complex_numbers

elixir/complex-numbers/.exercism/config.json

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+{
+  "authors": [
+    "jiegillet"
+  ],
+  "files": {
+    "solution": [
+      "lib/complex_numbers.ex"
+    ],
+    "test": [
+      "test/complex_numbers_test.exs"
+    ],
+    "example": [
+      ".meta/example.ex"
+    ]
+  },
+  "blurb": "Implement complex numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Complex_number"
+}

elixir/complex-numbers/.exercism/metadata.json

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+{"track":"elixir","exercise":"complex-numbers","id":"e861817a97db485aab96fb825626df43","url":"https://exercism.org/tracks/elixir/exercises/complex-numbers","handle":"negrienko","is_requester":true,"auto_approve":false}

elixir/complex-numbers/.formatter.exs

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+# Used by "mix format"
+[
+  inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
+]

elixir/complex-numbers/.gitignore

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+# 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").
+complex_numbers-*.tar
+

elixir/complex-numbers/HELP.md

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+# 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/complex_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.

elixir/complex-numbers/README.md

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+# Complex Numbers
+
+Welcome to Complex Numbers on Exercism's Elixir Track.
+If you need help running the tests or submitting your code, check out `HELP.md`.
+
+## Instructions
+
+A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+
+`a` is called the real part and `b` is called the imaginary part of `z`.
+The conjugate of the number `a + b * i` is the number `a - b * i`.
+The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate.
+
+The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
+`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
+`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
+
+Multiplication result is by definition
+`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
+
+The reciprocal of a non-zero complex number is
+`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
+
+Dividing a complex number `a + i * b` by another `c + i * d` gives:
+`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
+
+Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`.
+
+Implement the following operations:
+
+- addition, subtraction, multiplication and division of two complex numbers,
+- conjugate, absolute value, exponent of a given complex number.
+
+Assume the programming language you are using does not have an implementation of complex numbers.
+
+In this exercise, complex numbers are represented as a tuple-pair containing the real and imaginary parts.
+
+For example, the real number `1` is `{1, 0}`, the imaginary number `i` is `{0, 1}` and the complex number `4+3i` is `{4, 3}`.
+
+## Source
+
+### Created by
+
+- @jiegillet
+
+### Based on
+
+Wikipedia - https://en.wikipedia.org/wiki/Complex_number

elixir/complex-numbers/lib/complex_numbers.ex

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

elixir/complex-numbers/mix.exs

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+defmodule ComplexNumbers.MixProject do
+  use Mix.Project
+
+  def project do
+    [
+      app: :complex_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

