Determinant in Haskell

In linear algebra, the determinant is quite a useful operation that can be done on matrices. To further my understanding of Haskell, I decided to program a solver for systems of equations. One of the best ways to do this dynamically is through Cramer's Rule which needs to be able to calculate determinants. So, here's my recursive code for finding determinants:

determinant :: (Num a, Fractional a) => [[a]] -> a

determinant [[x]] = x
determinant mat =
 sum [(-1)^i*x*(determinant (getRest i mat)) | (i, x) <- zip [0..] (head mat)]

So, in this code, the base case is a 1x1 matrix. The getRest function simply returns the matrix without the head row (topmost) and without the \(i\)th column.

The code and tests are available on my github.

Creating a Sine Function in Haskell

Using Taylor Series derivation I found the following infinite sum expression for sin:
\[
  \sin \left(x \right) = \sum_{i = 1}^{\infty} \frac{x^{2 i - 1}}{\left( 2 i - 1 \right)!} \left( -1 \right)^{i - 1}
\]
The exact derivation is available as a PDF on github.

The translation of this sum into Haskell code was simple:

sin' :: (Num a, Fractional a) => a -> a
sin' x = sum [sinTerm x i | i <- [1..33]]


sinTerm :: (Num a, Fractional a) => a -> Integer -> a
sinTerm x i = (x^oddTerm / fromIntegral (factorial oddTerm))*(-1)^(i-1)
  where oddTerm = 2*i - 1

So, this code is pretty straight forward, if you wanted to get more accuracy on the results you could change "33" to be some greater value (33 says that we will sum up 33-1=32 terms of the taylor series).

Of course this code references factorial which is defined simply as:

factorial :: Integer -> Integer
factorial 1 = 1
factorial n = n * factorial (n-1)

As usual, code and tests are available on github.