Polynom-0.1: A commutative algebra package Contents Index

Data.MonoidPlus

Synopsis

class (Monoid a, Ord a) => OrdMonoid a class (OrdMonoid a, Show a) => GoodMonoid a class Monoid a => GradedMonoid a where degree :: a -> Integer class GoodMonoid a => GroebnerMonoid a where (×) :: a -> a -> a (÷) :: a -> a -> a lcm_monom :: a -> a -> a lcm2_monom :: a -> a -> (a, a) gcd_monom :: a -> a -> a divides :: a -> a -> Bool

Documentation

class (Monoid a, Ord a) => OrdMonoid a

A class for ordered monoids. Instances VarList a => OrdMonoid (Monom a) (Num r, Ord r, OrdMonoid m) => OrdMonoid (MonoidRing r m) (OrdMonoid a, OrdMonoid b) => OrdMonoid (EliminationMonoid a b)

class (OrdMonoid a, Show a) => GoodMonoid a

The class GoodMonoid of good monoids is the preferred class to use to generate rings with good properties, for example rings with a Show method. Instances (Show a, VarList a) => GoodMonoid (Monom a) (GoodMonoid a, GoodMonoid b) => GoodMonoid (EliminationMonoid a b)

class Monoid a => GradedMonoid a where

Define a class for graded monoids, like free commutative monoids. Methods degree :: a -> Integer Instances VarList a => GradedMonoid (Monom a) (Num r, OrdMonoid m, GradedMonoid m) => GradedMonoid (MonoidRing r m)

class GoodMonoid a => GroebnerMonoid a where

The GroebnerMonoid class gathers monoids with enough structure to allow computation of Groebner bases Methods (×) :: a -> a -> a Multiplication (÷) :: a -> a -> a Division, which should only be used if exponents remain positive lcm_monom :: a -> a -> a Returns the least common multiple of monomials. lcm2_monom :: a -> a -> (a, a) Returns the least common multiple of monomials and the complements. gcd_monom :: a -> a -> a Returns the greatest common divisor of monomials. divides :: a -> a -> Bool Tests divisibility Instances VarList a => GroebnerMonoid (Monom a) (GroebnerMonoid a, GroebnerMonoid b) => GroebnerMonoid (EliminationMonoid a b)

Produced by Haddock version 2.3.0