/Crystal

# struct BigRational

## Overview

Rational numbers are represented as the quotient of arbitrarily large numerators and denominators. Rationals are canonicalized such that the denominator and the numerator have no common factors, and that the denominator is positive. Zero has the unique representation 0/1.

```require "big"

r = BigRational.new(7.to_big_i, 3.to_big_i)
r.to_s # => "7/3"

r = BigRational.new(3, -9)
r.to_s # => "-1/3"```

It is implemented under the hood with GMP.

## Defined in:

big.cr
big/big_decimal.cr
big/big_rational.cr
big/number.cr

## Instance Method Summary

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## Constructor Detail

### def self.new(numerator : Int, denominator : Int)Source

Creates a new `BigRational`.

If denominator is 0, this will raise an exception.

### def self.new(num : Int)Source

Creates a new `BigRational` with num as the numerator and 1 for denominator.

### def self.new(num : Float)Source

Creates a exact representation of float as rational.

### def self.new(num : BigRational)Source

Creates a `BigRational` from the given num.

### def self.new(num : BigDecimal)Source

Creates a `BigRational` from the given num.

## Instance Method Detail

### def **(other : Int) : BigRationalSource

Raises the rational to the otherth power

This will raise `DivisionByZeroError` if rational is 0 and other is negative.

```require "big"

BigRational.new(2, 3) ** 2  # => 4/9
BigRational.new(2, 3) ** -1 # => 3/2```

### def <<(other : Int)Source

Multiplies the rational by (2 ** other)

```require "big"

BigRational.new(2, 3) << 2 # => 8/3```

### def <=>(other : BigDecimal)Source

Description copied from module Comparable(BigDecimal)

The comparison operator. Returns `0` if the two objects are equal, a negative number if this object is considered less than other, a positive number if this object is considered greter than other, or `nil` if the two objects are not comparable.

Subclasses define this method to provide class-specific ordering.

The comparison operator is usually used to sort values:

```# Sort in a descending way:
[3, 1, 2].sort { |x, y| y <=> x } # => [3, 2, 1]

# Sort in an ascending way:
[3, 1, 2].sort { |x, y| x <=> y } # => [1, 2, 3]```

### def >>(other : Int)Source

Divides the rational by (2 ** other)

```require "big"

BigRational.new(2, 3) >> 2 # => 1/6```

### def absSource

Description copied from struct Number

Returns the absolute value of this number.

```123.abs  # => 123
-123.abs # => 123```

### def hash(hasher)Source

TODO improve this

### def inspect : StringSource

Description copied from class Object

Returns a `String` representation of this object suitable to be embedded inside other expressions, sometimes providing more information about this object.

`#inspect` (and `#inspect(io)`) are the methods used when you invoke `#to_s` or `#inspect` on an object that holds other objects and wants to show them. For example when you invoke `Array#to_s`, `#inspect` will be invoked on each element:

```ary = ["one", "two", "three, etc."]
ary.inspect # => ["one", "two", "three, etc."]```

Note that if Array invoked `#to_s` on each of the elements above, the output would have been this:

```ary = ["one", "two", "three, etc."]
# If inspect invoked to_s on each element...
ary.inspect # => [one, two, three, etc.]```

Note that it's not clear how many elements the array has, or which are they, because `#to_s` doesn't guarantee that the string representation is clearly delimited (in the case of `String` the quotes are not shown).

Also note that sometimes the output of `#inspect` will look like a Crystal expression that will compile, but this isn't always the case, nor is it necessary. Notably, `Reference#inspect` and `Struct#inspect` return values that don't compile.

Classes must usually not override this method. Instead, they must override `#inspect(io)`, which must append to the given `IO` object.

### def inspect(io : IO) : NilSource

Description copied from class Object

Appends a string representation of this object to the given `IO` object.

Similar to `#to_s(io)`, but usually appends more information about this object. See `#inspect`.

### def invSource

Returns a new `BigRational` as 1/r.

This will raise an exception if rational is 0.

### def to_big_dSource

Converts `self` to `BigDecimal`.

### def to_fSource

Returns the `Float64` representing this rational.

### def to_s(io : IO, base : Int = 10) : NilSource

Description copied from class Object

Appends a `String` representation of this object to the given `IO` object.

An object must never append itself to the io argument, as this will in turn call `#to_s(io)` on it.

### def to_s(base : Int = 10) : StringSource

Returns the string representing this rational.

Optionally takes a radix base (2 through 36).

```require "big"

r = BigRational.new(8243243, 562828882)
r.to_s     # => "8243243/562828882"
r.to_s(16) # => "7dc82b/218c1652"
r.to_s(36) # => "4woiz/9b3djm"```