class Rational

A rational number can be represented as a pair of integer numbers: a/b (b>0), where a is the numerator and b is the denominator. Integer a equals rational a/1 mathematically.

You can create a Rational object explicitly with:

A rational literal.

You can convert certain objects to Rationals with:

Method #Rational.

Examples

Rational(1)      #=> (1/1)
Rational(2, 3)   #=> (2/3)
Rational(4, -6)  #=> (-2/3) # Reduced.
3.to_r           #=> (3/1)
2/3r             #=> (2/3)

You can also create rational objects from floating-point numbers or strings.

Rational(0.3)    #=> (5404319552844595/18014398509481984)
Rational('0.3')  #=> (3/10)
Rational('2/3')  #=> (2/3)

0.3.to_r         #=> (5404319552844595/18014398509481984)
'0.3'.to_r       #=> (3/10)
'2/3'.to_r       #=> (2/3)
0.3.rationalize  #=> (3/10)

A rational object is an exact number, which helps you to write programs without any rounding errors.

10.times.inject(0) {|t| t + 0.1 }              #=> 0.9999999999999999
10.times.inject(0) {|t| t + Rational('0.1') }  #=> (1/1)

However, when an expression includes an inexact component (numerical value or operation), it will produce an inexact result.

Rational(10) / 3   #=> (10/3)
Rational(10) / 3.0 #=> 3.3333333333333335

Rational(-8) ** Rational(1, 3)
                   #=> (1.0000000000000002+1.7320508075688772i)

Public Class Methods

json_create (object)

(Hash[String, String | Integer] object) → instance

Source

# File vendor/bundle/ruby/4.0.0/gems/json-2.21.2/lib/json/add/rational.rb, line 9
def self.json_create(object)
  Rational(object['n'], object['d'])
end

Public Instance Methods

(Integer) → Rational
(Float) → Float
(Rational) → Rational
(Numeric) → Numeric

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 49
def %: (Integer) -> Rational
       | (Float) -> Float
       | (Rational) -> Rational
       | (Numeric) -> Numeric

(BigDecimal) → BigDecimal

Source

# File vendor/bundle/ruby/4.0.0/gems/bigdecimal-4.1.2/sig/big_decimal.rbs, line 1407
def *: (BigDecimal) -> BigDecimal
       | ...

Performs multiplication.

Rational(2, 3)  * Rational(2, 3)   #=> (4/9)
Rational(900)   * Rational(1)      #=> (900/1)
Rational(-2, 9) * Rational(-9, 2)  #=> (1/1)
Rational(9, 8)  * 4                #=> (9/2)
Rational(20, 9) * 9.8              #=> 21.77777777777778

Returns the numeric product of self and other:

Rational(9, 8)  * 4               #=> (9/2)
Rational(20, 9) * 9.8             #=> 21.77777777777778
Rational(9, 8)  * Complex(1, 2)   # => ((9/8)+(9/4)*i)
Rational(2, 3)  * Rational(2, 3)  #=> (4/9)
Rational(900)   * Rational(1)     #=> (900/1)
Rational(-2, 9) * Rational(-9, 2) #=> (1/1)

Returns the numeric product of self and other:

Rational(9, 8)  * 4               #=> (9/2)
Rational(20, 9) * 9.8             #=> 21.77777777777778
Rational(9, 8)  * Complex(1, 2)   # => ((9/8)+(9/4)*i)
Rational(2, 3)  * Rational(2, 3)  #=> (4/9)
Rational(900)   * Rational(1)     #=> (900/1)
Rational(-2, 9) * Rational(-9, 2) #=> (1/1)

(Complex) → Complex
(Numeric) → Numeric

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 84
def **: (Complex) -> Complex
        | (Numeric) -> Numeric

Returns self raised to the power exponent:

Rational(2)    ** Rational(3)     #=> (8/1)
Rational(10)   ** -2              #=> (1/100)
Rational(10)   ** -2.0            #=> 0.01
Rational(-4)   ** Rational(1, 2)  #=> (0.0+2.0i)
Rational(1, 2) ** 0               #=> (1/1)
Rational(1, 2) ** 0.0             #=> 1.0

(BigDecimal) → BigDecimal

Source

# File vendor/bundle/ruby/4.0.0/gems/bigdecimal-4.1.2/sig/big_decimal.rbs, line 1422
def +: (BigDecimal) -> BigDecimal
       | ...

Performs addition.

