algebra-simple
Safe HaskellNone
LanguageHaskell2010

Numeric.Algebra.Rings.Quartaring

Description

Provides the Quartaring typeclass.

Since: 0.1

Synopsis

Documentation

class (ASemigroup r, MSemigroup r) => Quartaring r Source #

Defines a Quartaring i.e. a structure with addition and multiplication. In other words, a semiring that has no identity requirement. Should satisfy:

  • Distributive property:

    a .*. (b .+. c) === (a .*. b) .+. (a .*. c)
    (b .+. c) .*. a === (b .*. a) .+. (c .*. a)
    

Examples:

Expand
  • \( \mathbb{Z}^{\gt 1} \), the integers greater than one.
>>> :{
  -- Addition
  f1 :: (Quartaring r) => r -> r
  f1 x = x .+. x
:}
>>> f1 5
10
>>> :{
  -- Multiplication
  f2 :: (Quartaring r) => r -> r
  f2 x = x .*. x
:}
>>> f2 5
25

Since: 0.1

Instances

Instances details
Quartaring Int16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Int32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Int64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Int8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Word16 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Word32 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Word64 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Word8 Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Integer Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Natural Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Double Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Float Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Int Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring Word Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

RealFloat a => Quartaring (Complex a) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring (Ratio Integer) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

Quartaring (Ratio Natural) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring

HasResolution k => Quartaring (Fixed k) Source #

Since: 0.1

Instance details

Defined in Numeric.Algebra.Rings.Quartaring