From 3c7f1d64f5f6c0ff4585050a5aae68d5eb0b519c Mon Sep 17 00:00:00 2001
From: Danylo Negrienko <danil@negrienko.com>
Date: Sun, 10 Mar 2024 07:27:55 -0400
Subject: [PATCH] rational_numbers

---
 elixir/rational-numbers/.exercism/config.json |  23 ++
 .../rational-numbers/.exercism/metadata.json  |   1 +
 elixir/rational-numbers/.formatter.exs        |   4 +
 elixir/rational-numbers/.gitignore            |  24 ++
 elixir/rational-numbers/HELP.md               |  75 ++++++
 elixir/rational-numbers/README.md             |  62 +++++
 .../rational-numbers/lib/rational_numbers.ex  |  80 ++++++
 elixir/rational-numbers/mix.exs               |  28 ++
 .../test/rational_numbers_test.exs            | 243 ++++++++++++++++++
 elixir/rational-numbers/test/test_helper.exs  |   2 +
 10 files changed, 542 insertions(+)
 create mode 100644 elixir/rational-numbers/.exercism/config.json
 create mode 100644 elixir/rational-numbers/.exercism/metadata.json
 create mode 100644 elixir/rational-numbers/.formatter.exs
 create mode 100644 elixir/rational-numbers/.gitignore
 create mode 100644 elixir/rational-numbers/HELP.md
 create mode 100644 elixir/rational-numbers/README.md
 create mode 100644 elixir/rational-numbers/lib/rational_numbers.ex
 create mode 100644 elixir/rational-numbers/mix.exs
 create mode 100644 elixir/rational-numbers/test/rational_numbers_test.exs
 create mode 100644 elixir/rational-numbers/test/test_helper.exs

diff --git a/elixir/rational-numbers/.exercism/config.json b/elixir/rational-numbers/.exercism/config.json
new file mode 100644
index 0000000..8d93ada
--- /dev/null
+++ b/elixir/rational-numbers/.exercism/config.json
@@ -0,0 +1,23 @@
+{
+  "authors": [
+    "jiegillet"
+  ],
+  "contributors": [
+    "angelikatyborska",
+    "kszambelanczyk"
+  ],
+  "files": {
+    "solution": [
+      "lib/rational_numbers.ex"
+    ],
+    "test": [
+      "test/rational_numbers_test.exs"
+    ],
+    "example": [
+      ".meta/example.ex"
+    ]
+  },
+  "blurb": "Implement rational numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Rational_number"
+}
diff --git a/elixir/rational-numbers/.exercism/metadata.json b/elixir/rational-numbers/.exercism/metadata.json
new file mode 100644
index 0000000..7c6bc87
--- /dev/null
+++ b/elixir/rational-numbers/.exercism/metadata.json
@@ -0,0 +1 @@
+{"track":"elixir","exercise":"rational-numbers","id":"7dc127adcbfe4b6082e20167dc621378","url":"https://exercism.org/tracks/elixir/exercises/rational-numbers","handle":"negrienko","is_requester":true,"auto_approve":false}
\ No newline at end of file
diff --git a/elixir/rational-numbers/.formatter.exs b/elixir/rational-numbers/.formatter.exs
new file mode 100644
index 0000000..d2cda26
--- /dev/null
+++ b/elixir/rational-numbers/.formatter.exs
@@ -0,0 +1,4 @@
+# Used by "mix format"
+[
+  inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
+]
diff --git a/elixir/rational-numbers/.gitignore b/elixir/rational-numbers/.gitignore
new file mode 100644
index 0000000..9117615
--- /dev/null
+++ b/elixir/rational-numbers/.gitignore
@@ -0,0 +1,24 @@
+# The directory Mix will write compiled artifacts to.
+/_build/
+
+# If you run "mix test --cover", coverage assets end up here.
+/cover/
+
+# The directory Mix downloads your dependencies sources to.
+/deps/
+
+# Where third-party dependencies like ExDoc output generated docs.
+/doc/
+
+# Ignore .fetch files in case you like to edit your project deps locally.
