Polynom-0.1: A commutative algebra packageContentsIndex
Data.MonoidRing
Synopsis
data (Num r, OrdMonoid m) => MonoidRing r m = MakePolynom (Map m r)
zero_ring :: (Num r, OrdMonoid m) => MonoidRing r m
ringsum :: (Num r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m -> MonoidRing r m
ringprod :: (Num r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m -> MonoidRing r m
smallmap :: (Num r, OrdMonoid m, OrdMonoid n) => (r, m) -> (m -> MonoidRing r n) -> MonoidRing r n
(>>°) :: (Num r, OrdMonoid m, OrdMonoid n) => MonoidRing r m -> (m -> MonoidRing r n) -> MonoidRing r n
returnr :: (Num r, OrdMonoid m) => m -> MonoidRing r m
leading_thing :: (Num r, OrdMonoid m) => MonoidRing r m -> (m, r)
leading_term :: (Num r, OrdMonoid m) => MonoidRing r m -> m
leading_coef :: (Num r, OrdMonoid m) => MonoidRing r m -> r
unitize :: (Fractional r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m
degree_pol :: (Num r, OrdMonoid m, GradedMonoid m) => MonoidRing r m -> Integer
prettyshow_add :: (Num r, Show m, Ord m) => [(m, r)] -> String
Documentation
data (Num r, OrdMonoid m) => MonoidRing r m
Constructors
MakePolynom (Map m r)
show/hide Instances
(Num r, OrdMonoid m) => Eq (MonoidRing r m)
(Num r, GoodMonoid m) => Num (MonoidRing r m)
(Num r, Ord r, OrdMonoid m) => Ord (MonoidRing r m)
(Num r, GoodMonoid m) => Show (MonoidRing r m)
(Num r, OrdMonoid m) => Monoid (MonoidRing r m)
(Num r, OrdMonoid m, GradedMonoid m) => GradedMonoid (MonoidRing r m)
(Num r, Ord r, OrdMonoid m) => OrdMonoid (MonoidRing r m)
(Num r, OrdMonoid m) => Ring (MonoidRing r m)
zero_ring :: (Num r, OrdMonoid m) => MonoidRing r m
ringsum :: (Num r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m -> MonoidRing r m
ringprod :: (Num r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m -> MonoidRing r m
smallmap :: (Num r, OrdMonoid m, OrdMonoid n) => (r, m) -> (m -> MonoidRing r n) -> MonoidRing r n
(>>°) :: (Num r, OrdMonoid m, OrdMonoid n) => MonoidRing r m -> (m -> MonoidRing r n) -> MonoidRing r n
Monadic map of rings R[M] -> R[N] specified by a morphism M -> R[N]
returnr :: (Num r, OrdMonoid m) => m -> MonoidRing r m
leading_thing :: (Num r, OrdMonoid m) => MonoidRing r m -> (m, r)
leading_term :: (Num r, OrdMonoid m) => MonoidRing r m -> m
The leading_term function selects the leading monomial, taking the maximal leaf of the associated binary tree.
leading_coef :: (Num r, OrdMonoid m) => MonoidRing r m -> r
unitize :: (Fractional r, OrdMonoid m) => MonoidRing r m -> MonoidRing r m
degree_pol :: (Num r, OrdMonoid m, GradedMonoid m) => MonoidRing r m -> Integer
The degree_pol function returns the degree of an element.
prettyshow_add :: (Num r, Show m, Ord m) => [(m, r)] -> String
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