Returns a string containing the place-value representation of self in radix base (in 2..36).
12345.to_s # => "12345" 12345.to_s(2) # => "11000000111001" 12345.to_s(8) # => "30071" 12345.to_s(10) # => "12345" 12345.to_s(16) # => "3039" 12345.to_s(36) # => "9ix" 78546939656932.to_s(36) # => "rubyrules"
Raises an exception if base is out of range.
Since self is already an Integer, always returns true.
Returns 1.
Returns a new Complex object formed from the arguments, each of which must be an instance of Numeric, or an instance of one of its subclasses: Complex, Float, Integer, Rational; see Rectangular Coordinates:
Complex.rect(3) # => (3+0i) Complex.rect(3, Math::PI) # => (3+3.141592653589793i) Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)
Complex.rectangular is an alias for Complex.rect.
Returns the imaginary value for self:
Complex.rect(7).imag # => 0 Complex.rect(9, -4).imag # => -4
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.
Returns the argument (angle) for self in radians; see polar coordinates:
Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660
If self was created with rectangular coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
Returns the array [self.real, self.imag]:
Complex.rect(1, 2).rect # => [1, 2]
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965]
Complex#rectangular is an alias for Complex#rect.
Returns the denominator of self, which is the least common multiple of self.real.denominator and self.imag.denominator:
Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6
Note that n.denominator of a non-rational numeric is 1.
Related: Complex#numerator.
Returns a string representation of self:
Complex.rect(2).inspect # => "(2+0i)" Complex.rect(-8, 6).inspect # => "(-8+6i)" Complex.rect(0, Rational(1, 2)).inspect # => "(0+(1/2)*i)" Complex.rect(0, Float::INFINITY).inspect # => "(0+Infinity*i)" Complex.rect(Float::NAN, Float::NAN).inspect # => "(NaN+NaN*i)"
Returns true if both self.real.finite? and self.imag.finite? are true, false otherwise:
Complex.rect(1, 1).finite? # => true Complex.rect(Float::INFINITY, 0).finite? # => false
Related: Numeric#finite?, Float#finite?.
Returns zero if self is positive, Math::PI otherwise.
Returns array [self, 0].
Returns the remainder after dividing self by other.
Of the Core and Standard Library classes, only Float and Rational use this implementation.
Examples:
11.0.remainder(4) # => 3.0 11.0.remainder(-4) # => 3.0 -11.0.remainder(4) # => -3.0 -11.0.remainder(-4) # => -3.0 12.0.remainder(4) # => 0.0 12.0.remainder(-4) # => 0.0 -12.0.remainder(4) # => -0.0 -12.0.remainder(-4) # => -0.0 13.0.remainder(4.0) # => 1.0 13.0.remainder(Rational(4, 1)) # => 1.0 Rational(13, 1).remainder(4) # => (1/1) Rational(13, 1).remainder(-4) # => (1/1) Rational(-13, 1).remainder(4) # => (-1/1) Rational(-13, 1).remainder(-4) # => (-1/1)
Returns self truncated (toward zero) to a precision of digits decimal digits.
Numeric implements this by converting self to a Float and invoking Float#truncate.
Generates a sequence of numbers; with a block given, traverses the sequence.
Of the Core and Standard Library classes, Integer, Float, and Rational use this implementation.
A quick example:
squares = [] 1.step(by: 2, to: 10) {|i| squares.push(i*i) } squares # => [1, 9, 25, 49, 81]
The generated sequence:
Begins with self.
Continues at intervals of by (which may not be zero).
Ends with the last number that is within or equal to to; that is, less than or equal to to if by is positive, greater than or equal to to if by is negative. If to is nil, the sequence is of infinite length.
If a block is given, calls the block with each number in the sequence; returns self. If no block is given, returns an Enumerator::ArithmeticSequence.
Keyword Arguments
With keyword arguments by and to, their values (or defaults) determine the step and limit:
# Both keywords given. squares = [] 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4 squares # => [16, 36, 64, 100] cubes = [] 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3 cubes # => [27.0, 3.375, 0.0, -3.375, -27.0] squares = [] 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) } squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0] squares = [] Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) } squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0] # Only keyword to given. squares = [] 4.step(to: 10) {|i| squares.push(i*i) } # => 4 squares # => [16, 25, 36, 49, 64, 81, 100] # Only by given. # Only keyword by given squares = [] 4.step(by:2) {|i| squares.push(i*i); break if i > 10 } squares # => [16, 36, 64, 100, 144] # No block given. e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3)) e.class # => Enumerator::ArithmeticSequence
Positional Arguments
With optional positional arguments to and by, their values (or defaults) determine the step and limit:
squares = [] 4.step(10, 2) {|i| squares.push(i*i) } # => 4 squares # => [16, 36, 64, 100] squares = [] 4.step(10) {|i| squares.push(i*i) } squares # => [16, 25, 36, 49, 64, 81, 100] squares = [] 4.step {|i| squares.push(i*i); break if i > 10 } # => nil squares # => [16, 25, 36, 49, 64, 81, 100, 121]
Implementation Notes
If all the arguments are integers, the loop operates using an integer counter.
If any of the arguments are floating point numbers, all are converted to floats, and the loop is executed floor(n + n*Float::EPSILON) + 1 times, where n = (limit - self)/step.
Returns true if self is a finite number, false otherwise.
Returns zero.
Returns the denominator (always positive).
Returns 0 if self is positive, Math::PI otherwise.
Returns self truncated (toward zero) to a precision of ndigits decimal digits.
When ndigits is positive, returns a float with ndigits digits after the decimal point (as available):
f = 12345.6789 f.truncate(1) # => 12345.6 f.truncate(3) # => 12345.678 f = -12345.6789 f.truncate(1) # => -12345.6 f.truncate(3) # => -12345.678
When ndigits is negative, returns an integer with at least ndigits.abs trailing zeros:
f = 12345.6789 f.truncate(0) # => 12345 f.truncate(-3) # => 12000 f = -12345.6789 f.truncate(0) # => -12345 f.truncate(-3) # => -12000
Note that the limited precision of floating-point arithmetic may lead to surprising results:
(0.3 / 0.1).truncate #=> 2 (!)
Related: Float#round.
Returns true if self is not Infinity, -Infinity, or NaN, false otherwise:
f = 2.0 # => 2.0 f.finite? # => true f = 1.0/0.0 # => Infinity f.finite? # => false f = -1.0/0.0 # => -Infinity f.finite? # => false f = 0.0/0.0 # => NaN f.finite? # => false
Returns a string containing a representation of self; depending of the value of self, the string representation may contain:
A fixed-point number.
3.14.to_s # => "3.14"
A number in “scientific notation” (containing an exponent).
(10.1**50).to_s # => "1.644631821843879e+50"
‘Infinity’.
(10.1**500).to_s # => "Infinity"
‘-Infinity’.
(-10.1**500).to_s # => "-Infinity"
‘NaN’ (indicating not-a-number).
(0.0/0.0).to_s # => "NaN"
Returns the denominator (always positive). The result is machine dependent.
See also Float#numerator.