diff --git a/config.json b/config.json index d5a7e2f94..eb3849c4e 100644 --- a/config.json +++ b/config.json @@ -1234,6 +1234,25 @@ ], "difficulty": 8 }, + { + "slug": "rational-numbers", + "name": "Rational Numbers", + "uuid": "52563082-7349-4047-a34c-d9dbeb140c1e", + "practices": [ + "maths", + "custom-type" + ], + "prerequisites": [ + "maths", + "custom-type", + "int", + "float", + "case", + "result", + "recursion" + ], + "difficulty": 5 + }, { "slug": "largest-series-product", "name": "Largest Series Product", diff --git a/exercises/practice/rational-numbers/.docs/instructions.md b/exercises/practice/rational-numbers/.docs/instructions.md new file mode 100644 index 000000000..f64fc0f28 --- /dev/null +++ b/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. diff --git a/exercises/practice/rational-numbers/.gitignore b/exercises/practice/rational-numbers/.gitignore new file mode 100644 index 000000000..170cca981 --- /dev/null +++ b/exercises/practice/rational-numbers/.gitignore @@ -0,0 +1,4 @@ +*.beam +*.ez +build +erl_crash.dump diff --git a/exercises/practice/rational-numbers/.meta/config.json b/exercises/practice/rational-numbers/.meta/config.json new file mode 100644 index 000000000..c111f77fe --- /dev/null +++ b/exercises/practice/rational-numbers/.meta/config.json @@ -0,0 +1,23 @@ +{ + "authors": [ + "natanaelsirqueira" + ], + "files": { + "solution": [ + "src/rational_numbers.gleam" + ], + "test": [ + "test/rational_numbers_test.gleam" + ], + "example": [ + ".meta/example.gleam" + ], + "invalidator": [ + "gleam.toml", + "manifest.toml" + ] + }, + "blurb": "Implement rational numbers.", + "source": "Wikipedia", + "source_url": "https://en.wikipedia.org/wiki/Rational_number" +} diff --git a/exercises/practice/rational-numbers/.meta/example.gleam b/exercises/practice/rational-numbers/.meta/example.gleam new file mode 100644 index 000000000..8bbb6dd13 --- /dev/null +++ b/exercises/practice/rational-numbers/.meta/example.gleam @@ -0,0 +1,110 @@ +import gleam/int +import gleam/float +import gleam/result + +pub type RationalNumber { + RationalNumber(numerator: Int, denominator: Int) +} + +pub fn add(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + let RationalNumber(a, b) = r1 + let RationalNumber(c, d) = r2 + + reduce(RationalNumber(numerator: a * d + c * b, denominator: b * d)) +} + +pub fn subtract(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + let RationalNumber(a, b) = r1 + let RationalNumber(c, d) = r2 + + reduce(RationalNumber(numerator: a * d - c * b, denominator: b * d)) +} + +pub fn multiply(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + let RationalNumber(a, b) = r1 + let RationalNumber(c, d) = r2 + + reduce(RationalNumber(numerator: a * c, denominator: b * d)) +} + +pub fn divide(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + let RationalNumber(a, b) = r1 + let RationalNumber(c, d) = r2 + + reduce(RationalNumber(numerator: a * d, denominator: c * b)) +} + +pub fn absolute_value(r: RationalNumber) -> RationalNumber { + let RationalNumber(numerator, denominator) = reduce(r) + + RationalNumber( + numerator: int.absolute_value(numerator), + denominator: denominator, + ) +} + +pub fn power_of_rational( + number base: RationalNumber, + to exponent: Int, +) -> RationalNumber { + case base { + RationalNumber(numerator, denominator) if exponent < 0 -> + power_of_rational( + RationalNumber(numerator: denominator, denominator: numerator), + to: int.absolute_value(exponent), + ) + + RationalNumber(numerator, denominator) -> { + let numerator = power_of_integer(numerator, to: exponent) + let denominator = power_of_integer(denominator, to: exponent) + + reduce(RationalNumber(numerator, denominator)) + } + } +} + +pub fn power_of_real( + number base: Float, + to exponent: RationalNumber, +) -> Result(Float, Nil) { + let RationalNumber(numerator, denominator) = exponent + + use power <- result.then(float.power(base, int.to_float(numerator))) + + nth_root(denominator, of: power) +} + +pub fn reduce(r: RationalNumber) -> RationalNumber { + let RationalNumber(numerator, denominator) = r + + let gcd = gcd(numerator, denominator) + + case numerator / gcd, denominator / gcd { + numerator, denominator if