algebra-simple
Safe HaskellNone
LanguageHaskell2010

Numeric.Algebra.Rings.Demiring

Description

Provides the Demiring typeclass.

Since: 0.1

Synopsis

Documentation

class (MMonoid r, Quartaring r) => Demiring r Source #

Defines a Demiring i.e. a Quartaring with multiplicative identity. In other words, a semiring without additive identity.

Examples:

Expand
  • \( \mathbb{Z}^{\times} \), the positive integers.
>>> :{
  -- Addition
  f1 :: (Demiring r) => r -> r
  f1 x = x .+. x
:}
>>> f1 5
10
>>> :{
  -- Multiplication
  f2 :: (Demiring r) => r -> r
  f2 x = x .*. x
:}
>>> f2 5
25
>>> :{
  -- One
  f3 :: (Demiring r) => r -> r
  f3 x = x .*. one
:}
>>> f3 5
5

Since: 0.1

Instances

Instances details
Demiring Int16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Int32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Int64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Int8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Word16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Word32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Word64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Word8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Integer Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Natural Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Double Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Float Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Int Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring Word Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

RealFloat a => Demiring (Complex a) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring (Ratio Integer) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

Demiring (Ratio Natural) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring

HasResolution k => Demiring (Fixed k) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Demiring