Class: Integer

Inherits:
Object
  • Object
show all
Defined in:
lib/tonal/extensions.rb

Instance Method Summary collapse

Instance Method Details

#coprime?(other) ⇒ Boolean

Returns if self is coprime with other number.

Examples:

25.coprime?(7) => true
25.coprime?(5) => false

Parameters:

  • other —

    number determining coprimeness

Returns:

  • (Boolean) —

    if self is coprime with other number



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# File 'lib/tonal/extensions.rb', line 298

def coprime?(other) = self.gcd(other) == 1

#coprimes ⇒ Array

Returns list of integers that are coprime with self, up to the value of self.

Examples:

10.coprimes => [1, 3, 7, 9]

Returns:

  • (Array) —

    list of integers that are coprime with self, up to the value of self



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# File 'lib/tonal/extensions.rb', line 304

def coprimes
  [].tap do |coprime_set|
    1.upto(self) do |i|
      coprime_set << i if i.coprime?(self)
    end
  end
end

#ed(modulo, equave: 2) ⇒ Tonal::ReducedRatio

Returns the ratio 2**(self/modulo).

Examples:

1.ed(12) => 1.06

Parameters:

  • modulo
  • equave (defaults to: 2)

Returns:



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# File 'lib/tonal/extensions.rb', line 272

def ed(modulo, equave: 2/1r) = Tonal::ReducedRatio.ed(self, modulo, equave:)

#factorial ⇒ Integer

Returns the factorial of self.

Examples:

5.factorial => 120

Returns:

  • (Integer) —

    the factorial of self



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# File 'lib/tonal/extensions.rb', line 290

def factorial = (2..self).reduce(1, :*)

#max_prime ⇒ Integer

Returns the maximum prime factor of self.

Examples:

72.max_prime => 3

Returns:

  • (Integer) —

    the maximum prime factor of self



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# File 'lib/tonal/extensions.rb', line 278

def max_prime = self.prime_division.map(&:first).max

#min_prime ⇒ Integer

Returns the minimum prime factor of self.

Examples:

72.min_prime => 2

Returns:

  • (Integer) —

    the minimum prime factor of self



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# File 'lib/tonal/extensions.rb', line 284

def min_prime = self.prime_division.map(&:first).min

#nsmooth(limit = 2) ⇒ Array

Note:

Adapted from rosettacode.org/wiki/N-smooth_numbers#Ruby

Returns of integers that are n-smooth with self.

Examples:

5.nsmooth(25)
=> [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]

Parameters:

  • limit (defaults to: 2)

Returns:

  • (Array) —

    of integers that are n-smooth with self



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# File 'lib/tonal/extensions.rb', line 334

def nsmooth(limit=2)
  ([0] * limit).tap do |ns|
    primes = Prime.each(self).to_a
    ns[0] = 1
    nextp = primes[0..primes.index(self)]

    indices = [0] * nextp.size
    (1...limit).each do |m|
      ns[m] = nextp.min
      (0...indices.size).each do |i|
        if ns[m] == nextp[i]
          indices[i] += 1
          nextp[i] = primes[i] * ns[indices[i]]
        end
      end
    end
  end
end

#phi ⇒ Integer Also known as: totient

Returns the count of coprimes less than self.

Examples:

10.phi => 4

Returns:

  • (Integer) —

    the count of coprimes less than self



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# File 'lib/tonal/extensions.rb', line 324

def phi = coprimes.count

#prime_signature ⇒ Array

Returns of signature of self.

Examples:

5.signature
=> [1]

Returns:

  • (Array) —

    of signature of self

Raises:

  • (ArgumentError) 


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# File 'lib/tonal/extensions.rb', line 358

def prime_signature
  raise ArgumentError, "applicable only to positive integers" if self <= 0

  n = self
  exponents = []
  i = 2
  while i * i <= n
    count = 0
    while n % i == 0
      n /= i
      count += 1
    end
    exponents << count if count > 0
    i += 1
  end
  exponents << 1 if n > 1  # n is prime at this point
  exponents.sort
end

#superparticular ⇒ Rational

Returns the superparticular ratio based on the given integer as the numerator.

Examples:

4.superparticular => 4/3

Returns:

  • (Rational) —

    the superparticular ratio based on the given integer as the numerator



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# File 'lib/tonal/extensions.rb', line 315

def superparticular
  return nil if self < 2
  Rational(self, self-1)
end