denominator < 0 -> + RationalNumber( + numerator: int.negate(numerator), + denominator: int.negate(denominator), + ) + + numerator, denominator -> RationalNumber(numerator, denominator) + } +} + +fn power_of_integer(number base: Int, to exponent: Int) -> Int { + let assert Ok(power) = int.power(base, int.to_float(exponent)) + + float.round(power) +} + +fn nth_root(n: Int, of p: Float) -> Result(Float, Nil) { + let n = int.to_float(n) + + float.power(p, 1.0 /. n) +} + +fn gcd(a: Int, b: Int) -> Int { + case a, b { + a, 0 -> a + a, b -> gcd(b, a % b) + } +} diff --git a/exercises/practice/rational-numbers/.meta/tests.toml b/exercises/practice/rational-numbers/.meta/tests.toml new file mode 100644 index 000000000..ddea7145c --- /dev/null +++ b/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" diff --git a/exercises/practice/rational-numbers/gleam.toml b/exercises/practice/rational-numbers/gleam.toml new file mode 100644 index 000000000..e27b1315f --- /dev/null +++ b/exercises/practice/rational-numbers/gleam.toml @@ -0,0 +1,9 @@ +name = "rational_numbers" +version = "0.1.0" + +[dependencies] +gleam_stdlib = "~> 0.26" +gleam_bitwise = "~> 1.2" + +[dev-dependencies] +gleeunit = "~> 0.10" diff --git a/exercises/practice/rational-numbers/manifest.toml b/exercises/practice/rational-numbers/manifest.toml new file mode 100644 index 000000000..91ca7b581 --- /dev/null +++ b/exercises/practice/rational-numbers/manifest.toml @@ -0,0 +1,13 @@ +# This file was generated by Gleam +# You typically do not need to edit this file + +packages = [ + { name = "gleam_bitwise", version = "1.2.0", build_tools = ["gleam"], requirements = ["gleam_stdlib"], otp_app = "gleam_bitwise", source = "hex", outer_checksum = "6064699EFBABB1CA392DCB193D0E8B402FB042B4B46857B01E6875E643B57F54" }, + { name = "gleam_stdlib", version = "0.27.0", build_tools = ["gleam"], requirements = [], otp_app = "gleam_stdlib", source = "hex", outer_checksum = "9DBDD21B48C654182CDD8AA15ACF85E8E74A0438583C68BD7EF08BE89F999C6F" }, + { name = "gleeunit", version = "0.10.1", build_tools = ["gleam"], requirements = ["gleam_stdlib"], otp_app = "gleeunit", source = "hex", outer_checksum = "ECEA2DE4BE6528D36AFE74F42A21CDF99966EC36D7F25DEB34D47DD0F7977BAF" }, +] + +[requirements] +gleam_bitwise = "~> 1.2" +gleam_stdlib = "~> 0.26" +gleeunit = "~> 0.10" diff --git a/exercises/practice/rational-numbers/src/rational_numbers.gleam b/exercises/practice/rational-numbers/src/rational_numbers.gleam new file mode 100644 index 000000000..97b20d1e0 --- /dev/null +++ b/exercises/practice/rational-numbers/src/rational_numbers.gleam @@ -0,0 +1,41 @@ +pub type RationalNumber { + RationalNumber(numerator: Int, denominator: Int) +} + +pub fn add(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + todo +} + +pub fn subtract(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + todo +} + +pub fn multiply(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + todo +} + +pub fn divide(r1: RationalNumber, r2: RationalNumber) -> RationalNumber { + todo +} + +pub fn absolute_value(r: RationalNumber) -> RationalNumber { + todo +} + +pub fn power_of_rational( + number base: RationalNumber, + to exponent: Int, +) -> RationalNumber { + todo +} + +pub fn power_of_real( + number base: Float, + to exponent: RationalNumber, +) -> Result(Float, Nil) { + todo +} + +pub fn reduce(r: RationalNumber) -> RationalNumber { + todo +} diff --git a/exercises/practice/rational-numbers/test/rational_numbers_test.gleam b/exercises/practice/rational-numbers/test/rational_numbers_test.gleam new file mode 100644 index 000000000..148219c25 --- /dev/null +++ b/exercises/practice/rational-numbers/test/rational_numbers_test.gleam @@ -0,0 +1,229 @@ +import gleeunit +import gleam/float +import rational_numbers.