Data.Ring.Module

class (Ring r) <= LeftModule x r | x -> r where

Left modules over rings.

Instances must satisfy the following laws:

• Left distributivity: r ^* (x ^+ y) = r ^* x ^+ r ^* y
• Left distributivity: (r + s) ^* x = r ^* x ^+ s ^* x
• Left compatibility: (r * s) ^* x = r ^* (s ^* x)
• Left identity: one ^* x = x

Members

• mzeroL :: x
• maddL :: x -> x -> x
• msubL :: x -> x -> x
• mmulL :: r -> x -> x

Instances

• (Ring a) => LeftModule Unit a

Operator alias for Data.Ring.Module.maddL (left-associative / precedence 6)

Operator alias for Data.Ring.Module.msubL (left-associative / precedence 6)

Operator alias for Data.Ring.Module.mmulL (left-associative / precedence 7)

mnegateL :: forall r x. LeftModule x r => x -> x

class (Ring r) <= RightModule x r | x -> r where

Right modules over rings.

Instances must satisfy the following laws:

• Right distributivity: (x +^ y) *^ r = x *^ r +^ y *^ r
• Right distributivity: x *^ (r + s) = x *^ r +^ x *^ s
• Right compatibility: x *^ (r * s) = (x *^ r) *^ s
• Right identity: x *^ one = x

Members

• mzeroR :: x
• maddR :: x -> x -> x
• msubR :: x -> x -> x
• mmulR :: x -> r -> x

Instances

• (Ring a) => RightModule Unit a

Operator alias for Data.Ring.Module.maddR (left-associative / precedence 6)

Operator alias for Data.Ring.Module.msubR (left-associative / precedence 6)

Operator alias for Data.Ring.Module.mmulR (left-associative / precedence 7)

mnegateR :: forall r x. RightModule x r => x -> x