Added Rational Numbers exercise (#1193)

* Added Rational Numbers exercise

* Incorporated review comments from #1193

config.json

@@ -1109,6 +1109,19 @@
           "number_theory"
         ]
       },
+      {
+        "slug": "rational-numbers",
+        "name": "Rational Numbers",
+        "uuid": "b4426fe9-2e49-48c5-9dea-c86032009687",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 3,
+        "topics": [
+          "define_type",
+          "math",
+          "number_theory"
+        ]
+      },
       {
         "slug": "largest-series-product",
         "name": "Largest Series Product",

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

@@ -0,0 +1,42 @@
+# 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.

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

@@ -0,0 +1,23 @@
+{
+  "authors": [
+    "tofische"
+  ],
+  "files": {
+    "solution": [
+      "src/RationalNumbers.hs",
+      "package.yaml"
+    ],
+    "test": [
+      "test/Tests.hs"
+    ],
+    "example": [
+      ".meta/examples/success-standard/src/RationalNumbers.hs"
+    ],
+    "invalidator": [
+      "stack.yaml"
+    ]
+  },
+  "blurb": "Implement rational numbers.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Rational_number"
+}

exercises/practice/rational-numbers/.meta/examples/success-standard/package.yaml

@@ -0,0 +1,16 @@
+name: rational-numbers
+
+dependencies:
+  - base
+
+library:
+  exposed-modules: RationalNumbers
+  source-dirs: src
+
+tests:
+  test:
+    main: Tests.hs
+    source-dirs: test
+    dependencies:
+      - rational-numbers
+      - hspec

exercises/practice/rational-numbers/.meta/examples/success-standard/src/RationalNumbers.hs

@@ -0,0 +1,57 @@
+module RationalNumbers
+(Rational,
+ abs,
+ numerator,
+ denominator,
+ add,
+ sub,
+ mul,
+ div,
+ pow,
+ expRational,
+ expReal,
+ rational) where
+
+import Prelude hiding (div, abs, Rational)
+import qualified Prelude as P
+
+-- Data definition -------------------------------------------------------------
+data Rational a = Rational a a deriving(Eq, Show)
+
+rational :: Integral a => (a, a) -> Rational a
+rational (n, d) = Rational (n' `quot` g) (d' `quot` g)
+    where
+        g = gcd n d
+        (n', d') = if d < 0 then (-n, -d) else (n, d)
+
+-- unary operators -------------------------------------------------------------
+abs :: Integral a => Rational a -> Rational a
+abs (Rational n d) = rational (P.abs n, P.abs d)
+
+numerator :: Integral a => Rational a -> a
+numerator (Rational n _) = n
+
+denominator :: Integral a => Rational a -> a
+denominator (Rational _ d) = d
+
+-- binary operators ------------------------------------------------------------
+add :: Integral a => Rational a -> Rational a -> Rational a
+add (Rational n1 d1) (Rational n2 d2) = let dd = d1*d2 in rational (n1*d2 + n2*d1, dd)
+
+sub :: Integral a => Rational a -> Rational a -> Rational a
+sub (Rational n1 d1) (Rational n2 d2) = let dd = d1*d2 in rational (n1*d2 - n2*d1, dd)
+
+mul :: Integral a => Rational a -> Rational a -> Rational a
+mul (Rational n1 d1) (Rational n2 d2) = rational (n1*n2, d1*d2)
+
+div :: Integral a => Rational a -> Rational a -> Rational a
+div (Rational n1 d1) (Rational n2 d2) = rational (n1*d2, d1*n2)
+
+pow :: Integral a => Rational a -> a -> Rational a
+pow (Rational n d) num = if num >= 0 then rational (n^num, d^num) else rational (d^(-num), n^(-num))
+
+expRational :: Integral a => Floating b => Rational a -> b -> b
+expRational (Rational n d) num = (fromIntegral n / fromIntegral d) ** num
+
+expReal :: Floating a => Integral b => a -> Rational b -> a
+expReal num (Rational n d) = num ** (fromIntegral n / fromIntegral d)