{RationalNumber} + +pub fn main() { + gleeunit.main() +} + +pub fn arithmetic_addition_add_two_positive_rational_numbers_test() { + let assert RationalNumber(7, 6) = + rational_numbers.add(RationalNumber(1, 2), RationalNumber(2, 3)) +} + +pub fn arithmetic_addition_add_a_positive_rational_number_and_a_negative_rational_number_test() { + let assert RationalNumber(-1, 6) = + rational_numbers.add(RationalNumber(1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_addition_add_two_negative_rational_numbers_test() { + let assert RationalNumber(-7, 6) = + rational_numbers.add(RationalNumber(-1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_addition_add_a_rational_number_to_its_additive_inverse_test() { + let assert RationalNumber(0, 1) = + rational_numbers.add(RationalNumber(1, 2), RationalNumber(-1, 2)) +} + +pub fn arithmetic_subtraction_subtract_two_positive_rational_numbers_test() { + let assert RationalNumber(-1, 6) = + rational_numbers.subtract(RationalNumber(1, 2), RationalNumber(2, 3)) +} + +pub fn arithmetic_subtraction_subtract_a_positive_rational_number_and_a_negative_rational_number_test() { + let assert RationalNumber(7, 6) = + rational_numbers.subtract(RationalNumber(1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_subtraction_subtract_two_negative_rational_numbers_test() { + let assert RationalNumber(1, 6) = + rational_numbers.subtract(RationalNumber(-1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_subtraction_subtract_a_rational_number_from_itself_test() { + let assert RationalNumber(0, 1) = + rational_numbers.subtract(RationalNumber(1, 2), RationalNumber(1, 2)) +} + +pub fn arithmetic_multiplication_multiply_two_positive_rational_numbers_test() { + let assert RationalNumber(1, 3) = + rational_numbers.multiply(RationalNumber(1, 2), RationalNumber(2, 3)) +} + +pub fn arithmetic_multiplication_multiply_a_negative_rational_number_by_a_positive_rational_number_test() { + let assert RationalNumber(-1, 3) = + rational_numbers.multiply(RationalNumber(-1, 2), RationalNumber(2, 3)) +} + +pub fn arithmetic_multiplication_multiply_two_negative_rational_numbers_test() { + let assert RationalNumber(1, 3) = + rational_numbers.multiply(RationalNumber(-1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_multiplication_multiply_a_rational_number_by_its_reciprocal_test() { + let assert RationalNumber(1, 1) = + rational_numbers.multiply(RationalNumber(1, 2), RationalNumber(2, 1)) +} + +pub fn arithmetic_multiplication_multiply_a_rational_number_by_1_test() { + let assert RationalNumber(1, 2) = + rational_numbers.multiply(RationalNumber(1, 2), RationalNumber(1, 1)) +} + +pub fn arithmetic_multiplication_multiply_a_rational_number_by_0_test() { + let assert RationalNumber(0, 1) = + rational_numbers.multiply(RationalNumber(1, 2), RationalNumber(0, 1)) +} + +pub fn arithmetic_division_divide_two_positive_rational_numbers_test() { + let assert RationalNumber(3, 4) = + rational_numbers.divide(RationalNumber(1, 2), RationalNumber(2, 3)) +} + +pub fn arithmetic_division_divide_a_positive_rational_number_by_a_negative_rational_number_test() { + let assert RationalNumber(-3, 4) = + rational_numbers.divide(RationalNumber(1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_division_divide_two_negative_rational_numbers_test() { + let assert RationalNumber(3, 4) = + rational_numbers.divide(RationalNumber(-1, 2), RationalNumber(-2, 3)) +} + +pub fn arithmetic_division_divide_a_rational_number_by_1_test() { + let assert RationalNumber(1, 2) = + rational_numbers.divide(RationalNumber(1, 2), RationalNumber(1, 1)) +} + +pub fn absolute_value_absolute_value_of_a_positive_rational_number_test() { + let assert RationalNumber(1, 2) = + rational_numbers.absolute_value(RationalNumber(1, 2)) +} + +pub fn absolute_value_absolute_value_of_a_positive_rational_number_with_negative_numerator_and_denominator_test() { + let assert RationalNumber(1, 2) = + rational_numbers.absolute_value(RationalNumber(-1, -2)) +} + +pub fn absolute_value_absolute_value_of_a_negative_rational_number_test() { + let assert RationalNumber(1, 2) = + rational_numbers.absolute_value(RationalNumber(-1, 2)) +} + +pub fn absolute_value_absolute_value_of_a_negative_rational_number_with_negative_denominator_test() { + let assert RationalNumber(1, 2) = + rational_numbers.absolute_value(RationalNumber(1, -2)) +} + +pub fn absolute_value_absolute_value_of_zero_test() { + let assert RationalNumber(0, 1) = + rational_numbers.absolute_value(RationalNumber(0, 1)) +} + +pub fn absolute_value_absolute_value_of_a_rational_number_is_reduced_to_lowest_terms_test() { + let assert RationalNumber(1, 