| Safe Haskell | Safe-Infered |
|---|
Algebra.Ring.Noetherian
Documentation
class (Commutative r, Ring r) => NoetherianRing r
Instances
| NoetherianRing Int | |
| NoetherianRing Integer | |
| Integral n => NoetherianRing (Ratio n) | |
| (Commutative (Complex r), Ring (Complex r)) => NoetherianRing (Complex r) | |
| (Eq r, NoetherianRing r) => NoetherianRing (Polynomial r) | |
| (IsOrder order, IsPolynomial r n) => NoetherianRing (OrderedPolynomial r order n) | By Hilbert's finite basis theorem, a polynomial ring over a noetherian ring is also a noetherian ring. |
data Ideal r
Instances
| (NoetherianRing r, Eq r, IsMonomialOrder ord) => Monomorphicable Nat (:.: * Nat Ideal (OrderedPolynomial r ord)) | |
| Eq r => Eq (Ideal r) | |
| Ord r => Ord (Ideal r) | |
| Show r => Show (Ideal r) |
addToIdeal :: r -> Ideal r -> Ideal r
toIdeal :: NoetherianRing r => [r] -> Ideal r
appendIdeal :: Ideal r -> Ideal r -> Ideal r
generators :: Ideal r -> [r]
filterIdeal :: NoetherianRing r => (r -> Bool) -> Ideal r -> Ideal r
principalIdeal :: r -> Ideal r