Rational(2, 3)  + Rational(2, 3)   #=> (4/3)
Rational(900)   + Rational(1)      #=> (901/1)
Rational(-2, 9) + Rational(-9, 2)  #=> (-85/18)
Rational(9, 8)  + 4                #=> (41/8)
Rational(20, 9) + 9.8              #=> 12.022222222222222

Returns the sum of self and other:

Rational(2, 3) + 0  # => (2/3)
Rational(2, 3) + 1  # => (5/3)
Rational(2, 3) + -1 # => (-1/3)

Rational(2, 3) + Complex(1, 0)     # => ((5/3)+0i)

Rational(2, 3) + Rational(1, 1)     # => (5/3)
Rational(2, 3) + Rational(3, 2)     # => (13/6)
Rational(2, 3) + Rational(3.0, 2.0) # => (13/6)
Rational(2, 3) + Rational(3.1, 2.1) # => (30399297484750849/14186338826217063)

For a computation involving Floats, the result may be inexact (see Float#+):

Rational(2, 3) + 1.0 # => 1.6666666666666665
Rational(2, 3) + Complex(1.0, 0.0) # => (1.6666666666666665+0.0i)

Returns the sum of self and other:

Rational(2, 3) + 0  # => (2/3)
Rational(2, 3) + 1  # => (5/3)
Rational(2, 3) + -1 # => (-1/3)

Rational(2, 3) + Complex(1, 0)     # => ((5/3)+0i)

Rational(2, 3) + Rational(1, 1)     # => (5/3)
Rational(2, 3) + Rational(3, 2)     # => (13/6)
Rational(2, 3) + Rational(3.0, 2.0) # => (13/6)
Rational(2, 3) + Rational(3.1, 2.1) # => (30399297484750849/14186338826217063)

For a computation involving Floats, the result may be inexact (see Float#+):

Rational(2, 3) + 1.0 # => 1.6666666666666665
Rational(2, 3) + Complex(1.0, 0.0) # => (1.6666666666666665+0.0i)

(BigDecimal) → BigDecimal

Source

# File vendor/bundle/ruby/4.0.0/gems/bigdecimal-4.1.2/sig/big_decimal.rbs, line 1437
def -: (BigDecimal) -> BigDecimal
       | ...

Performs subtraction.

Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
Rational(900)   - Rational(1)      #=> (899/1)
Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
Rational(9, 8)  - 4                #=> (-23/8)
Rational(20, 9) - 9.8              #=> -7.577777777777778

Returns the difference of self and other:

Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
Rational(900)   - Rational(1)      #=> (899/1)
Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
Rational(9, 8)  - 4                #=> (-23/8)
Rational(20, 9) - 9.8              #=> -7.577777777777778

Returns the difference of self and other:

Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
Rational(900)   - Rational(1)      #=> (899/1)
Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
Rational(9, 8)  - 4                #=> (-23/8)
Rational(20, 9) - 9.8              #=> -7.577777777777778

() → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 138
def -@: () -> Rational

Returns self, negated:

-(1/3r)   # => (-1/3)
-(-1/3r)  # => (1/3)

(BigDecimal) → BigDecimal

Source

# File vendor/bundle/ruby/4.0.0/gems/bigdecimal-4.1.2/sig/big_decimal.rbs, line 1392
def /: (BigDecimal) -> BigDecimal
       | ...

Performs division.

Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246

Returns the quotient of self and other:

Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246

Returns the quotient of self and other:

Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246

(Integer | Rational) → Integer
(untyped) → Integer?

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 182
def <=>: (Integer | Rational) -> Integer
         | (untyped) -> Integer?

Compares self and other.

Returns:

-1, if self is less than other.
0, if the two values are the same.
1, if self is greater than other.
nil, if the two values are incomparable.

Examples:

Rational(2, 3) <=> Rational(4, 3) # => -1
Rational(2, 1) <=> Rational(2, 1) # => 0
Rational(2, 1) <=> 2              # => 0
Rational(2, 1) <=> 2.0            # => 0
Rational(2, 1) <=> Complex(2, 0)  # => 0
Rational(4, 3) <=> Rational(2, 3) # => 1
Rational(4, 3) <=> :foo           # => nil

Class Rational includes module Comparable, each of whose methods uses Rational#<=> for comparison.

(untyped) → bool

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 197
def ==: (untyped) -> bool

Returns true if rat equals object numerically.

Rational(2, 3)  == Rational(2, 3)   #=> true
Rational(5)     == 5                #=> true
Rational(0)     == 0.0              #=> true
Rational('1/3') == 0.33             #=> false
Rational('1/2') == '1/2'            #=> false

() → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 209
def abs: () -> Rational

Returns the absolute value of rat.

(1/2r).abs    #=> (1/2)
(-1/2r).abs   #=> (1/2)

Also aliased as: magnitude

(*untyped) → Hash[String, String | Integer]

Source

# File vendor/bundle/ruby/4.0.0/gems/json-2.21.2/lib/json/add/rational.rb, line 29
def as_json(*)
  {
    JSON.create_id => self.class.name,
    'n'            => numerator,
    'd'            => denominator,
  }
end

Methods Rational#as_json and Rational.json_create may be used to serialize and deserialize a Rational object; see Marshal.