2) = + rational_numbers.absolute_value(RationalNumber(2, 4)) +} + +pub fn exponentiation_of_a_rational_number_raise_a_positive_rational_number_to_a_positive_integer_power_test() { + let assert RationalNumber(1, 8) = + rational_numbers.power_of_rational(number: RationalNumber(1, 2), to: 3) +} + +pub fn exponentiation_of_a_rational_number_raise_a_negative_rational_number_to_a_positive_integer_power_test() { + let assert RationalNumber(-1, 8) = + rational_numbers.power_of_rational(number: RationalNumber(-1, 2), to: 3) +} + +pub fn exponentiation_of_a_rational_number_raise_a_positive_rational_number_to_a_negative_integer_power_test() { + let assert RationalNumber(25, 9) = + rational_numbers.power_of_rational(number: RationalNumber(3, 5), to: -2) +} + +pub fn exponentiation_of_a_rational_number_raise_a_negative_rational_number_to_an_even_negative_integer_power_test() { + let assert RationalNumber(25, 9) = + rational_numbers.power_of_rational(number: RationalNumber(-3, 5), to: -2) +} + +pub fn exponentiation_of_a_rational_number_raise_a_negative_rational_number_to_an_odd_negative_integer_power_test() { + let assert RationalNumber(-125, 27) = + rational_numbers.power_of_rational(number: RationalNumber(-3, 5), to: -3) +} + +pub fn exponentiation_of_a_rational_number_raise_zero_to_an_integer_power_test() { + let assert RationalNumber(0, 1) = + rational_numbers.power_of_rational(number: RationalNumber(0, 1), to: 5) +} + +pub fn exponentiation_of_a_rational_number_raise_one_to_an_integer_power_test() { + let assert RationalNumber(1, 1) = + rational_numbers.power_of_rational(number: RationalNumber(1, 1), to: 4) +} + +pub fn exponentiation_of_a_rational_number_raise_a_positive_rational_number_to_the_power_of_zero_test() { + let assert RationalNumber(1, 1) = + rational_numbers.power_of_rational(number: RationalNumber(1, 2), to: 0) +} + +pub fn exponentiation_of_a_rational_number_raise_a_negative_rational_number_to_the_power_of_zero_test() { + let assert RationalNumber(1, 1) = + rational_numbers.power_of_rational(number: RationalNumber(-1, 2), to: 0) +} + +pub fn exponentiation_of_a_real_number_to_a_rational_number_raise_a_real_number_to_a_positive_rational_number_test() { + let assert Ok(power) = + rational_numbers.power_of_real(number: 8.0, to: RationalNumber(4, 3)) + + let assert True = float.loosely_equals(power, with: 16.0, tolerating: 0.001) +} + +pub fn exponentiation_of_a_real_number_to_a_rational_number_raise_a_real_number_to_a_negative_rational_number_test() { + let assert Ok(power) = + rational_numbers.power_of_real(number: 9.0, to: RationalNumber(-1, 2)) + + let assert True = + float.loosely_equals(power, with: 0.3333333333333333, tolerating: 0.001) +} + +pub fn exponentiation_of_a_real_number_to_a_rational_number_raise_a_real_number_to_a_zero_rational_number_test() { + let assert Ok(power) = + rational_numbers.power_of_real(number: 2.0, to: RationalNumber(0, 1)) + + let assert True = float.loosely_equals(power, with: 1.0, tolerating: 0.001) +} + +pub fn reduction_to_lowest_terms_reduce_a_positive_rational_number_to_lowest_terms_test() { + let assert RationalNumber(1, 2) = + rational_numbers.reduce(RationalNumber(2, 4)) +} + +pub fn reduction_to_lowest_terms_reduce_places_the_minus_sign_on_the_numerator_test() { + let assert RationalNumber(-3, 4) = + rational_numbers.reduce(RationalNumber(3, -4)) +} + +pub fn reduction_to_lowest_terms_reduce_a_negative_rational_number_to_lowest_terms_test() { + let assert RationalNumber(-2, 3) = + rational_numbers.reduce(RationalNumber(-4, 6)) +} + +pub fn reduction_to_lowest_terms_reduce_a_rational_number_with_a_negative_denominator_to_lowest_terms_test() { + let assert RationalNumber(-1, 3) = + rational_numbers.reduce(RationalNumber(3, -9)) +} + +pub fn reduction_to_lowest_terms_reduce_zero_to_lowest_terms_test() { + let assert RationalNumber(0, 1) = + rational_numbers.reduce(RationalNumber(0, 6)) +} + +pub fn reduction_to_lowest_terms_reduce_an_integer_to_lowest_terms_test() { + let assert RationalNumber(-2, 1) = + rational_numbers.reduce(RationalNumber(-14, 7)) +} + +pub fn reduction_to_lowest_terms_reduce_one_to_lowest_terms_test() { + let assert RationalNumber(1, 1) = + rational_numbers.reduce(RationalNumber(13, 13)) +}