algebra-simple
Safe HaskellNone
LanguageHaskell2010

Numeric.Algebra.Rings.Ring

Description

Provides the Ring typeclass.

Since: 0.1

Synopsis

Documentation

class (PseudoRing r, Semiring r) => Ring r Source #

Defines a Ring i.e. a structure that is an PseudoRing and a Semiring.

Examples:

Expand
  • \( \mathbb{Z} \), the integers.
>>> :{
  -- Addition
  f1 :: (Ring r) => r -> r
  f1 x = x .+. x
:}
>>> f1 5
10
>>> :{
  -- Zero
  f2 :: (Ring r) => r -> r
  f2 x = x .+. zero
:}
>>> f2 5
5
>>> :{
  -- Subtraction
  f3 :: (Ring r, Num r) => r -> r
  f3 x = x .-. 3
:}
>>> f3 5
2
>>> :{
  -- Multiplication
  f4 :: (Ring r) => r -> r
  f4 x = x .*. x
:}
>>> f4 5
25
>>> :{
  -- One
  f5 :: (Ring r) => r -> r
  f5 x = x .*. one
:}
>>> f5 5
5

Since: 0.1

Instances

Instances details
Ring Int16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Int32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Int64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Int8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Word16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Word32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Word64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Word8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Integer Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Double Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Float Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Int Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring Word Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

RealFloat a => Ring (Complex a) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

Ring (Ratio Integer) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring

HasResolution k => Ring (Fixed k) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Ring