elixir/complex-numbers/test/complex_numbers_test.exs

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+defmodule ComplexNumbersTest do
+  use ExUnit.Case
+
+  def equal({a, b}, {c, d}) do
+    assert_in_delta a, c, 1.0e-12
+    assert_in_delta b, d, 1.0e-12
+  end
+
+  def equal(a, b) do
+    assert_in_delta a, b, 1.0e-12
+  end
+
+  describe "Real part" do
+    test "Real part of a purely real number" do
+      z = {1, 0}
+      output = ComplexNumbers.real(z)
+      expected = 1
+
+      equal(output, expected)
+    end
+
+    test "Real part of a purely imaginary number" do
+      z = {0, 1}
+      output = ComplexNumbers.real(z)
+      expected = 0
+
+      equal(output, expected)
+    end
+
+    test "Real part of a number with real and imaginary part" do
+      z = {1, 2}
+      output = ComplexNumbers.real(z)
+      expected = 1
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Imaginary part" do
+    test "Imaginary part of a purely real number" do
+      z = {1, 0}
+      output = ComplexNumbers.imaginary(z)
+      expected = 0
+
+      equal(output, expected)
+    end
+
+    test "Imaginary part of a purely imaginary number" do
+      z = {0, 1}
+      output = ComplexNumbers.imaginary(z)
+      expected = 1
+
+      equal(output, expected)
+    end
+
+    test "Imaginary part of a number with real and imaginary part" do
+      z = {1, 2}
+      output = ComplexNumbers.imaginary(z)
+      expected = 2
+
+      equal(output, expected)
+    end
+  end
+
+  test "Imaginary unit" do
+    z1 = {0, 1}
+    z2 = {0, 1}
+    output = ComplexNumbers.mul(z1, z2)
+    expected = {-1, 0}
+
+    equal(output, expected)
+  end
+
+  describe "Addition" do
+    test "Add purely real numbers" do
+      z1 = {1, 0}
+      z2 = {2, 0}
+      output = ComplexNumbers.add(z1, z2)
+      expected = {3, 0}
+
+      equal(output, expected)
+    end
+
+    test "Add purely imaginary numbers" do
+      z1 = {0, 1}
+      z2 = {0, 2}
+      output = ComplexNumbers.add(z1, z2)
+      expected = {0, 3}
+
+      equal(output, expected)
+    end
+
+    test "Add numbers with real and imaginary part" do
+      z1 = {1, 2}
+      z2 = {3, 4}
+      output = ComplexNumbers.add(z1, z2)
+      expected = {4, 6}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Subtraction" do
+    test "Subtract purely real numbers" do
+      z1 = {1, 0}
+      z2 = {2, 0}
+      output = ComplexNumbers.sub(z1, z2)
+      expected = {-1, 0}
+
+      equal(output, expected)
+    end
+
+    test "Subtract purely imaginary numbers" do
+      z1 = {0, 1}
+      z2 = {0, 2}
+      output = ComplexNumbers.sub(z1, z2)
+      expected = {0, -1}
+
+      equal(output, expected)
+    end
+
+    test "Subtract numbers with real and imaginary part" do
+      z1 = {1, 2}
+      z2 = {3, 4}
+      output = ComplexNumbers.sub(z1, z2)
+      expected = {-2, -2}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Multiplication" do
+    test "Multiply purely real numbers" do
+      z1 = {1, 0}
+      z2 = {2, 0}
+      output = ComplexNumbers.mul(z1, z2)
+      expected = {2, 0}
+
+      equal(output, expected)
+    end
+
+    test "Multiply purely imaginary numbers" do
+      z1 = {0, 1}
+      z2 = {0, 2}
+      output = ComplexNumbers.mul(z1, z2)
+      expected = {-2, 0}
+
+      equal(output, expected)
+    end
+
+    test "Multiply numbers with real and imaginary part" do
+      z1 = {1, 2}
+      z2 = {3, 4}
+      output = ComplexNumbers.mul(z1, z2)
+      expected = {-5, 10}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Division" do
+    test "Divide purely real numbers" do
+      z1 = {1, 0}
+      z2 = {2, 0}
+      output = ComplexNumbers.div(z1, z2)
+      expected = {0.5, 0}
+
+      equal(output, expected)
+    end
+
+    test "Divide purely imaginary numbers" do
+      z1 = {0, 1}
+      z2 = {0, 2}
+      output = ComplexNumbers.div(z1, z2)
+      expected = {0.5, 0}
+
+      equal(output, expected)
+    end
+
+    test "Divide numbers with real and imaginary part" do
+      z1 = {1, 2}
+      z2 = {3, 4}
+      output = ComplexNumbers.div(z1, z2)
+      expected = {0.44, 0.08}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Absolute value" do
+    test "Absolute value of a positive purely real number" do
+      z = {5, 0}
