complex-numbers (#61)

Author: glennj

config.json

@@ -470,6 +470,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 6
+      },
+      {
+        "slug": "complex-numbers",
+        "name": "Complex Numbers",
+        "uuid": "29567d07-2cf5-444b-aa82-5cbd6a9820d0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
       }
     ]
   },

exercises/practice/complex-numbers/.busted

@@ -0,0 +1,5 @@
+return {
+  default = {
+    ROOT = { '.' }
+  }
+}

exercises/practice/complex-numbers/.docs/instructions.append.md

@@ -0,0 +1,17 @@
+# dummy
+
+## MoonScript-specific instructions
+
+This is an object-oriented exercise: you're implementing ComplexNumbers as a class.
+
+The tests will be comparing two complex number instances for equality.
+This means your class will have to implement the `__eq` [metamethod][metamethods].
+
+The tests also perform arithmetic operations on complex numbers, so there are arithmetic metamethods to implement.
+
+~~~~exercism/caution
+Some of the complex number functions will be doing math with floating point numbers.
+Your "equality" will have to deal with numbers being _approximately equal_.
+~~~~
+
+[metamethods]: https://www.lua.org/manual/5.4/manual.html#2.4

exercises/practice/complex-numbers/.docs/instructions.md

@@ -0,0 +1,100 @@
+# Instructions
+
+A **complex number** is expressed in the form `z = a + b * i`, where:
+
+- `a` is the **real part** (a real number),
+
+- `b` is the **imaginary part** (also a real number), and
+
+- `i` is the **imaginary unit** satisfying `i^2 = -1`.
+
+## Operations on Complex Numbers
+
+### Conjugate
+
+The conjugate of the complex number `z = a + b * i` is given by:
+
+```text
+zc = a - b * i
+```
+
+### Absolute Value
+
+The absolute value (or modulus) of `z` is defined as:
+
+```text
+|z| = sqrt(a^2 + b^2)
+```
+
+The square of the absolute value is computed as the product of `z` and its conjugate `zc`:
+
+```text
+|z|^2 = z * zc = a^2 + b^2
+```
+
+### Addition
+
+The sum of two complex numbers `z1 = a + b * i` and `z2 = c + d * i` is computed by adding their real and imaginary parts separately:
+
+```text
+z1 + z2 = (a + b * i) + (c + d * i)
+        = (a + c) + (b + d) * i
+```
+
+### Subtraction
+
+The difference of two complex numbers is obtained by subtracting their respective parts:
+
+```text
+z1 - z2 = (a + b * i) - (c + d * i)
+        = (a - c) + (b - d) * i
+```
+
+### Multiplication
+
+The product of two complex numbers is defined as:
+
+```text
+z1 * z2 = (a + b * i) * (c + d * i)
+        = (a * c - b * d) + (b * c + a * d) * i
+```
+
+### Reciprocal
+
+The reciprocal of a non-zero complex number is given by:
+
+```text
+1 / z = 1 / (a + b * i)
+      = a / (a^2 + b^2) - b / (a^2 + b^2) * i
+```
+
+### Division
+
+The division of one complex number by another is given by:
+
+```text
+z1 / z2 = z1 * (1 / z2)
+        = (a + b * i) / (c + d * i)
+        = (a * c + b * d) / (c^2 + d^2) + (b * c - a * d) / (c^2 + d^2) * i
+```
+
+### Exponentiation
+
+Raising _e_ (the base of the natural logarithm) to a complex exponent can be expressed using Euler's formula:
+
+```text
+e^(a + b * i) = e^a * e^(b * i)
+              = e^a * (cos(b) + i * sin(b))
+```
+
+## Implementation Requirements
+
+Given that you should not use built-in support for complex numbers, implement the following operations:
+
+- **addition** of two complex numbers
+- **subtraction** of two complex numbers
+- **multiplication** of two complex numbers
+- **division** of two complex numbers
+- **conjugate** of a complex number
+- **absolute value** of a complex number
+- **exponentiation** of _e_ (the base of the natural logarithm) to a complex number

exercises/practice/complex-numbers/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glennj"
+  ],
+  "files": {
+    "solution": [
+      "complex_numbers.moon"
+    ],
+    "test": [
+      "complex_numbers_spec.moon"
+    ],
+    "example": [
+      ".meta/example.moon"
+    ]
+  },
+  "blurb": "Implement complex numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Complex_number"
+}

