noether alternatives and similar packages
Based on the "Math" category.
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vector
An efficient implementation of Intindexed arrays (both mutable and immutable), with a powerful loop optimisation framework . 
statistics
A fast, high quality library for computing with statistics in Haskell. 
HerbiePlugin
GHC plugin that improves Haskell code's numerical stability 
hgeometry
HGeometry is a library for computing with geometric objects in Haskell. It defines basic geometric types and primitives, and it implements some geometric data structures and algorithms. The main two focusses are: (1) Strong type safety, and (2) implementations of geometric algorithms and data structures that have good asymptotic running time guarantees. 
dimensional
Dimensional library variant built on Data Kinds, Closed Type Families, TypeNats (GHC 7.8+). 
computationalalgebra
GeneralPurpose Computer Algebra System as an EDSL in Haskell 
mwcrandom
A very fast Haskell library for generating high quality pseudorandom numbers. 
numhask
A haskell numeric prelude, providing a clean structure for numbers and operations that combine them. 
poly
Fast polynomial arithmetic in Haskell (dense and sparse, univariate and multivariate, usual and Laurent) 
cf
"Exact" real arithmetic for Haskell using continued fractions (Not formally proven correct) 
optimization
Some numerical optimization methods implemented in Haskell 
equationalreasoning
Agdastyle equational reasoning in Haskell 
safedecimal
Safe and very efficient arithmetic operations on fixed decimal point numbers 
polynomial
Haskell library for manipulating and evaluating polynomials 
monoidsubclasses
Subclasses of Monoid with a solid theoretical foundation and practical purposes 
eigen
Haskel binding for Eigen library. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
Less time debugging, more time building
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README
Noether
FULLPOLYMORPHIC™ number theory / abstract algebra in Haskell.
The part I'm working on at present develops a highly polymorphic numeric hierarchy. Unlike almost every other project (including the great subhask
, which is by far the biggest inspiration for this project), all typeclasses representing algebraic structures are "tagged" with the operations that the base type supports. The intention is to have, without newtyping, things like automatically specified Lvector space instances for any Kvector space with K / L a (nice) field extension.
<! While it may not be inevitable, my inexperienced preliminary encoding of these ideas has delightful consequences like >
<! haskell >
<! instance {# INCOHERENT #} >
<! ( DotProductSpace' k v >
<! , DotProductSpace' k w >
<! , p ~ Add >
<! , m ~ Mul >
<! ) => InnerProductSpace DotProduct p m k Add (v, w) where >
<!
>
<! that I don't know how to "kill with fire". >
<! Obviously, I'm still exploring the design space to try and find a good balance between avoiding arbitrary choices (e.g. no privileged Monoid
instances for Double
and the like) and a useful level of type inference. In large part, this means that I'm trying not to run up against trouble with instance resolution and failing hard (see above), or discovering that associated types are sometimes less permissive than one would like. >
<! The numeric hierarchy, at present, extends to functions like this: >
<! ```haskell > <! (%<) :: LeftModule' r v => r > v > v > <! r %< v = leftAct AddP AddP MulP r v >
<!   Linear interpolation. > <!  lerp λ v w = λv + (1  λ)w > <! lerp > <! :: VectorSpace' r v > <! => r > v > v > v > <! lerp lambda v w = lambda %< v + w >% (one  lambda) >
<! lol :: (Complex Double, Complex Double) > <! lol = > <! (1, 3) * lerp lambda (3, 3) (4, 5) + (1, 0) >% lambda + v + lambda %< w + > <! (lambda, lambda) >
<! where > <! lambda :: Complex Double > <! lambda = 0.3 :+ 1 >
<! v = (3, 3) > <! w = (2, 7) > <! ``` >
<! A preliminary implementation of linear maps between (what should be) free modules is being developed after the design in Conal Elliott's "Reimagining matrices". The added polymorphism and lack of fixed Scalar a
esque base fields is an interesting challenge, and Conal's basic GADT decomposition of linear maps changes in my case to >
<! haskell >
<! data (\>) :: (* > * > * > *) where >
<!
>
<! where the first "slot" is for the base field. With a nice ~>
type operator (which is basically $
), a linear map between two kvector space types a
and b
has the type >
<! haskell >
<! func :: k \> a ~> b >
<!
>
<! paving the way for the representation of the category kVect as (\>) k :: (* > * > *)
. >
<! Some sample function signatures: >
<! ```haskell >
<!   Converts a linear map into a function. > <! apply :: k > a ~> b > a > b >
<! compose > <! :: k > a ~> b > <! > k > b ~> c > <! > k > a ~> c > <! ``` >
<! Usage looks like this for now: >
<! >
<! > apply (rotate (pi / 4 :: Double)) (1,1) >
<! (1.1102230246251565e16,1.414213562373095) >
<!
>
Other stuff
Some other stuff I'm thinking about includes polymorphic numeric literals, possibly along the lines of this:
type family NumericLit (n :: Nat) = (c :: * > Constraint) where
NumericLit 0 = Neutral Add
NumericLit 1 = Neutral Mul
 NumericLit 2 = Field Add Mul
 NumericLit n = NumericLit (n  1)
NumericLit n = Ring Add Mul
fromIntegerP :: forall n a. (KnownNat n, NumericLit n a) => Proxy n > a
fromIntegerP p =
case sameNat p (Proxy :: Proxy 0) of
Just prf > gcastWith prf zero'
Nothing > case sameNat p (Proxy :: Proxy 1) of
Just prf > gcastWith prf one'
Nothing > undefined  unsafeCoerce (val (Proxy :: Proxy a))
 where
 val :: (Field Add Mul b) => Proxy b > b
 val _ = one + undefined  fromIntegerP (Proxy :: Proxy (n  1))
The original core of the project is a short implementation of elliptic curve addition over Q, which I've put on hold temporarily as I try to work out the issues outlined above first. This part uses a Protolude "fork" called Lemmata that I expect will evolve over time.