+/.fetch
+
+# If the VM crashes, it generates a dump, let's ignore it too.
+erl_crash.dump
+
+# Also ignore archive artifacts (built via "mix archive.build").
+*.ez
+
+# Ignore package tarball (built via "mix hex.build").
+rational_numbers-*.tar
+
diff --git a/elixir/rational-numbers/HELP.md b/elixir/rational-numbers/HELP.md
new file mode 100644
index 0000000..095ebe1
--- /dev/null
+++ b/elixir/rational-numbers/HELP.md
@@ -0,0 +1,75 @@
+# Help
+
+## Running the tests
+
+From the terminal, change to the base directory of the exercise then execute the tests with:
+
+```bash
+$ mix test
+```
+
+This will execute the test file found in the `test` subfolder -- a file ending in `_test.exs`
+
+Documentation:
+
+* [`mix test` - Elixir's test execution tool](https://hexdocs.pm/mix/Mix.Tasks.Test.html)
+* [`ExUnit` - Elixir's unit test library](https://hexdocs.pm/ex_unit/ExUnit.html)
+
+## Pending tests
+
+In test suites of practice exercises, all but the first test have been tagged to be skipped.
+
+Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.
+
+For example:
+
+```elixir
+# @tag :pending
+test "shouting" do
+  assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
+end
+```
+
+If you wish to run all tests at once, you can include all skipped test by using the `--include` flag on the `mix test` command:
+
+```bash
+$ mix test --include pending
+```
+
+Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the file `test/test_helper.exs`.
+
+```elixir
+# ExUnit.configure(exclude: :pending, trace: true)
+```
+
+## Useful `mix test` options
+
+* `test/<FILE>.exs:LINENUM` - runs only a single test, the test from `<FILE>.exs` whose definition is on line `LINENUM`
+* `--failed` - runs only tests that failed the last time they ran
+* `--max-failures` - the suite stops evaluating tests when this number of test failures
+is reached
+* `--seed 0` - disables randomization so the tests in a single file will always be ran
+in the same order they were defined in
+
+## Submitting your solution
+
+You can submit your solution using the `exercism submit lib/rational_numbers.ex` command.
+This command will upload your solution to the Exercism website and print the solution page's URL.
+
+It's possible to submit an incomplete solution which allows you to:
+
+- See how others have completed the exercise
+- Request help from a mentor
+
+## Need to get help?
+
+If you'd like help solving the exercise, check the following pages:
+
+- The [Elixir track's documentation](https://exercism.org/docs/tracks/elixir)
+- The [Elixir track's programming category on the forum](https://forum.exercism.org/c/programming/elixir)
+- [Exercism's programming category on the forum](https://forum.exercism.org/c/programming/5)
+- The [Frequently Asked Questions](https://exercism.org/docs/using/faqs)
+
+Should those resources not suffice, you could submit your (incomplete) solution to request mentoring.
+
+If you're stuck on something, it may help to look at some of the [available resources](https://exercism.org/docs/tracks/elixir/resources) out there where answers might be found.
\ No newline at end of file
diff --git a/elixir/rational-numbers/README.md b/elixir/rational-numbers/README.md
new file mode 100644
index 0000000..25936af
--- /dev/null
+++ b/elixir/rational-numbers/README.md
@@ -0,0 +1,62 @@
+# Rational Numbers
+
+Welcome to Rational Numbers on Exercism's Elixir Track.
+If you need help running the tests or submitting your code, check out `HELP.md`.
+
+## Instructions
+
+A rational number is defined as the quotient of two integers `a` and `b`, called the numerator and denominator, respectively, where `b != 0`.
+
+~~~~exercism/note
+Note that mathematically, the denominator can't be zero.
+However in many implementations of rational numbers, you will find that the denominator is allowed to be zero with behaviour similar to positive or negative infinity in floating point numbers.
+In those cases, the denominator and numerator generally still can't both be zero at once.
+~~~~
+
+The absolute value `|r|` of the rational number `r = a/b` is equal to `|a|/|b|`.