exercises/practice/complex-numbers/.meta/example.moon

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+class ComplexNumber
+  new: (@r, @i = 0) =>
+
+  real: => @r
+  imaginary: => @i
+
+  conjugate: => @@ @r, -@i
+
+  abs: => math.sqrt(@r^2 + @i^2)
+
+  __add: (other) =>
+    @@ (@r + other.r), (@i + other.i)
+
+  __sub: (other) =>
+    @@ (@r - other.r), (@i - other.i)
+
+  __mul: (other) =>
+    a = @r * other.r - @i * other.i
+    b = @i * other.r + @r * other.i
+    @@ a, b
+
+  reciprocal: =>
+    denom = @r^2 + @i^2
+    @@ @r / denom, -@i / denom
+
+  __div: (other) => self * other\reciprocal!
+
+  exp: =>
+    factor = math.exp(@r)
+    @@ factor * math.cos(@i), factor * math.sin(@i)
+
+  __eq: (other) =>
+    approx_equal = (a, b) -> math.abs(a - b) <= 1e-15
+    approx_equal(@r, other.r) and approx_equal(@i, other.i)
+
+
+tocomplex = (a) -> if type(a) == 'number' then ComplexNumber a else a
+
+add = (a, b) -> tocomplex(a) + tocomplex(b)
+sub = (a, b) -> tocomplex(a) - tocomplex(b)
+mul = (a, b) -> tocomplex(a) * tocomplex(b)
+div = (a, b) -> tocomplex(a) / tocomplex(b)
+
+{ :ComplexNumber, :add, :sub, :mul, :div }

exercises/practice/complex-numbers/.meta/spec_generator.moon

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+op = add: '+', sub: '-', mul: '*', div: '/'
+
+cn = (z) ->
+  switch type(z)
+    when 'number' then z
+    when 'table'  then "ComplexNumber(#{z[1]}, #{z[2]})"
+
+
+require 'moon.all'
+{
+  module_imports: {'ComplexNumber', 'add', 'sub', 'mul', 'div'},
+
+  test_helpers: [[
+  pi = math.pi
+  e  = math.exp(1)
+  ln = math.log
+]]
+
+  generate_test: (case, level) ->
+    local lines
+    switch case.property
+      when 'real', 'imaginary', 'abs'
+        lines = {
+          "c = #{cn case.input.z}",
+          "result = c\\#{case.property}!",
+          "assert.are.equal #{case.expected}, result"
+        }
+      when 'add', 'sub', 'mul', 'div'
+        if type(case.input.z1) == 'number' or type(case.input.z2) == 'number'
+          lines = {
+            "result = #{case.property} #{cn case.input.z1}, #{cn case.input.z2}",
+            "expected = #{cn case.expected}",
+            "assert.are.equal expected, result"
+          }
+        else
+          lines = {
+            "c1 = #{cn case.input.z1}",
+            "c2 = #{cn case.input.z2}",
+            "result = c1 #{op[case.property]} c2",
+            "expected = #{cn case.expected}",
+            "assert.are.equal expected, result"
+          }
+      when 'conjugate', 'exp'
+        lines = {
+          "c = #{cn case.input.z}",
+          "result = c\\#{case.property}!",
+          "expected = #{cn case.expected}",
+          "assert.are.equal expected, result"
+        }
+
+    table.concat [indent line, level for line in *lines], '\n'
+}