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

@@ -0,0 +1,139 @@
+# 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.
+
+[0ba4d988-044c-4ed5-9215-4d0bb8d0ae9f]
+description = "Arithmetic -> Addition -> Add two positive rational numbers"
+
+[88ebc342-a2ac-4812-a656-7b664f718b6a]
+description = "Arithmetic -> Addition -> Add a positive rational number and a negative rational number"
+
+[92ed09c2-991e-4082-a602-13557080205c]
+description = "Arithmetic -> Addition -> Add two negative rational numbers"
+
+[6e58999e-3350-45fb-a104-aac7f4a9dd11]
+description = "Arithmetic -> Addition -> Add a rational number to its additive inverse"
+
+[47bba350-9db1-4ab9-b412-4a7e1f72a66e]
+description = "Arithmetic -> Subtraction -> Subtract two positive rational numbers"
+
+[93926e2a-3e82-4aee-98a7-fc33fb328e87]
+description = "Arithmetic -> Subtraction -> Subtract a positive rational number and a negative rational number"
+
+[a965ba45-9b26-442b-bdc7-7728e4b8d4cc]
+description = "Arithmetic -> Subtraction -> Subtract two negative rational numbers"
+
+[0df0e003-f68e-4209-8c6e-6a4e76af5058]
+description = "Arithmetic -> Subtraction -> Subtract a rational number from itself"
+
+[34fde77a-75f4-4204-8050-8d3a937958d3]
+description = "Arithmetic -> Multiplication -> Multiply two positive rational numbers"
+
+[6d015cf0-0ea3-41f1-93de-0b8e38e88bae]
+description = "Arithmetic -> Multiplication -> Multiply a negative rational number by a positive rational number"
+
+[d1bf1b55-954e-41b1-8c92-9fc6beeb76fa]
+description = "Arithmetic -> Multiplication -> Multiply two negative rational numbers"
+
+[a9b8f529-9ec7-4c79-a517-19365d779040]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by its reciprocal"
+
+[d89d6429-22fa-4368-ab04-9e01a44d3b48]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by 1"
+
+[0d95c8b9-1482-4ed7-bac9-b8694fa90145]
+description = "Arithmetic -> Multiplication -> Multiply a rational number by 0"
+
+[1de088f4-64be-4e6e-93fd-5997ae7c9798]
+description = "Arithmetic -> Division -> Divide two positive rational numbers"
+
+[7d7983db-652a-4e66-981a-e921fb38d9a9]
+description = "Arithmetic -> Division -> Divide a positive rational number by a negative rational number"
+
+[1b434d1b-5b38-4cee-aaf5-b9495c399e34]
+description = "Arithmetic -> Division -> Divide two negative rational numbers"
+
+[d81c2ebf-3612-45a6-b4e0-f0d47812bd59]
+description = "Arithmetic -> Division -> Divide a rational number by 1"
+
+[5fee0d8e-5955-4324-acbe-54cdca94ddaa]
+description = "Absolute value -> Absolute value of a positive rational number"
+
+[3cb570b6-c36a-4963-a380-c0834321bcaa]
+description = "Absolute value -> Absolute value of a positive rational number with negative numerator and denominator"
+
+[6a05f9a0-1f6b-470b-8ff7-41af81773f25]
+description = "Absolute value -> Absolute value of a negative rational number"
+
+[5d0f2336-3694-464f-8df9-f5852fda99dd]
+description = "Absolute value -> Absolute value of a negative rational number with negative denominator"
+
+[f8e1ed4b-9dca-47fb-a01e-5311457b3118]
+description = "Absolute value -> Absolute value of zero"
+
+[4a8c939f-f958-473b-9f88-6ad0f83bb4c4]
+description = "Absolute value -> Absolute value of a rational number is reduced to lowest terms"
+
+[ea2ad2af-3dab-41e7-bb9f-bd6819668a84]
+description = "Exponentiation of a rational number -> Raise a positive rational number to a positive integer power"
+
+[8168edd2-0af3-45b1-b03f-72c01332e10a]
+description = "Exponentiation of a rational number -> Raise a negative rational number to a positive integer power"
+
+[c291cfae-cfd8-44f5-aa6c-b175c148a492]
+description = "Exponentiation of a rational number -> Raise a positive rational number to a negative integer power"
+
+[45cb3288-4ae4-4465-9ae5-c129de4fac8e]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an even negative integer power"
+
+[2d47f945-ffe1-4916-a399-c2e8c27d7f72]
+description = "Exponentiation of a rational number -> Raise a negative rational number to an odd negative integer power"
+
+[e2f25b1d-e4de-4102-abc3-c2bb7c4591e4]
+description = "Exponentiation of a rational number -> Raise zero to an integer power"
+
+[431cac50-ab8b-4d58-8e73-319d5404b762]
+description = "Exponentiation of a rational number -> Raise one to an integer power"
+
+[7d164739-d68a-4a9c-b99f-dd77ce5d55e6]
+description = "Exponentiation of a rational number -> Raise a positive rational number to the power of zero"
+
+[eb6bd5f5-f880-4bcd-8103-e736cb6e41d1]
+description = "Exponentiation of a rational number -> Raise a negative rational number to the power of zero"
+
+[30b467dd-c158-46f5-9ffb-c106de2fd6fa]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a positive rational number"
+
+[6e026bcc-be40-4b7b-ae22-eeaafc5a1789]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a negative rational number"
+
+[9f866da7-e893-407f-8cd2-ee85d496eec5]
+description = "Exponentiation of a real number to a rational number -> Raise a real number to a zero rational number"
+
+[0a63fbde-b59c-4c26-8237-1e0c73354d0a]
+description = "Reduction to lowest terms -> Reduce a positive rational number to lowest terms"
+
+[5ed6f248-ad8d-4d4e-a545-9146c6727f33]
+description = "Reduction to lowest terms -> Reduce places the minus sign on the numerator"
+
+[f87c2a4e-d29c-496e-a193-318c503e4402]
+description = "Reduction to lowest terms -> Reduce a negative rational number to lowest terms"
+
+[3b92ffc0-5b70-4a43-8885-8acee79cdaaf]
+description = "Reduction to lowest terms -> Reduce a rational number with a negative denominator to lowest terms"
+
+[c9dbd2e6-5ac0-4a41-84c1-48b645b4f663]
+description = "Reduction to lowest terms -> Reduce zero to lowest terms"
+
+[297b45ad-2054-4874-84d4-0358dc1b8887]
+description = "Reduction to lowest terms -> Reduce an integer to lowest terms"
+
+[a73a17fe-fe8c-4a1c-a63b-e7579e333d9e]
+description = "Reduction to lowest terms -> Reduce one to lowest terms"