+
+The sum of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ + r₂ = a₁/b₁ + a₂/b₂ = (a₁ * b₂ + a₂ * b₁) / (b₁ * b₂)`.
+
+The difference of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ - r₂ = a₁/b₁ - a₂/b₂ = (a₁ * b₂ - a₂ * b₁) / (b₁ * b₂)`.
+
+The product (multiplication) of two rational numbers `r₁ = a₁/b₁` and `r₂ = a₂/b₂` is `r₁ * r₂ = (a₁ * a₂) / (b₁ * b₂)`.
+
+Dividing a rational number `r₁ = a₁/b₁` by another `r₂ = a₂/b₂` is `r₁ / r₂ = (a₁ * b₂) / (a₂ * b₁)` if `a₂` is not zero.
+
+Exponentiation of a rational number `r = a/b` to a non-negative integer power `n` is `r^n = (a^n)/(b^n)`.
+
+Exponentiation of a rational number `r = a/b` to a negative integer power `n` is `r^n = (b^m)/(a^m)`, where `m = |n|`.
+
+Exponentiation of a rational number `r = a/b` to a real (floating-point) number `x` is the quotient `(a^x)/(b^x)`, which is a real number.
+
+Exponentiation of a real number `x` to a rational number `r = a/b` is `x^(a/b) = root(x^a, b)`, where `root(p, q)` is the `q`th root of `p`.
+
+Implement the following operations:
+
+- addition, subtraction, multiplication and division of two rational numbers,
+- absolute value, exponentiation of a given rational number to an integer power, exponentiation of a given rational number to a real (floating-point) power, exponentiation of a real number to a rational number.
+
+Your implementation of rational numbers should always be reduced to lowest terms.
+For example, `4/4` should reduce to `1/1`, `30/60` should reduce to `1/2`, `12/8` should reduce to `3/2`, etc.
+To reduce a rational number `r = a/b`, divide `a` and `b` by the greatest common divisor (gcd) of `a` and `b`.
+So, for example, `gcd(12, 8) = 4`, so `r = 12/8` can be reduced to `(12/4)/(8/4) = 3/2`.
+The reduced form of a rational number should be in "standard form" (the denominator should always be a positive integer).
+If a denominator with a negative integer is present, multiply both numerator and denominator by `-1` to ensure standard form is reached.
+For example, `3/-4` should be reduced to `-3/4`
+
+Assume that the programming language you are using does not have an implementation of rational numbers.
+
+## Source
+
+### Created by
+
+- @jiegillet
+
+### Contributed to by
+
+- @angelikatyborska
+- @kszambelanczyk
+
+### Based on
+
+Wikipedia - https://en.wikipedia.org/wiki/Rational_number
\ No newline at end of file
diff --git a/elixir/rational-numbers/lib/rational_numbers.ex b/elixir/rational-numbers/lib/rational_numbers.ex
new file mode 100644
index 0000000..66fce04
--- /dev/null
+++ b/elixir/rational-numbers/lib/rational_numbers.ex
@@ -0,0 +1,80 @@
+defmodule RationalNumbers do
+  @type rational :: {integer, integer}
+  alias Kernel, as: K
+
+  @doc """
+  Add two rational numbers
+  """
+  @spec add(a :: rational, b :: rational) :: rational
+  def add({an, ad}, {bn, bd}), do: {an * bd + bn * ad, ad * bd} |> reduce()
+
+  @doc """
+  Subtract two rational numbers
+  """
