diff --git a/config.json b/config.json index a544a547..0836aa8c 100644 --- a/config.json +++ b/config.json @@ -728,6 +728,14 @@ "practices": ["classes"], "prerequisites": [], "difficulty": 5 + }, + { + "slug": "rational-numbers", + "name": "Rational Numbers", + "uuid": "5d76a98a-f130-41b3-af1f-1b8d32d2f6e6", + "practices": ["operator-overloading"], + "prerequisites": [], + "difficulty": 5 } ] }, diff --git a/exercises/practice/rational-numbers/.docs/instructions.md b/exercises/practice/rational-numbers/.docs/instructions.md new file mode 100644 index 00000000..5de9966a --- /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/.meta/RationalNumbers.example.ps1 b/exercises/practice/rational-numbers/.meta/RationalNumbers.example.ps1 new file mode 100644 index 00000000..6240b067 --- /dev/null +++ b/exercises/practice/rational-numbers/.meta/RationalNumbers.example.ps1 @@ -0,0 +1,119 @@ +<# +.SYNOPSIS + Implement a class represent a rational number. + +.DESCRIPTION + A rational number is defined as the quotient of two integers 'a' (numerator) and 'b' (denominator) where 'b != 0'. + Please 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. + +.EXAMPLE + $r1 = [Rational]::new(3,4) + $r2 = [Rational]::new(5,6) + + $add = $r1 + $r2 + $add.ToString() + Return: 19/12 + + $sub = $r1 - $r2 + $sub.ToString() + Return: -1/12 + + $exp = $r1.Power(2) + $exp.ToString() + Return: 9/16 +#> + +Class Rational { + [int] hidden $Numer + [int] hidden $Denom + + Rational([int] $Numer, [int] $Denom) { + $this.Numer = $Numer + $this.Denom = $Denom + $this.Reduce() + } + + [bool] Equals($other) { + return ($this.Numer -eq $other.Numer) -and ($this.Denom -eq $other.Denom) + } + + [string] ToString() { + return "$($this.Numer)/$($this.Denom)" + } + + static [Rational] op_Addition([Rational]$self, [Rational]$other) { + $newNumer = $self.Numer * $other.Denom + $other.Numer * $self.Denom + $newDenom = $self.Denom * $other.Denom + return [Rational]::new($newNumer, $newDenom) + } + + static [Rational] op_Subtraction([Rational]$self, [Rational]$other) { + $newNumer = $self.Numer * $other.Denom - $other.Numer * $self.Denom + $newDenom = $self.Denom * $other.Denom + return [Rational]::new($newNumer, $newDenom) + } + + static [Rational] op_Multiply([Rational]$self, [Rational]$other) { + $newNumer = $self.Numer * $other.Numer + $newDenom = $self.Denom * $other.Denom + return [Rational]::new($newNumer, $newDenom) + } + + static [Rational] op_Division([Rational]$self, [Rational]$other) { + if ($other.Numer -eq 0) {Throw "Can't divide by zero"} + $newNumer = $self.Numer * $other.Denom + $newDenom = $other.Numer * $self.Denom + return [Rational]::new($newNumer, $newDenom) + } + + [Rational] Abs() { + $this.Numer = $this.Numer -lt 0 ? $this.Numer * -1 : $this.Numer + return [Rational]::new($this.Numer, $this.Denom) + } + + [object] Power($power) { + if ($power -is [int]) { + if ($power -ge 0) { + $newNumer = [Math]::Pow($this.Numer, $power) + $newDenom = [Math]::Pow($this.Denom, $power) + return [Rational]::new($newNumer, $newDenom) + }else { + $power *= -1 + $newNumer = [Math]::Pow($this.Denom, $power) + $newDenom = [Math]::Pow($this.Numer, $power) + return [Rational]::new($newNumer, $newDenom) + } + }elseif ($power -is [double]) { + return [Math]::Pow($this.Numer, $power) / [Math]::Pow($this.Denom, $power) + } + return $this + } + + [double] ReversePower($base) { + $tempBase = [Math]::Pow($base, $this.Numer) + $power = 1 / $this.Denom + return [Math]::Pow($tempBase, $power) + } + + [int] hidden GetGCD($a,$b){ + while ($b) { + $a, $b = $b, ($a % $b) + } + return [Math]::Abs($a) + } + + [void] hidden Reduce() { + $gcd = $this.GetGCD($this.Numer,$this.Denom) + if ($this.Denom -lt 0) { + $this.Numer /= -$gcd + $this.Denom /= -$gcd + }else { + $this.Numer /= $gcd + $this.Denom /= $gcd + } + } +} \ No newline at end of file diff --git a/exercises/practice/rational-numbers/.meta/config.json b/exercises/practice/rational-numbers/.meta/config.json new file mode 100644 index 00000000..7d89e515 --- /dev/null +++ b/exercises/practice/rational-numbers/.meta/config.json @@ -0,0 +1,19 @@ +{ + "authors": [ + "glaxxie" + ], + "files": { + "solution": [ + "RationalNumbers.ps1" + ], + "test": [ + "RationalNumbers.tests.ps1" + ], + "example": [ + ".meta/RationalNumbers.example.ps1" + ] + }, + "blurb": "Implement rational numbers.", + "source": "Wikipedia", + "source_url": "https://en.wikipedia.org/wiki/Rational_number" +} diff --git a/exercises/practice/rational-numbers/.meta/tests.toml b/exercises/practice/rational-numbers/.meta/tests.toml new file mode 100644 index 00000000..ddea7145 --- /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" + 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+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" + 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+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/RationalNumbers.ps1 b/exercises/practice/rational-numbers/RationalNumbers.ps1 new file mode 100644 index 00000000..7ba09de5 --- /dev/null +++ b/exercises/practice/rational-numbers/RationalNumbers.ps1 @@ -0,0 +1,73 @@ +<# +.SYNOPSIS + Implement a class represent a rational number. + +.DESCRIPTION + A rational number is defined as the quotient of two integers 'a' (numerator) and 'b' (denominator) where 'b != 0'. + Please 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. + +.EXAMPLE + $r1 = [Rational]::new(3,4) + $r2 = [Rational]::new(5,6) + + $add = $r1 + $r2 + $add.ToString() + Return: 19/12 + + $sub = $r1 - $r2 + $sub.ToString() + Return: -1/12 + + $exp = $r1.Power(2) + $exp.ToString() + Return: 9/16 +#> + +Class Rational { + [int] $Numer + [int] $Denom + + Rational() { + Throw "Please implement this class" + } + + [bool] Equals($other) { + return ($this.Numer -eq $other.Numer) -and ($this.Denom -eq $other.Denom) + } + + [string] ToString() { + return "$($this.Numer)/$($this.Denom)" + } + + op_Addition() { + Throw "Please implement this function" + } + + op_Subtraction() { + Throw "Please implement this function" + } + + op_Multiply() { + Throw "Please implement this function" + } + + op_Division() { + Throw "Please implement this function" + } + + Abs() { + Throw "Please implement this function" + } + + Power() { + Throw "Please implement this function" + } + + ReversePower() { + Throw "Please implement this function" + } +} \ No newline at end of file diff --git a/exercises/practice/rational-numbers/RationalNumbers.tests.ps1 b/exercises/practice/rational-numbers/RationalNumbers.tests.ps1 new file mode 100644 index 00000000..d98e58e2 --- /dev/null +++ b/exercises/practice/rational-numbers/RationalNumbers.tests.ps1 @@ -0,0 +1,325 @@ +BeforeAll { + . "./RationalNumbers.ps1" +} + +Describe "RationalNumbers test cases" { + Context "Addition operations" { + It "Add two positive rational numbers" { + $got = [Rational]::new(1, 2) + [Rational]::new(2, 3) + $want = [Rational]::new(7, 6) + + $got | Should -BeExactly $want + } + + It "Add a positive rational number and a negative rational number" { + $got = [Rational]::new(1, 2) + [Rational]::new(-2, 3) + $want = [Rational]::new(-1, 6) + + $got | Should -BeExactly $want + } + + It "Add two negative rational numbers" { + $got = [Rational]::new(-1, 2) + [Rational]::new(-2, 3) + $want = [Rational]::new(-7, 6) + + $got | Should -BeExactly $want + } + + It "Add a rational number to its additive inverse" { + $got = [Rational]::new(1, 2) + [Rational]::new(-1, 2) + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + } + + Context "Subtraction operation" { + It "Subtract two positive rational numbers" { + $got = [Rational]::new(1, 2) - [Rational]::new(2, 3) + $want = [Rational]::new(-1, 6) + + $got | Should -BeExactly $want + } + + It "Subtract a positive rational number and a negative rational number" { + $got = [Rational]::new(1, 2) - [Rational]::new(-2, 3) + $want = [Rational]::new(7, 6) + + $got | Should -BeExactly $want + } + + It "Subtract two negative rational numbers" { + $got = [Rational]::new(-1, 2) - [Rational]::new(-2, 3) + $want = [Rational]::new(1, 6) + + $got | Should -BeExactly $want + } + + It "Subtract a rational number from itself" { + $got = [Rational]::new(1, 2) - [Rational]::new(1, 2) + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + } + + Context "Multiplication operation" { + It "Multiply two positive rational numbers" { + $got = [Rational]::new(1, 2) * [Rational]::new(2, 3) + $want = [Rational]::new(1, 3) + + $got | Should -BeExactly $want + } + + It "Multiply a negative rational number by a positive rational number" { + $got = [Rational]::new(-1, 2) * [Rational]::new(2, 3) + $want = [Rational]::new(-1, 3) + + $got | Should -BeExactly $want + } + + It "Multiply two negative rational numbers" { + $got = [Rational]::new(-1, 2) * [Rational]::new(-2, 3) + $want = [Rational]::new(1, 3) + + $got | Should -BeExactly $want + } + + It "Multiply a rational number by its reciprocal" { + $got = [Rational]::new(1, 2) * [Rational]::new(2, 1) + $want = [Rational]::new(1, 1) + + $got | Should -BeExactly $want + } + + It "Multiply a rational number by 1" { + $got = [Rational]::new(1, 2) * [Rational]::new(1, 1) + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Multiply a rational number by 0" { + $got = [Rational]::new(1, 2) * [Rational]::new(0, 1) + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + } + + Context "Division operation" { + It "Divide two positive rational numbers" { + $got = [Rational]::new(1, 2) / [Rational]::new(2, 3) + $want = [Rational]::new(3, 4) + + $got | Should -BeExactly $want + } + + It "Divide a positive rational number by a negative rational number" { + $got = [Rational]::new(1, 2) / [Rational]::new(-2, 3) + $want = [Rational]::new(-3, 4) + + $got | Should -BeExactly $want + } + + It "Divide two negative rational numbers" { + $got = [Rational]::new(-1, 2) / [Rational]::new(-2, 3) + $want = [Rational]::new(3, 4) + + $got | Should -BeExactly $want + } + + It "Divide a rational number by 1" { + $got = [Rational]::new(1, 2) / [Rational]::new(1, 1) + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + } + + Context "Absolute value" { + It "Absolute value of a positive rational number" { + $got = [Rational]::new(1, 2).Abs() + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Absolute value of a positive rational number with negative numerator and denominator" { + $got = [Rational]::new(-1, -2).Abs() + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Absolute value of a negative rational number" { + $got = [Rational]::new(-1, 2).Abs() + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Absolute value of a negative rational number with negative denominator" { + $got = [Rational]::new(1, -2).Abs() + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Absolute value of zero" { + $got = [Rational]::new(0, 1).Abs() + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + + It "Absolute value of a rational number is reduced