74 lines
2.5 KiB
Elixir
74 lines
2.5 KiB
Elixir
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defmodule ComplexNumbers do
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@typedoc """
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In this module, complex numbers are represented as a tuple-pair containing the real and
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imaginary parts.
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For example, the real number `1` is `{1, 0}`, the imaginary number `i` is `{0, 1}` and
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the complex number `4+3i` is `{4, 3}'.
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"""
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@type complex :: {number, number}
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@doc """
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Return the real part of a complex number
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"""
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@spec real(a :: complex) :: number
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def real({r, _i}), do: r
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@doc """
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Return the imaginary part of a complex number
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"""
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@spec imaginary(a :: complex) :: number
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def imaginary({_r, i}), do: i
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@doc """
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Multiply two complex numbers, or a real and a complex number
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"""
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@spec mul(a :: complex | number, b :: complex | number) :: complex
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def mul(n, {r, i}) when is_number(n), do: mul({r, i}, to_complex(n))
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def mul({r, i}, n) when is_number(n), do: mul(to_complex(n), {r, i})
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def mul({ar, ai}, {br, bi}), do: {ar * br - ai * bi, ar * bi + ai * br}
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@doc """
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Add two complex numbers, or a real and a complex number
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"""
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@spec add(a :: complex | number, b :: complex | number) :: complex
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def add(n, {r, i}) when is_number(n), do: add({r, i}, to_complex(n))
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def add({r, i}, n) when is_number(n), do: add(to_complex(n), {r, i})
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def add({ar, ai}, {br, bi}), do: {ar + br, ai + bi}
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@doc """
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Subtract two complex numbers, or a real and a complex number
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"""
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@spec sub(a :: complex | number, b :: complex | number) :: complex
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def sub(n, {r, i}) when is_number(n), do: sub(to_complex(n), {r, i})
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def sub({r, i}, n) when is_number(n), do: sub({r, i}, to_complex(n))
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def sub({ar, ai}, {br, bi}), do: {ar - br, ai - bi}
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@doc """
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Divide two complex numbers, or a real and a complex number
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"""
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@spec div(a :: complex | number, b :: complex | number) :: complex
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def div(n, {r, i}) when is_number(n), do: __MODULE__.div(to_complex(n), {r, i})
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def div({r, i}, n) when is_number(n), do: __MODULE__.div({r, i}, to_complex(n))
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def div({ar, ai}, {br, bi}), do: {(ar * br + ai * bi)/(br ** 2 + bi ** 2), (ai * br - ar * bi)/(br ** 2 + bi ** 2)}
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@doc """
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Absolute value of a complex number
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"""
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@spec abs(a :: complex) :: number
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def abs({r, i}), do: (r ** 2 + i ** 2) ** 0.5
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@doc """
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Conjugate of a complex number
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"""
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@spec conjugate(a :: complex) :: complex
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def conjugate({r, i}), do: {r, -i}
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@doc """
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Exponential of a complex number
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"""
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@spec exp(a :: complex) :: complex
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def exp({r, i}), do: mul({:math.exp(r), 0}, {:math.cos(i), :math.sin(i)})
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defp to_complex(n) when is_number(n), do: {n, 0}
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end
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