MathObj.Monoid

Documentation

newtype GCD a

It is only a monoid for non-negative numbers.

idt <*> GCD (-2) = GCD 2

Thus, use this Monoid only for non-negative numbers!

Constructors

GCD

Fields

• runGCD :: a

Instances

Eq a => Eq (GCD a)

Methods

(==) :: GCD a -> GCD a -> Bool

(/=) :: GCD a -> GCD a -> Bool

Show a => Show (GCD a)

Methods

showsPrec :: Int -> GCD a -> ShowS

show :: GCD a -> String

showList :: [GCD a] -> ShowS

C a => C (GCD a)

Methods

idt :: GCD a

(<*>) :: GCD a -> GCD a -> GCD a

cumulate :: [GCD a] -> GCD a

newtype LCM a

Constructors

LCM

Fields

• runLCM :: a

Instances

Eq a => Eq (LCM a)

Methods

(==) :: LCM a -> LCM a -> Bool

(/=) :: LCM a -> LCM a -> Bool

Show a => Show (LCM a)

Methods

showsPrec :: Int -> LCM a -> ShowS

show :: LCM a -> String

showList :: [LCM a] -> ShowS

C a => C (LCM a)

Methods

idt :: LCM a

(<*>) :: LCM a -> LCM a -> LCM a

cumulate :: [LCM a] -> LCM a

newtype Min a

Nothing is the largest element.

Constructors

Min

Fields

• runMin :: Maybe a

Instances

Eq a => Eq (Min a)

Methods

(==) :: Min a -> Min a -> Bool

(/=) :: Min a -> Min a -> Bool

Show a => Show (Min a)

Methods

showsPrec :: Int -> Min a -> ShowS

show :: Min a -> String

showList :: [Min a] -> ShowS

Ord a => C (Min a)

Methods

idt :: Min a

(<*>) :: Min a -> Min a -> Min a

cumulate :: [Min a] -> Min a

newtype Max a

Nothing is the smallest element.

Constructors

Max

Fields

• runMax :: Maybe a

Instances

Eq a => Eq (Max a)

Methods

(==) :: Max a -> Max a -> Bool

(/=) :: Max a -> Max a -> Bool

Show a => Show (Max a)

Methods

showsPrec :: Int -> Max a -> ShowS

show :: Max a -> String

showList :: [Max a] -> ShowS

Ord a => C (Max a)

Methods

idt :: Max a

(<*>) :: Max a -> Max a -> Max a

cumulate :: [Max a] -> Max a