to lowest terms" { + $got = [Rational]::new(2, 4).Abs() + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + } + + Context "Exponentiation of a rational number" { + It "Raise a positive rational number to a positive integer power" { + $got = [Rational]::new(1, 2).Power(3) + $want = [Rational]::new(1, 8) + + $got | Should -BeExactly $want + } + + It "Raise a negative rational number to a positive integer power" { + $got = [Rational]::new(-1, 2).Power(3) + $want = [Rational]::new(-1, 8) + + $got | Should -BeExactly $want + } + + It "Raise a positive rational number to a negative integer power" { + $got = [Rational]::new(3, 5).Power(-2) + $want = [Rational]::new(25, 9) + + $got | Should -BeExactly $want + } + + It "Raise a negative rational number to an even negative integer power" { + $got = [Rational]::new(-3, 5).Power(-2) + $want = [Rational]::new(25, 9) + + $got | Should -BeExactly $want + } + + It "Raise a negative rational number to an odd negative integer power" { + $got = [Rational]::new(-3, 5).Power(-3) + $want = [Rational]::new(-125, 27) + + $got | Should -BeExactly $want + } + + It "Raise zero to an integer power" { + $got = [Rational]::new(0, 1).Power(5) + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + + It "Raise one to an integer power" { + $got = [Rational]::new(1, 1).Power(4) + $want = [Rational]::new(1, 1) + + $got | Should -BeExactly $want + } + + It "Raise a positive rational number to the power of zero" { + $got = [Rational]::new(1, 2).Power(0) + $want = [Rational]::new(1, 1) + + $got | Should -BeExactly $want + } + + It "Raise a negative rational number to the power of zero" { + $got = [Rational]::new(-1, 2).Power(0) + $want = [Rational]::new(1, 1) + + $got | Should -BeExactly $want + } + } + + Context "Exponentiation of a real number to a rational number" { + It "Raise a real number to a positive rational number" { + $got = [Rational]::new(4, 3).ReversePower(8) + $want = 16.0 + $tolerance = [Math]::Abs($got - $want) + + $tolerance | Should -BeLessOrEqual 0.00000001 + } + + It "Raise a real number to a negative rational number" { + $got = [Rational]::new(-1, 2).ReversePower(9) + $want = 0.3333333333333333 + $tolerance = [Math]::Abs($got - $want) + + $tolerance | Should -BeLessOrEqual 0.00000001 + } + + It "Raise a real number to a zero rational number" { + $got = [Rational]::new(0, 1).ReversePower(2) + $want = 1.0 + $tolerance = [Math]::Abs($got - $want) + + $tolerance | Should -BeLessOrEqual 0.00000001 + } + } + + Context "Reduction to lowest terms" { + It "Reduce a positive rational number to lowest terms" { + $got = [Rational]::new(2, 4) + $want = [Rational]::new(1, 2) + + $got | Should -BeExactly $want + } + + It "Reduce places the minus sign on the numerator" { + $got = [Rational]::new(3, -4) + $want = [Rational]::new(-3, 4) + + $got | Should -BeExactly $want + } + + It "Reduce a negative rational number to lowest terms" { + $got = [Rational]::new(-4, 6) + $want = [Rational]::new(-2, 3) + + $got | Should -BeExactly $want + } + + It "Reduce a rational number with a negative denominator to lowest terms" { + $got = [Rational]::new(3, -9) + $want = [Rational]::new(-1, 3) + + $got | Should -BeExactly $want + } + + It "Reduce zero to lowest terms" { + $got = [Rational]::new(0, 6) + $want = [Rational]::new(0, 1) + + $got | Should -BeExactly $want + } + + It "Reduce an integer to lowest terms" { + $got = [Rational]::new(-14, 7) + $want = [Rational]::new(-2, 1) + + $got | Should -BeExactly $want + } + + It "Reduce one to lowest terms" { + $got = [Rational]::new(13, 13) + $want = [Rational]::new(1, 1) + + $got | Should -BeExactly $want + } + } +}