81 lines
2.5 KiB
Elixir
81 lines
2.5 KiB
Elixir
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defmodule RationalNumbers do
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@type rational :: {integer, integer}
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alias Kernel, as: K
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@doc """
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Add two rational numbers
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"""
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@spec add(a :: rational, b :: rational) :: rational
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def add({an, ad}, {bn, bd}), do: {an * bd + bn * ad, ad * bd} |> reduce()
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@doc """
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Subtract two rational numbers
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"""
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@spec subtract(a :: rational, b :: rational) :: rational
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def subtract({an, ad}, {bn, bd}), do: {an * bd - bn * ad, ad * bd} |> reduce()
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@doc """
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Multiply two rational numbers
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"""
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@spec multiply(a :: rational, b :: rational) :: rational
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def multiply({an, ad}, {bn, bd}), do: {an * bn, ad * bd} |> reduce()
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@doc """
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Divide two rational numbers
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"""
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@spec divide_by(num :: rational, den :: rational) :: rational
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def divide_by({an, ad}, {bn, bd}) when bn != 0, do: {an * bd, bn * ad} |> reduce()
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@doc """
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Absolute value of a rational number
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"""
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@spec abs(a :: rational) :: rational
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def abs({an, ad}), do: {K.abs(an), K.abs(ad)} |> reduce()
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@doc """
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Exponentiation of a rational number by an integer
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"""
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@spec pow_rational(a :: rational, n :: integer | float) :: rational
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def pow_rational({an, ad}, n) when is_integer(n) and n >= 0, do: {an ** n, ad ** n} |> reduce()
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def pow_rational({an, ad}, n) when is_integer(n) and n < 0,
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do: {ad ** K.abs(n), an ** K.abs(n)} |> reduce()
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def pow_rational({an, ad}, x) when is_float(x), do: ad ** x / an ** x
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@doc """
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Exponentiation of a real number by a rational number
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"""
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@spec pow_real(x :: integer, n :: rational) :: float
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def pow_real(x, {_nn, nd} = n) when is_integer(x) and nd < 0, do: pow_real(x, normalize(n))
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def pow_real(x, {nn, nd}) when is_integer(x), do: x ** nn ** (1 / nd)
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@doc """
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Reduce a rational number to its lowest terms
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"""
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@spec reduce(a :: rational) :: rational
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def reduce({an, ad} = a),
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do: a |> normalize() |> cut(Integer.gcd(an, ad))
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# @doc """
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# Divides a nominator and denominator by integer
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# """
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@spec cut(a :: rational, n :: integer) :: rational
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defp cut({an, ad}, n), do: {K.div(an, n), K.div(ad, n)}
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# @doc """
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# Turns signs of nominator and denominator when negative denominator
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# """
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@spec normalize(a :: rational) :: rational
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defp normalize({an, ad}) when ad < 0, do: {K.-(an), K.-(ad)}
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defp normalize({an, ad}), do: {an, ad}
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# @doc """
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# Calculate a greatest common divisor of two integers
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# """
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# @spec gcd(i :: integer, j :: integer) :: integer
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# defp gcd(i, 0), do: K.abs(i)
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# defp gcd(0, j), do: K.abs(j)
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# defp gcd(i, j), do: gcd(j, K.rem(i, j))
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end
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