Method Rational#as_json serializes self, returning a 2-element hash representing self:

require 'json/add/rational'
x = Rational(2, 3).as_json
# => {"json_class"=>"Rational", "n"=>2, "d"=>3}

Method JSON.create deserializes such a hash, returning a Rational object:

Rational.json_create(x)
# => (2/3)

Methods Rational#as_json and Rational.json_create may be used to serialize and deserialize a Rational object; see Marshal.

Method Rational#as_json serializes self, returning a 2-element hash representing self:

require 'json/add/rational'
x = Rational(2, 3).as_json
# => {"json_class"=>"Rational", "n"=>2, "d"=>3}

Method JSON.create deserializes such a hash, returning a Rational object:

Rational.json_create(x)
# => (2/3)

() → Integer
(Integer digits) → (Integer | Rational)

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 234
def ceil: () -> Integer
          | (Integer digits) -> (Integer | Rational)

Returns the smallest number greater than or equal to rat with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).ceil      #=> 3
Rational(2, 3).ceil   #=> 1
Rational(-3, 2).ceil  #=> -1

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').ceil(+1).to_f  #=> -123.4
Rational('-123.456').ceil(-1)       #=> -120

(Numeric) → [ Numeric, Numeric ]

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 237
def coerce: (Numeric) -> [ Numeric, Numeric ]

() → Integer

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 250
def denominator: () -> Integer

Returns the denominator (always positive).

Rational(7).denominator             #=> 1
Rational(7, 1).denominator          #=> 1
Rational(9, -4).denominator         #=> 4
Rational(-2, -10).denominator       #=> 5

(Integer | Float | Rational) → [ Integer, Rational ]
(Numeric) → [ Numeric, Numeric ]

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 252
def divmod: (Integer | Float | Rational) -> [ Integer, Rational ]
            | (Numeric) -> [ Numeric, Numeric ]

(Numeric) → Float

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 265
def fdiv: (Numeric) -> Float

Performs division and returns the value as a Float.

Rational(2, 3).fdiv(1)       #=> 0.6666666666666666
Rational(2, 3).fdiv(0.5)     #=> 1.3333333333333333
Rational(2).fdiv(3)          #=> 0.6666666666666666

() → Integer
(Integer digits) → (Integer | Rational)

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 290
def floor: () -> Integer
           | (Integer digits) -> (Integer | Rational)

Returns the largest number less than or equal to rat with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).floor      #=> 3
Rational(2, 3).floor   #=> 0
Rational(-3, 2).floor  #=> -2

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').floor(+1).to_f  #=> -123.5
Rational('-123.456').floor(-1)       #=> -130

() → Integer

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 298
def hash: () -> Integer

() → String

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 310
def inspect: () -> String

Returns the value as a string for inspection.

Rational(2).inspect      #=> "(2/1)"
Rational(-8, 6).inspect  #=> "(-4/3)"
Rational('1/2').inspect  #=> "(1/2)"

() → Rational

Returns the absolute value of rat.

(1/2r).abs    #=> (1/2)
(-1/2r).abs   #=> (1/2)

Alias for: abs

(Float) → Float
(Numeric) → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 320
def modulo: (Float) -> Float
            | (Numeric) -> Rational

() → bool

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 329
def negative?: () -> bool

Returns true if rat is less than 0.

() → Integer

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 342
def numerator: () -> Integer

Returns the numerator.

Rational(7).numerator        #=> 7
Rational(7, 1).numerator     #=> 7
Rational(9, -4).numerator    #=> -9
Rational(-2, -10).numerator  #=> 1

() → [ Rational, Integer | Float ]

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 344
def polar: () -> [ Rational, Integer | Float ]

() → bool

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 352
def positive?: () -> bool

Returns true if rat is greater than 0.

(Float) → Float
(Complex) → Complex
(Numeric) → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 363
def quo: (Float) -> Float
         | (Complex) -> Complex
         | (Numeric) -> Rational

Returns the quotient of self and other:

Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246

(?Numeric eps) → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 380
def rationalize: (?Numeric eps) -> Rational

Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.

r = Rational(5033165, 16777216)
r.rationalize                    #=> (5033165/16777216)
r.rationalize(Rational('0.01'))  #=> (3/10)
r.rationalize(Rational('0.1'))   #=> (1/3)

() → [ Rational, Numeric ]

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 382
def rect: () -> [ Rational, Numeric ]

(Float) → Float
(Numeric) → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 384
def remainder: (Float) -> Float
               | (Numeric) -> Rational

(?half: :up | :down | :even) → Integer
(Integer digits, ?half: :up | :down | :even) → (Integer | Rational)

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 422
def round: (?half: :up | :down | :even) -> Integer
           | (Integer digits, ?half: :up | :down | :even) -> (Integer | Rational)

Returns rat rounded to the nearest value with a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).round      #=> 3
Rational(2, 3).round   #=> 1
Rational(-3, 2).round  #=> -2

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').round(+1).to_f  #=> -123.5
Rational('-123.456').round(-1)       #=> -120

The optional half keyword argument is available similar to Float#round.

