algebra-simple
Safe HaskellNone
LanguageHaskell2010

Numeric.Algebra.Rings.PseudoRing

Description

Provides the PseudoRing typeclass.

Since: 0.1

Synopsis

Documentation

class (AGroup r, Hemiring r) => PseudoRing r Source #

Defines a PseudoRing i.e. a ring without multiplicative identity. Often called an Rng.

Examples:

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

Since: 0.1

Instances

Instances details
PseudoRing Int16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Int32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Int64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Int8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Word16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Word32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Word64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Word8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Integer Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Double Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Float Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Int Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing Word Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

RealFloat a => PseudoRing (Complex a) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

PseudoRing (Ratio Integer) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing

HasResolution k => PseudoRing (Fixed k) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.PseudoRing