[{"name":"ComplexNumbers","comment":" A module for complex numbers\n\n\n# Types\n\n@docs Real\n@docs Imaginary\n@docs ComplexNumber\n\n\n# Values\n\n@docs i\n@docs zero\n@docs one\n\n\n# Arithmetic operations on complex numbers\n\n@docs real\n@docs imaginary\n@docs add\n@docs multiply\n@docs subtract\n@docs divide\n@docs modulus\n@docs conjugate\n@docs power\n@docs convertFromCartesianToPolar\n@docs convertFromPolarToCartesian\n@docs euler\n\n\n# Semigroup, Monoid, Group, Ring, Field, Functor, Applicative Functor, and Monad\n\n@docs complexSumSemigroup, complexProductSemigroup, complexSumCommutativeSemigroup, complexProductCommutativeSemigroup\n@docs complexSumMonoid, complexProductMonoid, complexSumCommutativeMonoid, complexProductCommutativeMonoid\n@docs complexSumGroup, complexProductGroup, complexAbelianGroup\n@docs complexRing, complexDivisionRing, complexCommutativeRing, complexCommutativeDivisionRing\n@docs complexField\n@docs map\n@docs pure\n@docs andMap\n@docs andThen\n\n#Equality\n\n@docs equal\n\n\n# Read and Print\n\n@docs parseComplexNumber\n@docs read\n@docs print\n\n","unions":[{"name":"ComplexNumber","comment":" Cartesian representation of a complex number\n","args":["a"],"cases":[["ComplexNumber",["ComplexNumbers.Real a","ComplexNumbers.Imaginary a"]]]},{"name":"Imaginary","comment":" Imaginary portion\n","args":["i"],"cases":[["Imaginary",["i"]]]},{"name":"Real","comment":" Real portion\n","args":["r"],"cases":[["Real",["r"]]]}],"aliases":[],"values":[{"name":"add","comment":" Add two complex numbers together\n","type":"ComplexNumbers.ComplexNumber number -> ComplexNumbers.ComplexNumber number -> ComplexNumbers.ComplexNumber number"},{"name":"andMap","comment":" Apply for Complex Number Cartesian representaiton applicative\n","type":"ComplexNumbers.ComplexNumber a -> ComplexNumbers.ComplexNumber (a -> b) -> ComplexNumbers.ComplexNumber b"},{"name":"andThen","comment":" Monadic bind for Complex Number Cartesian representaiton\n","type":"(a -> ComplexNumbers.ComplexNumber b) -> ComplexNumbers.ComplexNumber a -> ComplexNumbers.ComplexNumber b"},{"name":"complexAbelianGroup","comment":" Group for Complex Numbers with addition as the operation\n","type":"AbelianGroup.AbelianGroup (ComplexNumbers.ComplexNumber number)"},{"name":"complexCommutativeDivisionRing","comment":" Commutative Division Ring for Complex Numbers\n","type":"CommutativeDivisionRing.CommutativeDivisionRing (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexCommutativeRing","comment":" Commutative Ring for Complex Numbers\n","type":"CommutativeRing.CommutativeRing (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexDivisionRing","comment":" Division Ring for Complex Numbers\n","type":"DivisionRing.DivisionRing (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexField","comment":" Field for Complex Numbers\n","type":"Field.Field (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexProductCommutativeMonoid","comment":" Monoid for Complex Numbers with multiplication as the operation\n","type":"CommutativeMonoid.CommutativeMonoid (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexProductCommutativeSemigroup","comment":" Semigroup for Complex Numbers with multiplicatoin as the operation\n","type":"CommutativeSemigroup.CommutativeSemigroup (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexProductGroup","comment":" Group for Complex Numbers with multiplication as the operation\n","type":"Group.Group (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexProductMonoid","comment":" Monoid for Complex Numbers with multiplication as the operation\n","type":"Monoid.Monoid (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexProductSemigroup","comment":" Semigroup for Complex Numbers with addition as the operation\n","type":"Semigroup.Semigroup (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexRing","comment":" Ring for Complex Numbers\n","type":"Ring.Ring (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"complexSumCommutativeMonoid","comment":" Monoid for Complex Numbers with addition as the operation\n","type":"CommutativeMonoid.CommutativeMonoid (ComplexNumbers.ComplexNumber number)"},{"name":"complexSumCommutativeSemigroup","comment":" Semigroup for Complex Numbers with addition as the operation\n","type":"CommutativeSemigroup.CommutativeSemigroup (ComplexNumbers.ComplexNumber number)"},{"name":"complexSumGroup","comment":" Group for Complex Numbers with addition as the operation\n","type":"Group.Group (ComplexNumbers.ComplexNumber number)"},{"name":"complexSumMonoid","comment":" Monoid for Complex Numbers with addition as the operation\n","type":"Monoid.Monoid (ComplexNumbers.ComplexNumber number)"},{"name":"complexSumSemigroup","comment":" Semigroup for Complex Numbers with addition as the operation\n","type":"Semigroup.Semigroup (ComplexNumbers.ComplexNumber number)"},{"name":"conjugate","comment":" Calculate the conjugate of a complex number\n","type":"ComplexNumbers.ComplexNumber number -> ComplexNumbers.ComplexNumber number"},{"name":"convertFromCartesianToPolar","comment":" Convert from the Cartesian representation of a complex number to the polar representation\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> Internal.ComplexNumbers.ComplexNumber Basics.Float"},{"name":"convertFromPolarToCartesian","comment":" Convert from the polar representation of a complex number to the Cartesian representation\n","type":"Internal.ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float"},{"name":"divide","comment":" Divide two complex numbers together\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float"},{"name":"equal","comment":" Compare two ComplexNumbers for equality\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float -> Basics.Bool"},{"name":"euler","comment":" Euler's equation\n","type":"Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float"},{"name":"i","comment":" The number i\n","type":"ComplexNumbers.ComplexNumber number"},{"name":"imaginary","comment":" Extracts the imaginary part of a complex number\n","type":"ComplexNumbers.ComplexNumber a -> a"},{"name":"map","comment":" Map over a complex number\n","type":"(a -> b) -> ComplexNumbers.ComplexNumber a -> ComplexNumbers.ComplexNumber b"},{"name":"modulus","comment":" Calculate the modulus of a complex number\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> Basics.Float"},{"name":"multiply","comment":" Multiply two complex numbers together\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float"},{"name":"one","comment":" one\n","type":"ComplexNumbers.ComplexNumber number"},{"name":"parseComplexNumber","comment":" Parse ComplexNumber\n","type":"Parser.Parser (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"power","comment":" Calculate a complex number raised to a power\n","type":"Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float -> ComplexNumbers.ComplexNumber Basics.Float"},{"name":"print","comment":" Print ComplexNumber\n","type":"ComplexNumbers.ComplexNumber Basics.Float -> String.String"},{"name":"pure","comment":" Place a value in the minimal Complex Number Cartesian context\n","type":"a -> ComplexNumbers.ComplexNumber a"},{"name":"read","comment":" Read ComplexNumber\n","type":"String.String -> Result.Result (List.List Parser.DeadEnd) (ComplexNumbers.ComplexNumber Basics.Float)"},{"name":"real","comment":" Extracts the real part of a complex number\n","type":"ComplexNumbers.ComplexNumber a -> a"},{"name":"subtract","comment":" Subtract two complex numbers together\n","type":"ComplexNumbers.ComplexNumber number -> ComplexNumbers.ComplexNumber number -> ComplexNumbers.ComplexNumber number"},{"name":"zero","comment":" zero\n","type":"ComplexNumbers.ComplexNumber number"}],"binops":[]}]