Rational(25, 100).round(1, half: :up)    #=> (3/10)
Rational(25, 100).round(1, half: :down)  #=> (1/5)
Rational(25, 100).round(1, half: :even)  #=> (1/5)
Rational(35, 100).round(1, half: :up)    #=> (2/5)
Rational(35, 100).round(1, half: :down)  #=> (3/10)
Rational(35, 100).round(1, half: :even)  #=> (2/5)
Rational(-25, 100).round(1, half: :up)   #=> (-3/10)
Rational(-25, 100).round(1, half: :down) #=> (-1/5)
Rational(-25, 100).round(1, half: :even) #=> (-1/5)

to_d(precision) → bigdecimal

(Integer precision) → BigDecimal

Source

# File vendor/bundle/ruby/4.0.0/gems/bigdecimal-4.1.2/lib/bigdecimal/util.rb, line 135
def to_d(precision=0)
  BigDecimal(self, precision)
end

Returns the value as a BigDecimal.

The precision parameter is used to determine the number of significant digits for the result. When precision is set to 0, the number of digits to represent the float being converted is determined automatically. The default precision is 0.

require 'bigdecimal'
require 'bigdecimal/util'

Rational(22, 7).to_d(3)   # => 0.314e1

See also Kernel.BigDecimal.

Returns the value as a BigDecimal.

The precision parameter is used to determine the number of significant digits for the result. When precision is set to 0, the number of digits to represent the float being converted is determined automatically. The default precision is 0.

require 'bigdecimal'
require 'bigdecimal/util'

Rational(22, 7).to_d(3)   # => 0.314e1

See also Kernel.BigDecimal.

Returns the value as a BigDecimal.

The required precision parameter is used to determine the number of significant digits for the result.

require 'bigdecimal'
require 'bigdecimal/util'

Rational(22, 7).to_d(3)   # => 0.314e1

See also Kernel.BigDecimal.

() → Float

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 436
def to_f: () -> Float

Returns the value as a Float.

Rational(2).to_f      #=> 2.0
Rational(9, 4).to_f   #=> 2.25
Rational(-3, 4).to_f  #=> -0.75
Rational(20, 3).to_f  #=> 6.666666666666667

() → Integer

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 452
def to_i: () -> Integer

Returns the truncated value as an integer.

Equivalent to Rational#truncate.

Rational(2, 3).to_i    #=> 0
Rational(3).to_i       #=> 3
Rational(300.6).to_i   #=> 300
Rational(98, 71).to_i  #=> 1
Rational(-31, 2).to_i  #=> -15

to_json (*args)

(?JSON::State? state) → String

Source

# File vendor/bundle/ruby/4.0.0/gems/json-2.21.2/lib/json/add/rational.rb, line 46
def to_json(*args)
  as_json.to_json(*args)
end

Returns a JSON string representing self:

require 'json/add/rational'
puts Rational(2, 3).to_json

Output:

{"json_class":"Rational","n":2,"d":3}

Returns a JSON string representing self:

require 'json/add/rational'
puts Rational(2, 3).to_json

Output:

{"json_class":"Rational","n":2,"d":3}

() → Rational

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 463
def to_r: () -> Rational

Returns self.

Rational(2).to_r      #=> (2/1)
Rational(-8, 6).to_r  #=> (-4/3)

() → String

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 475
def to_s: () -> String

Returns the value as a string.

Rational(2).to_s      #=> "2/1"
Rational(-8, 6).to_s  #=> "-4/3"
Rational('1/2').to_s  #=> "1/2"

() → Integer
(Integer ndigits) → (Integer | Rational)

Source

# File vendor/bundle/ruby/4.0.0/gems/rbs-4.1.3/core/rational.rbs, line 500
def truncate: () -> Integer
              | (Integer ndigits) -> (Integer | Rational)

Returns rat truncated (toward zero) to a precision of ndigits decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).truncate      #=> 3
Rational(2, 3).truncate   #=> 0
Rational(-3, 2).truncate  #=> -1

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').truncate(+1).to_f  #=> -123.4
Rational('-123.456').truncate(-1)       #=> -120