done at compiletime. Compile time operations is done in TemplateHaskell.
Interactive Usage
thcas
supports interactive usage like mathematica.
To start repl, type "stack ghci".
Variables are defined by V
of dataconstructor.
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,xy=: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 compiletime.
So there is no overhead at executiontime.
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