+  @spec subtract(a :: rational, b :: rational) :: rational
+  def subtract({an, ad}, {bn, bd}), do: {an * bd - bn * ad, ad * bd} |> reduce()
+
+  @doc """
+  Multiply two rational numbers
+  """
+  @spec multiply(a :: rational, b :: rational) :: rational
+  def multiply({an, ad}, {bn, bd}), do: {an * bn, ad * bd} |> reduce()
+
+  @doc """
+  Divide two rational numbers
+  """
+  @spec divide_by(num :: rational, den :: rational) :: rational
+  def divide_by({an, ad}, {bn, bd}) when bn != 0, do: {an * bd, bn * ad} |> reduce()
+
+  @doc """
+  Absolute value of a rational number
+  """
+  @spec abs(a :: rational) :: rational
+  def abs({an, ad}), do: {K.abs(an), K.abs(ad)} |> reduce()
+
+  @doc """
+  Exponentiation of a rational number by an integer
+  """
+  @spec pow_rational(a :: rational, n :: integer | float) :: rational
+  def pow_rational({an, ad}, n) when is_integer(n) and n >= 0, do: {an ** n, ad ** n} |> reduce()
+
+  def pow_rational({an, ad}, n) when is_integer(n) and n < 0,
+    do: {ad ** K.abs(n), an ** K.abs(n)} |> reduce()
+
+  def pow_rational({an, ad}, x) when is_float(x), do: ad ** x / an ** x
+
+  @doc """
+  Exponentiation of a real number by a rational number
+  """
+  @spec pow_real(x :: integer, n :: rational) :: float
+  def pow_real(x, {_nn, nd} = n) when is_integer(x) and nd < 0, do: pow_real(x, normalize(n))
+  def pow_real(x, {nn, nd}) when is_integer(x), do: x ** nn ** (1 / nd)
+
+  @doc """
+  Reduce a rational number to its lowest terms
+  """
+  @spec reduce(a :: rational) :: rational
+  def reduce({an, ad} = a),
+    do: a |> normalize() |> cut(Integer.gcd(an, ad))
+
+  # @doc """
+  # Divides a nominator and denominator by integer
+  # """
+  @spec cut(a :: rational, n :: integer) :: rational
+  defp cut({an, ad}, n), do: {K.div(an, n), K.div(ad, n)}
+
+  # @doc """
+  # Turns signs of nominator and denominator when negative denominator
+  # """
+  @spec normalize(a :: rational) :: rational
+  defp normalize({an, ad}) when ad < 0, do: {K.-(an), K.-(ad)}
+  defp normalize({an, ad}), do: {an, ad}
+
+  # @doc """
+  # Calculate a greatest common divisor of two integers
+  # """
+  # @spec gcd(i :: integer, j :: integer) :: integer
+  # defp gcd(i, 0), do: K.abs(i)
+  # defp gcd(0, j), do: K.abs(j)
+  # defp gcd(i, j), do: gcd(j, K.rem(i, j))
+end
diff --git a/elixir/rational-numbers/mix.exs b/elixir/rational-numbers/mix.exs
new file mode 100644
index 0000000..84af9a6
--- /dev/null
+++ b/elixir/rational-numbers/mix.exs
@@ -0,0 +1,28 @@
+defmodule RationalNumbers.MixProject do
+  use Mix.Project
+
+  def project do
+    [
+      app: :rational_numbers,
+      version: "0.1.0",
+      # elixir: "~> 1.8",
+      start_permanent: Mix.env() == :prod,
+      deps: deps()
+    ]
+  end
+
+  # Run "mix help compile.app" to learn about applications.
+  def application do
+    [
+      extra_applications: [:logger]
+    ]
+  end
+
+  # Run "mix help deps" to learn about dependencies.
