1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
|
module Numeric.Exp
( Exp(..)
) where
import Data.Function (on)
import Numeric.Algebra
import Prelude hiding ((+),(-),negate,replicate,subtract)
newtype Exp r = Exp { runExp :: r }
instance Additive r => Multiplicative (Exp r) where
Exp a * Exp b = Exp (a + b)
productWith1 f = Exp . sumWith1 (runExp . f)
pow1p (Exp m) n = Exp (sinnum1p n m)
instance Monoidal r => Unital (Exp r) where
one = Exp zero
pow (Exp m) n = Exp (sinnum n m)
productWith f = Exp . sumWith (runExp . f)
instance Group r => Division (Exp r) where
Exp a / Exp b = Exp (a - b)
recip (Exp a) = Exp (negate a)
Exp a \\ Exp b = Exp (subtract a b)
Exp m ^ n = Exp (times n m)
instance Abelian r => Commutative (Exp r)
instance Idempotent r => Band (Exp r)
instance Partitionable r => Factorable (Exp r) where
factorWith f = partitionWith (f `on` Exp) . runExp
|
