[{"name":"ComplexNumbers","comment":" A module for complex numbers\n\n\n# Types\n\n@docs Real\n@docs Imaginary\n@docs Modulus\n@docs Theta\n@docs ComplexNumberCartesian\n@docs ComplexNumberPolar\n\n\n# Arithmetic operations on complex numbers\n\n@docs i\n@docs zero\n@docs one\n@docs realPart\n@docs imaginaryPart\n@docs modulusPart\n@docs thetaPart\n@docs add\n@docs sum\n@docs multiply\n@docs product\n@docs subtract\n@docs divide\n@docs modulus\n@docs negate\n@docs conjugate\n@docs convertFromCartesianToPolar\n@docs convertFromPolarToCartesian\n@docs multiplyPolar\n@docs dividePolar\n@docs power\n@docs mapCartesian\n@docs mapPolar\n@docs pureCartesian\n@docs purePolar\n@docs applyCartesian\n@docs applyPolar\n@docs bindCartesian\n@docs bindPolar\n\n","unions":[{"name":"ComplexNumberCartesian","comment":" Cartesian representation of a complex number\n","args":["a"],"cases":[["ComplexNumberCartesian",["ComplexNumbers.Real a","ComplexNumbers.Imaginary a"]]]},{"name":"ComplexNumberPolar","comment":" Polar representation of a complex number\n","args":["a"],"cases":[["ComplexNumberPolar",["ComplexNumbers.Modulus a","ComplexNumbers.Theta a"]]]},{"name":"Imaginary","comment":" Imaginary portion\n","args":["i"],"cases":[["Imaginary",["i"]]]},{"name":"Modulus","comment":" Modulus or magnitude portion\n","args":["m"],"cases":[["Modulus",["m"]]]},{"name":"Real","comment":" Real portion\n","args":["r"],"cases":[["Real",["r"]]]},{"name":"Theta","comment":" Angle in real-complex plane of modulus\n","args":["t"],"cases":[["Theta",["t"]]]}],"aliases":[],"values":[{"name":"add","comment":" Add two complex numbers together\n","type":"ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"applyCartesian","comment":" Apply for Complex Number Cartesian representaiton applicative\n","type":"ComplexNumbers.ComplexNumberCartesian (a -> b) -> ComplexNumbers.ComplexNumberCartesian a -> ComplexNumbers.ComplexNumberCartesian b"},{"name":"applyPolar","comment":" Apply for Complex Number polar representaiton applicative\n","type":"ComplexNumbers.ComplexNumberPolar (a -> b) -> ComplexNumbers.ComplexNumberPolar a -> ComplexNumbers.ComplexNumberPolar b"},{"name":"bindCartesian","comment":" Monadic bind for Complex Number Cartesian representaiton\n","type":"ComplexNumbers.ComplexNumberCartesian a -> (a -> ComplexNumbers.ComplexNumberCartesian b) -> ComplexNumbers.ComplexNumberCartesian b"},{"name":"bindPolar","comment":" Monadic bind for Complex Number polar representaiton\n","type":"ComplexNumbers.ComplexNumberPolar a -> (a -> ComplexNumbers.ComplexNumberPolar b) -> ComplexNumbers.ComplexNumberPolar b"},{"name":"conjugate","comment":" Calculate the conjugate of a complex number\n","type":"ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"convertFromCartesianToPolar","comment":" Convert from the Cartesian representation of a complex number to the polar representation\n","type":"ComplexNumbers.ComplexNumberCartesian Basics.Float -> ComplexNumbers.ComplexNumberPolar Basics.Float"},{"name":"convertFromPolarToCartesian","comment":" Convert from the polar representation of a complex number to the Cartesian representation\n","type":"ComplexNumbers.ComplexNumberPolar Basics.Float -> ComplexNumbers.ComplexNumberCartesian Basics.Float"},{"name":"divide","comment":" Divide two complex numbers together\n","type":"ComplexNumbers.ComplexNumberCartesian Basics.Float -> ComplexNumbers.ComplexNumberCartesian Basics.Float -> Result.Result String.String (ComplexNumbers.ComplexNumberCartesian Basics.Float)"},{"name":"dividePolar","comment":" Divide two complex numbers in polar representations together\n","type":"ComplexNumbers.ComplexNumberPolar Basics.Float -> ComplexNumbers.ComplexNumberPolar Basics.Float -> Result.Result String.String (ComplexNumbers.ComplexNumberPolar Basics.Float)"},{"name":"i","comment":" The number i\n","type":"ComplexNumbers.ComplexNumberCartesian number"},{"name":"imaginaryPart","comment":" Extracts the imaginary part of a complex number\n","type":"ComplexNumbers.ComplexNumberCartesian a -> a"},{"name":"mapCartesian","comment":" Map over a complex number\n","type":"(a -> b) -> ComplexNumbers.ComplexNumberCartesian a -> ComplexNumbers.ComplexNumberCartesian b"},{"name":"mapPolar","comment":" Map over a complex number in polar representation\n","type":"(a -> b) -> ComplexNumbers.ComplexNumberPolar a -> ComplexNumbers.ComplexNumberPolar b"},{"name":"modulus","comment":" Calculate the modulus of a complex number\n","type":"ComplexNumbers.ComplexNumberCartesian Basics.Float -> Basics.Float"},{"name":"modulusPart","comment":" Extracts the modulus part of a complex number\n","type":"ComplexNumbers.ComplexNumberPolar a -> a"},{"name":"multiply","comment":" Multiply two complex numbers together\n","type":"ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"multiplyPolar","comment":" Multiply two complex numbers in polar representations together\n","type":"ComplexNumbers.ComplexNumberPolar number -> ComplexNumbers.ComplexNumberPolar number -> ComplexNumbers.ComplexNumberPolar number"},{"name":"negate","comment":" negate a complex number\n","type":"ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"one","comment":" one\n","type":"ComplexNumbers.ComplexNumberCartesian number"},{"name":"power","comment":" Calculate a complex number raised to a power\n","type":"number -> ComplexNumbers.ComplexNumberPolar number -> ComplexNumbers.ComplexNumberPolar number"},{"name":"product","comment":" Monoidally multiply two complex numbers together\n","type":"Monoid.Monoid (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"pureCartesian","comment":" Place a value in the minimal Complex Number Cartesian context\n","type":"a -> ComplexNumbers.ComplexNumberCartesian a"},{"name":"purePolar","comment":" Place a value in the minimal Complex Number polar context\n","type":"a -> ComplexNumbers.ComplexNumberPolar a"},{"name":"realPart","comment":" Extracts the real part of a complex number\n","type":"ComplexNumbers.ComplexNumberCartesian a -> a"},{"name":"subtract","comment":" Subtract two complex numbers together\n","type":"ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"sum","comment":" Monoidally add two complex numbers together\n","type":"Monoid.Monoid (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"thetaPart","comment":" Extracts the imaginary part of a complex number\n","type":"ComplexNumbers.ComplexNumberPolar a -> a"},{"name":"zero","comment":" zero\n","type":"ComplexNumbers.ComplexNumberCartesian number"}],"binops":[]}]