+  defp deps do
+    [
+      # {:dep_from_hexpm, "~> 0.3.0"},
+      # {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
+    ]
+  end
+end
diff --git a/elixir/rational-numbers/test/rational_numbers_test.exs b/elixir/rational-numbers/test/rational_numbers_test.exs
new file mode 100644
index 0000000..5f1770f
--- /dev/null
+++ b/elixir/rational-numbers/test/rational_numbers_test.exs
@@ -0,0 +1,243 @@
+defmodule RationalNumbersTest do
+  use ExUnit.Case
+
+  describe "Addition" do
+    # # @tag :pending
+    test "Add two positive rational numbers" do
+      assert RationalNumbers.add({1, 2}, {2, 3}) == {7, 6}
+    end
+
+    # @tag :pending
+    test "Add a positive rational number and a negative rational number" do
+      assert RationalNumbers.add({1, 2}, {-2, 3}) == {-1, 6}
+    end
+
+    # @tag :pending
+    test "Add two negative rational numbers" do
+      assert RationalNumbers.add({-1, 2}, {-2, 3}) == {-7, 6}
+    end
+
+    # @tag :pending
+    test "Add a rational number to its additive inverse" do
+      assert RationalNumbers.add({1, 2}, {-1, 2}) == {0, 1}
+    end
+  end
+
+  describe "Subtraction" do
+    # @tag :pending
+    test "Subtract two positive rational numbers" do
+      assert RationalNumbers.subtract({1, 2}, {2, 3}) == {-1, 6}
+    end
+
+    # @tag :pending
+    test "Subtract a positive rational number and a negative rational number" do
+      assert RationalNumbers.subtract({1, 2}, {-2, 3}) == {7, 6}
+    end
+
+    # @tag :pending
+    test "Subtract two negative rational numbers" do
+      assert RationalNumbers.subtract({-1, 2}, {-2, 3}) == {1, 6}
+    end
+
+    # @tag :pending
+    test "Subtract a rational number from itself" do
+      assert RationalNumbers.subtract({1, 2}, {1, 2}) == {0, 1}
+    end
+  end
+
+  describe "Multiplication" do
+    # @tag :pending
+    test "Multiply two positive rational numbers" do
+      assert RationalNumbers.multiply({1, 2}, {2, 3}) == {1, 3}
+    end
+
+    # @tag :pending
+    test "Multiply a negative rational number by a positive rational number" do
+      assert RationalNumbers.multiply({-1, 2}, {2, 3}) == {-1, 3}
+    end
+
+    # @tag :pending
+    test "Multiply two negative rational numbers" do
+      assert RationalNumbers.multiply({-1, 2}, {-2, 3}) == {1, 3}
+    end
+
+    # @tag :pending
+    test "Multiply a rational number by its reciprocal" do
+      assert RationalNumbers.multiply({1, 2}, {2, 1}) == {1, 1}
+    end
+
+    # @tag :pending
+    test "Multiply a rational number by 1" do
+      assert RationalNumbers.multiply({1, 2}, {1, 1}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Multiply a rational number by 0" do
+      assert RationalNumbers.multiply({1, 2}, {0, 1}) == {0, 1}
+    end
+  end
+
+  describe "Division" do
+    # @tag :pending
+    test "Divide two positive rational numbers" do
+      assert RationalNumbers.divide_by({1, 2}, {2, 3}) == {3, 4}
+    end
+
+    # @tag :pending
+    test "Divide a positive rational number by a negative rational number" do
+      assert RationalNumbers.divide_by({1, 2}, {-2, 3}) == {-3, 4}
+    end
+
+    # @tag :pending
+    test "Divide two negative rational numbers" do
+      assert RationalNumbers.divide_by({-1, 2}, {-2, 3}) == {3, 4}
+    end
+
+    # @tag :pending
+    test "Divide a rational number by 1" do
+      assert RationalNumbers.divide_by({1, 2}, {1, 1}) == {1, 2}
+    end
+  end
+
+  describe "Absolute value" do
+    # @tag :pending
+    test "Absolute value of a positive rational number" do
+      assert RationalNumbers.abs({1, 2}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Absolute value of a positive rational number with negative numerator and denominator" do
+      assert RationalNumbers.abs({-1, -2}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Absolute value of a negative rational number" do
+      assert RationalNumbers.abs({-1, 2}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Absolute value of a negative rational number with negative denominator" do