exercises/practice/rational-numbers/package.yaml

@@ -0,0 +1,21 @@
+name: rational-numbers
+version: 1.0.0.0
+
+dependencies:
+  - base
+
+library:
+  exposed-modules: RationalNumbers
+  source-dirs: src
+  ghc-options: -Wall
+  # dependencies:
+  # - foo       # List here the packages you
+  # - bar       # want to use in your solution.
+
+tests:
+  test:
+    main: Tests.hs
+    source-dirs: test
+    dependencies:
+      - rational-numbers
+      - hspec

exercises/practice/rational-numbers/src/RationalNumbers.hs

@@ -0,0 +1,53 @@
+module RationalNumbers
+(Rational,
+ abs,
+ numerator,
+ denominator,
+ add,
+ sub,
+ mul,
+ div,
+ pow,
+ expRational,
+ expReal,
+ rational) where
+
+import Prelude hiding (div, abs, Rational)
+
+-- Data definition -------------------------------------------------------------
+data Rational a = Dummy deriving(Eq, Show)
+
+rational :: Integral a => (a, a) -> Rational a
+rational = error "You need to implement this function"
+
+-- unary operators -------------------------------------------------------------
+abs :: Integral a => Rational a -> Rational a
+abs = error "You need to implement this function"
+
+numerator :: Integral a => Rational a -> a
+numerator = error "You need to implement this function"
+
+denominator :: Integral a => Rational a -> a
+denominator = error "You need to implement this function"
+
+-- binary operators ------------------------------------------------------------
+add :: Integral a => Rational a -> Rational a -> Rational a
+add = error "You need to implement this function"
+
+sub :: Integral a => Rational a -> Rational a -> Rational a
+sub = error "You need to implement this function"
+
+mul :: Integral a => Rational a -> Rational a -> Rational a
+mul = error "You need to implement this function"
+
+div :: Integral a => Rational a -> Rational a -> Rational a
+div = error "You need to implement this function"
+
+pow :: Integral a => Rational a -> a -> Rational a
+pow = error "You need to implement this function"
+
+expRational :: Integral a => Floating b => Rational a -> b -> b
+expRational = error "You need to implement this function"
+
+expReal :: Floating a => Integral b => a -> Rational b -> a
+expReal = error "You need to implement this function"

exercises/practice/rational-numbers/stack.yaml

@@ -0,0 +1 @@
+resolver: lts-20.18