Haskell library like SymPy?

Question

I need to manipulate expressions like 1 + sqrt(3) and do basic arithmetic like addition, subtraction, and division. I'd like the result to be in some sort of canonical form so that it can be used as a key in a map. Turning 1 + sqrt(3) into a float is not feasible due to roundoff problems.

I used SymPy for this task in Python. Is there an equivalent native library for Haskell?

Answer 1

Please check out the numbers package. If all you need is to store exact numbers like "1 + √3", you may want to use Data.Number.CReal instead of symbolic arithmetics. It stores the expressions and can be computed to arbitrary number of digits when needed.

Prelude Data.Number.CReal> let cx = 1 + sqrt (3 :: CReal)
Prelude Data.Number.CReal> showCReal 400 cx 
"2.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507566183481296061009476021871903250831458295239598329977898245082887144638329173472241639845878553977"

There is also a Data.Number.Symbolic module in the package but the description says "It's mainly useful for debugging".

Answer 2

It seems you are looking for Computer Algebra System (CAS) in Haskell. Inspite of so many references to algebraic objects in the names of Haskell packages/modules, I've never heard of a general purpose and well-maintained CA system in Haskell (like SymPy or Sage in Python).

However in the list of Computer Algebra Systems on Wikipedia I've found a reference to

DoCon. The Algebraic Domain Constructor

It uses a non-standard license, but I dare say it is still Open Source (though with rename and attribution requirements). As of July 2010 docon-2.11 still builds with GHC 6.12.1 and runs demos/tests (I only had to insert a LANGUAGE FlexibleContexts pragma in one file of the demo).

DoCon is well documented (362 pages of the Manual). Its Manual is packed inside of the zip with sources, so I put it online separately for convenience:

DoCon 2.11 Manual.ps

Please look through to check if it suits your needs.