+      assert RationalNumbers.abs({1, -2}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Absolute value of zero" do
+      assert RationalNumbers.abs({0, 1}) == {0, 1}
+    end
+
+    # @tag :pending
+    test "Absolute value of a rational number is reduced to lowest terms" do
+      assert RationalNumbers.abs({2, 4}) == {1, 2}
+    end
+  end
+
+  describe "Exponentiation of a rational number" do
+    # @tag :pending
+    test "Raise a positive rational number to a positive integer power" do
+      assert RationalNumbers.pow_rational({1, 2}, 3) == {1, 8}
+    end
+
+    # @tag :pending
+    test "Raise a negative rational number to a positive integer power" do
+      assert RationalNumbers.pow_rational({-1, 2}, 3) == {-1, 8}
+    end
+
+    # @tag :pending
+    test "Raise a positive rational number to a negative integer power" do
+      assert RationalNumbers.pow_rational({3, 5}, -2) == {25, 9}
+    end
+
+    # @tag :pending
+    test "Raise a negative rational number to an even negative integer power" do
+      assert RationalNumbers.pow_rational({-3, 5}, -2) == {25, 9}
+    end
+
+    # @tag :pending
+    test "Raise a negative rational number to an odd negative integer power" do
+      assert RationalNumbers.pow_rational({-3, 5}, -3) == {-125, 27}
+    end
+
+    # @tag :pending
+    test "Raise zero to an integer power" do
+      assert RationalNumbers.pow_rational({0, 1}, 5) == {0, 1}
+    end
+
+    # @tag :pending
+    test "Raise one to an integer power" do
+      assert RationalNumbers.pow_rational({1, 1}, 4) == {1, 1}
+    end
+
+    # @tag :pending
+    test "Raise a positive rational number to the power of zero" do
+      assert RationalNumbers.pow_rational({1, 2}, 0) == {1, 1}
+    end
+
+    # @tag :pending
+    test "Raise a negative rational number to the power of zero" do
+      assert RationalNumbers.pow_rational({-1, 2}, 0) == {1, 1}
+    end
+  end
+
+  describe "Exponentiation of a real number to a rational number" do
+    # @tag :pending
+    test "Raise a real number to a positive rational number" do
+      x = 8
+      r = {4, 3}
+      result = 16.0
+      assert_in_delta RationalNumbers.pow_real(x, r), result, 1.0e-10
+    end
+
+    # @tag :pending
+    test "Raise a real number to a negative rational number" do
+      x = 9
+      r = {-1, 2}
+      result = 0.3333333333333333
+      assert_in_delta RationalNumbers.pow_real(x, r), result, 1.0e-10
+    end
+
+    # @tag :pending
+    test "Raise a real number to a zero rational number" do
+      x = 2
+      r = {0, 1}
+      result = 1.0
+      assert_in_delta RationalNumbers.pow_real(x, r), result, 1.0e-10
+    end
+  end
+
+  describe "Reduction to lowest terms" do
+    # @tag :pending
+    test "Reduce a positive rational number to lowest terms" do
+      assert RationalNumbers.reduce({2, 4}) == {1, 2}
+    end
+
+    # @tag :pending
+    test "Reduce places the minus sign on the numerator" do
+      assert RationalNumbers.reduce({3, -4}) == {-3, 4}
+    end
+
+    # @tag :pending
+    test "Reduce a negative rational number to lowest terms" do
+      assert RationalNumbers.reduce({-4, 6}) == {-2, 3}
+    end
+
+    # @tag :pending
+    test "Reduce a rational number with a negative denominator to lowest terms" do
+      assert RationalNumbers.reduce({3, -9}) == {-1, 3}
+    end
+
+    # @tag :pending
+    test "Reduce zero to lowest terms" do
+      assert RationalNumbers.reduce({0, 6}) == {0, 1}
+    end
+
+    # @tag :pending
+    test "Reduce an integer to lowest terms" do
+      assert RationalNumbers.reduce({-14, 7}) == {-2, 1}
+    end
+
+    # @tag :pending
+    test "Reduce one to lowest terms" do
+      assert RationalNumbers.reduce({13, 13}) == {1, 1}
+    end
+  end
+end
diff --git a/elixir/rational-numbers/test/test_helper.exs b/elixir/rational-numbers/test/test_helper.exs
new file mode 100644
index 0000000..35fc5bf
--- /dev/null
+++ b/elixir/rational-numbers/test/test_helper.exs
@@ -0,0 +1,2 @@
+ExUnit.start()
+ExUnit.configure(exclude: :pending, trace: true)