+      output = ComplexNumbers.abs(z)
+      expected = 5
+
+      equal(output, expected)
+    end
+
+    test "Absolute value of a negative purely real number" do
+      z = {-5, 0}
+      output = ComplexNumbers.abs(z)
+      expected = 5
+
+      equal(output, expected)
+    end
+
+    test "Absolute value of a purely imaginary number with positive imaginary part" do
+      z = {0, 5}
+      output = ComplexNumbers.abs(z)
+      expected = 5
+
+      equal(output, expected)
+    end
+
+    test "Absolute value of a purely imaginary number with negative imaginary part" do
+      z = {0, -5}
+      output = ComplexNumbers.abs(z)
+      expected = 5
+
+      equal(output, expected)
+    end
+
+    test "Absolute value of a number with real and imaginary part" do
+      z = {3, 4}
+      output = ComplexNumbers.abs(z)
+      expected = 5
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Complex conjugate" do
+    test "Conjugate a purely real number" do
+      z = {5, 0}
+      output = ComplexNumbers.conjugate(z)
+      expected = {5, 0}
+
+      equal(output, expected)
+    end
+
+    test "Conjugate a purely imaginary number" do
+      z = {0, 5}
+      output = ComplexNumbers.conjugate(z)
+      expected = {0, -5}
+
+      equal(output, expected)
+    end
+
+    test "Conjugate a number with real and imaginary part" do
+      z = {1, 1}
+      output = ComplexNumbers.conjugate(z)
+      expected = {1, -1}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Complex exponential function" do
+    test "Euler's identity/formula" do
+      z = {0, :math.pi()}
+      output = ComplexNumbers.exp(z)
+      expected = {-1, 0}
+
+      equal(output, expected)
+    end
+
+    test "Exponential of 0" do
+      z = {0, 0}
+      output = ComplexNumbers.exp(z)
+      expected = {1, 0}
+
+      equal(output, expected)
+    end
+
+    test "Exponential of a purely real number" do
+      z = {1, 0}
+      output = ComplexNumbers.exp(z)
+      expected = {:math.exp(1), 0}
+
+      equal(output, expected)
+    end
+
+    test "Exponential of a number with real and imaginary part" do
+      z = {:math.log(2), :math.pi()}
+      output = ComplexNumbers.exp(z)
+      expected = {-2, 0}
+
+      equal(output, expected)
+    end
+
+    test "Exponential resulting in a number with real and imaginary part" do
+      z = {:math.log(2) / 2, :math.pi() / 4}
+      output = ComplexNumbers.exp(z)
+      expected = {1, 1}
+
+      equal(output, expected)
+    end
+  end
+
+  describe "Operations between real numbers and complex numbers" do
+    test "Add real number to complex number" do
+      z = {1, 2}
+      r = 5
+      output = ComplexNumbers.add(z, r)
+      expected = {6, 2}
+
+      equal(output, expected)
+    end
+
+    test "Add complex number to real number" do
+      r = 5
+      z = {1, 2}
+      output = ComplexNumbers.add(r, z)
+      expected = {6, 2}
+
+      equal(output, expected)
+    end
+
+    test "Subtract real number from complex number" do
+      z = {5, 7}
+      r = 4
+      output = ComplexNumbers.sub(z, r)
+      expected = {1, 7}
+
+      equal(output, expected)
+    end
+
+    test "Subtract complex number from real number" do
+      r = 4
+      z = {5, 7}
+      output = ComplexNumbers.sub(r, z)
+      expected = {-1, -7}
+
+      equal(output, expected)
+    end
+
+    test "Multiply complex number by real number" do
+      z = {2, 5}
+      r = 5
+      output = ComplexNumbers.mul(z, r)
+      expected = {10, 25}
+
+      equal(output, expected)
+    end
+
+    test "Multiply real number by complex number" do
+      r = 5
+      z = {2, 5}
+      output = ComplexNumbers.mul(r, z)
+      expected = {10, 25}
+
+      equal(output, expected)
+    end
+
+    test "Divide complex number by real number" do
+      z = {10, 100}
+      r = 10
+      output = ComplexNumbers.div(z, r)
+      expected = {1, 10}
+
+      equal(output, expected)
+    end
+
+    test "Divide real number by complex number" do
+      r = 5
+      z = {1, 1}
+      output = ComplexNumbers.div(r, z)
+      expected = {2.5, -2.5}
+
+      equal(output, expected)
+    end
+  end
+end

elixir/complex-numbers/test/test_helper.exs

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+ExUnit.start()
+ExUnit.configure(exclude: :pending, trace: true)