[Haskell-cafe] Is there any "purely algebraic" Linear Algebra library?

[Hiromi ISHII]

Hi,

I'm recently implementing computational algebra library (available on http://hackage.haskell.org/package/computational-algebra ), build on top of ekmett's `algebra` library.

My `computational-algebra` library currently provides very basic functionalities which is rather slow.
There are many techniques to speeding up calculation utilizing linear algebra. So I want to implement those efficient algorithms.

But, I couldn't find any *purely algebraic* linear-algebra library.

As for the most famous library `hmatrix`, this library requires "Field" to be convertible between Double or Real numbers, and due to such constraints, it cannot treat genral coefficient fields, such as Rational (which is not closed under sin or exponentials) or finite fields. So I have to give up using this library.

I noticed there are some additional candidates such as:

* `linear` by Edward Kmett
* `vector-space` by Conal Elliot

But neither of them provides necessary functionalities which is available in `hmatrix`, such as determinant for arbitrary dimensional matrices and rank function , etc.

Is there any other library providing the functionalities like above which can be used with general coefficient fields?
Or is there any good document on the efficient implementation for linear algebra on Haskell?

-- Hiromi ISHII
konn.jinro at gmail.com