New practice exercise: complex-numbers

config.json

@@ -847,6 +847,20 @@
           "result",
           "pattern-matching"
         ]
+      },
+      {
+        "slug": "complex-numbers",
+        "name": "Complex Numbers",
+        "uuid": "e982e16c-810c-477c-a478-7abf64e6132f",
+        "practices": [
+          "custom-types"
+        ],
+        "prerequisites": [
+          "basics-1",
+          "basics-2",
+          "custom-types"
+        ],
+        "difficulty": 4
       }
     ]
   }

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

@@ -0,0 +1,29 @@
+# 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.

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

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "jiegillet"
+  ],
+  "files": {
+    "solution": [
+      "src/ComplexNumbers.elm"
+    ],
+    "test": [
+      "tests/Tests.elm"
+    ],
+    "example": [
+      ".meta/src/ComplexNumbers.example.elm"
+    ]
+  },
+  "blurb": "Implement complex numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Complex_number"
+}

exercises/practice/complex-numbers/.meta/src/ComplexNumbers.example.elm

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+module ComplexNumbers exposing
+    ( Complex
+    , abs
+    , add
+    , conjugate
+    , div
+    , exp
+    , fromPair
+    , fromReal
+    , imaginary
+    , mul
+    , real
+    , sub
+    )
+
+
+type Complex
+    = Complex Float Float
+
+
+fromPair : ( Float, Float ) -> Complex
+fromPair ( re, im ) =
+    Complex re im
+
+
+fromReal : Float -> Complex
+fromReal re =
+    Complex re 0
+
+
+real : Complex -> Float
+real (Complex re _) =
+    re
+
+
+imaginary : Complex -> Float
+imaginary (Complex _ im) =
+    im
+
+
+conjugate : Complex -> Complex
+conjugate (Complex re im) =
+    Complex re -im
+
+
+abs : Complex -> Float
+abs (Complex re im) =
+    sqrt (re ^ 2 + im ^ 2)
+
+
+add : Complex -> Complex -> Complex
+add (Complex re1 im1) (Complex re2 im2) =
+    Complex (re1 + re2) (im1 + im2)
+
+
+sub : Complex -> Complex -> Complex
+sub (Complex re1 im1) (Complex re2 im2) =
+    Complex (re1 - re2) (im1 - im2)
+
+
+mul : Complex -> Complex -> Complex
+mul (Complex re1 im1) (Complex re2 im2) =
+    Complex (re1 * re2 - im1 * im2)
+        (im1 * re2 + re1 * im2)
+
+
+div : Complex -> Complex -> Complex
+div (Complex re1 im1) (Complex re2 im2) =
+    Complex ((re1 * re2 + im1 * im2) / (re2 ^ 2 + im2 ^ 2))
+        ((im1 * re2 - re1 * im2) / (re2 ^ 2 + im2 ^ 2))
+
+
+exp : Complex -> Complex
+exp (Complex re im) =
+    Complex (e ^ re * cos im) (e ^ re * sin im)

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

@@ -0,0 +1,127 @@
+# 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"
+
+[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"

exercises/practice/complex-numbers/elm.json

@@ -0,0 +1,28 @@
+{
+    "type": "application",
+    "source-directories": [
+        "src"
+    ],
+    "elm-version": "0.19.1",
+    "dependencies": {
+        "direct": {
+            "elm/core": "1.0.5",
+            "elm/json": "1.1.3",
+            "elm/parser": "1.1.0",
+            "elm/random": "1.0.0",
+            "elm/regex": "1.0.0",
+            "elm/time": "1.0.0"
+        },
+        "indirect": {}
+    },
+    "test-dependencies": {
+        "direct": {
+            "elm-explorations/test": "1.2.2",
+            "rtfeldman/elm-iso8601-date-strings": "1.1.3"
+        },
+        "indirect": {
+            "elm/html": "1.0.0",
+            "elm/virtual-dom": "1.0.2"
+        }
+    }
+}

exercises/practice/complex-numbers/src/ComplexNumbers.elm

@@ -0,0 +1,73 @@
+module ComplexNumbers exposing
+    ( Complex
+    , abs
+    , add
+    , conjugate
+    , div
+    , exp
+    , fromPair
+    , fromReal
+    , imaginary
+    , mul
+    , real
+    , sub
+    )
+
+
+type Complex
+    = Todo
+
+
+fromPair : ( Float, Float ) -> Complex
+fromPair pair =
+    Debug.todo "Please implement fromPair."
+
+
+fromReal : Float -> Complex
+fromReal real =
+    Debug.todo "Please implement fromReal."
+
+
+real : Complex -> Float
+real z =
+    Debug.todo "Please implement real."
+
+
+imaginary : Complex -> Float
+imaginary z =
+    Debug.todo "Please implement imaginary."
+
+
+conjugate : Complex -> Complex
+conjugate z =
+    Debug.todo "Please implement conjugate."
+
+
+abs : Complex -> Float
+abs z =
+    Debug.todo "Please implement abs."
+
+
+add : Complex -> Complex -> Complex
+add z1 z2 =
+    Debug.todo "Please implement add."
+
+
+sub : Complex -> Complex -> Complex
+sub z1 z2 =
+    Debug.todo "Please implement sub."
+
+
+mul : Complex -> Complex -> Complex
+mul z1 z2 =
+    Debug.todo "Please implement mul."
+
+
+div : Complex -> Complex -> Complex
+div z1 z2 =
+    Debug.todo "Please implement div."
+
+
+exp : Complex -> Complex
+exp z =
+    Debug.todo "Please implement exp."