| Safe Haskell | None |
|---|
Numeric.Domain.Euclidean
Documentation
class (Ring r, DecidableZero r, DecidableUnits r, Domain r) => Euclidean r whereSource
Methods
splitUnit :: r -> (r, r)Source
splitUnit r calculates its leading unit and normal form.
let (u, n) = splitUnit r in r == u * n && fst (splitUnit n) == one && isUnit u
degree :: r -> Maybe NaturalSource
Euclidean (degree) function on r.
Arguments
| :: r | elements divided by |
| -> r | divisor |
| -> (r, r) | quotient and remin |
Division algorithm. a calculates
quotient and reminder of divide ba divided by b.
let (q, r) = divide a p in p*q + r == a && degree r < degree q
gcd a ba and b.
euclid :: r -> r -> [(r, r, r)]Source
Extended euclidean algorithm.
euclid f g == xs ==> all (\(r, s, t) -> r == f * s + g * t) xs
leadingUnit :: Euclidean r => r -> rSource
Arguments
| :: Euclidean r | |
| => [(r, r)] | List of |
| -> r |
|