exercises/practice/complex-numbers/.meta/tests.toml

@@ -0,0 +1,130 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[9f98e133-eb7f-45b0-9676-cce001cd6f7a]
+description = "Real part -> Real part of a purely real number"
+
+[07988e20-f287-4bb7-90cf-b32c4bffe0f3]
+description = "Real part -> Real part of a purely imaginary number"
+
+[4a370e86-939e-43de-a895-a00ca32da60a]
+description = "Real part -> Real part of a number with real and imaginary part"
+
+[9b3fddef-4c12-4a99-b8f8-e3a42c7ccef6]
+description = "Imaginary part -> Imaginary part of a purely real number"
+
+[a8dafedd-535a-4ed3-8a39-fda103a2b01e]
+description = "Imaginary part -> Imaginary part of a purely imaginary number"
+
+[0f998f19-69ee-4c64-80ef-01b086feab80]
+description = "Imaginary part -> Imaginary part of a number with real and imaginary part"
+
+[a39b7fd6-6527-492f-8c34-609d2c913879]
+description = "Imaginary unit"
+
+[9a2c8de9-f068-4f6f-b41c-82232cc6c33e]
+description = "Arithmetic -> Addition -> Add purely real numbers"
+
+[657c55e1-b14b-4ba7-bd5c-19db22b7d659]
+description = "Arithmetic -> Addition -> Add purely imaginary numbers"
+
+[4e1395f5-572b-4ce8-bfa9-9a63056888da]
+description = "Arithmetic -> Addition -> Add numbers with real and imaginary part"
+
+[1155dc45-e4f7-44b8-af34-a91aa431475d]
+description = "Arithmetic -> Subtraction -> Subtract purely real numbers"
+
+[f95e9da8-acd5-4da4-ac7c-c861b02f774b]
+description = "Arithmetic -> Subtraction -> Subtract purely imaginary numbers"
+
+[f876feb1-f9d1-4d34-b067-b599a8746400]
+description = "Arithmetic -> Subtraction -> Subtract numbers with real and imaginary part"
+
+[8a0366c0-9e16-431f-9fd7-40ac46ff4ec4]
+description = "Arithmetic -> Multiplication -> Multiply purely real numbers"
+
+[e560ed2b-0b80-4b4f-90f2-63cefc911aaf]
+description = "Arithmetic -> Multiplication -> Multiply purely imaginary numbers"
+
+[4d1d10f0-f8d4-48a0-b1d0-f284ada567e6]
+description = "Arithmetic -> Multiplication -> Multiply numbers with real and imaginary part"
+
+[b0571ddb-9045-412b-9c15-cd1d816d36c1]
+description = "Arithmetic -> Division -> Divide purely real numbers"
+
+[5bb4c7e4-9934-4237-93cc-5780764fdbdd]
+description = "Arithmetic -> Division -> Divide purely imaginary numbers"
+
+[c4e7fef5-64ac-4537-91c2-c6529707701f]
+description = "Arithmetic -> Division -> Divide numbers with real and imaginary part"
+
+[c56a7332-aad2-4437-83a0-b3580ecee843]
+description = "Absolute value -> Absolute value of a positive purely real number"
+
+[cf88d7d3-ee74-4f4e-8a88-a1b0090ecb0c]
+description = "Absolute value -> Absolute value of a negative purely real number"
+
+[bbe26568-86c1-4bb4-ba7a-da5697e2b994]
+description = "Absolute value -> Absolute value of a purely imaginary number with positive imaginary part"
+
+[3b48233d-468e-4276-9f59-70f4ca1f26f3]
+description = "Absolute value -> Absolute value of a purely imaginary number with negative imaginary part"
+
+[fe400a9f-aa22-4b49-af92-51e0f5a2a6d3]
+description = "Absolute value -> Absolute value of a number with real and imaginary part"
+
+[fb2d0792-e55a-4484-9443-df1eddfc84a2]
+description = "Complex conjugate -> Conjugate a purely real number"
+
+[e37fe7ac-a968-4694-a460-66cb605f8691]
+description = "Complex conjugate -> Conjugate a purely imaginary number"
+
+[f7704498-d0be-4192-aaf5-a1f3a7f43e68]
+description = "Complex conjugate -> Conjugate a number with real and imaginary part"
+
+[6d96d4c6-2edb-445b-94a2-7de6d4caaf60]
+description = "Complex exponential function -> Euler's identity/formula"
+
+[2d2c05a0-4038-4427-a24d-72f6624aa45f]
+description = "Complex exponential function -> Exponential of 0"
+
+[ed87f1bd-b187-45d6-8ece-7e331232c809]
+description = "Complex exponential function -> Exponential of a purely real number"
+
+[08eedacc-5a95-44fc-8789-1547b27a8702]
+description = "Complex exponential function -> Exponential of a number with real and imaginary part"
+
+[d2de4375-7537-479a-aa0e-d474f4f09859]
+description = "Complex exponential function -> Exponential resulting in a number with real and imaginary part"
+
+[06d793bf-73bd-4b02-b015-3030b2c952ec]
+description = "Operations between real numbers and complex numbers -> Add real number to complex number"
+
+[d77dbbdf-b8df-43f6-a58d-3acb96765328]
+description = "Operations between real numbers and complex numbers -> Add complex number to real number"
+
+[20432c8e-8960-4c40-ba83-c9d910ff0a0f]
+description = "Operations between real numbers and complex numbers -> Subtract real number from complex number"
+
+[b4b38c85-e1bf-437d-b04d-49bba6e55000]
+description = "Operations between real numbers and complex numbers -> Subtract complex number from real number"
+
+[dabe1c8c-b8f4-44dd-879d-37d77c4d06bd]
+description = "Operations between real numbers and complex numbers -> Multiply complex number by real number"
+
+[6c81b8c8-9851-46f0-9de5-d96d314c3a28]
+description = "Operations between real numbers and complex numbers -> Multiply real number by complex number"
+
+[8a400f75-710e-4d0c-bcb4-5e5a00c78aa0]
+description = "Operations between real numbers and complex numbers -> Divide complex number by real number"
+
+[9a867d1b-d736-4c41-a41e-90bd148e9d5e]
+description = "Operations between real numbers and complex numbers -> Divide real number by complex number"