Prime

Returns the default instance of Prime.

 
               # File prime.rb, line 106
def instance; @the_instance end
            

obsolete. Use Prime::instance or class methods of Prime.

 
               # File prime.rb, line 96
def initialize
  @generator = EratosthenesGenerator.new
  extend OldCompatibility
  warn "Prime::new is obsolete. use Prime::instance or class methods of Prime."
end
            

Iterates the given block over all prime numbers.

Parameters¶ ↑

ubound

Optional. An arbitrary positive number. The upper bound of enumeration. The method enumerates prime numbers infinitely if ubound is nil.

generator

Optional. An implementation of pseudo-prime generator.

Return value¶ ↑

An evaluated value of the given block at the last time. Or an enumerator which is compatible to an Enumerator if no block given.

Description¶ ↑

Calls block once for each prime number, passing the prime as a parameter.

ubound

Upper bound of prime numbers. The iterator stops after yields all prime numbers p <= ubound.

Note¶ ↑

Prime.new returns a object extended by Prime::OldCompatibility in order to compatibility to Ruby 1.8, and Prime#each is overwritten by Prime::OldCompatibility#each.

Prime.new is now obsolete. Use Prime.instance.each or simply Prime.each.

 
               # File prime.rb, line 147
def each(ubound = nil, generator = EratosthenesGenerator.new, &block)
  generator.upper_bound = ubound
  generator.each(&block)
end
            

Re-composes a prime factorization and returns the product.

Parameters¶ ↑

pd

Array of pairs of integers. The each internal pair consists of a prime number – a prime factor – and a natural number – an exponent.

Example¶ ↑

For [[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]], it returns:

p_1**e_1 * p_2**e_2 * .... * p_n**e_n.

Prime.int_from_prime_division([[2,2], [3,1]])  #=> 12

 
               # File prime.rb, line 182
def int_from_prime_division(pd)
  pd.inject(1){|value, (prime, index)|
    value *= prime**index
  }
end
            

Returns true if value is prime, false for a composite.

Parameters¶ ↑

value

an arbitrary integer to be checked.

generator

optional. A pseudo-prime generator.

 
               # File prime.rb, line 159
def prime?(value, generator = Prime::Generator23.new)
  value = -value if value < 0
  return false if value < 2
  for num in generator
    q,r = value.divmod num
    return true if q < num
    return false if r == 0
  end
end
            

Returns the factorization of value.

Parameters¶ ↑

value

An arbitrary integer.

generator

Optional. A pseudo-prime generator. generator.succ must return the next pseudo-prime number in the ascendent order. It must generate all prime numbers, but may generate non prime numbers.

Exceptions¶ ↑

ZeroDivisionError

when value is zero.

Example¶ ↑

For an arbitrary integer:

n = p_1**e_1 * p_2**e_2 * .... * p_n**e_n,

#prime_division(n) returns:

[[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]].

Prime.prime_division(12) #=> [[2,2], [3,1]]

 
               # File prime.rb, line 212
def prime_division(value, generator= Prime::Generator23.new)
  raise ZeroDivisionError if value == 0
  if value < 0
    value = -value
    pv = [[-1, 1]]
  else
    pv = []
  end
  for prime in generator
    count = 0
    while (value1, mod = value.divmod(prime)
           mod) == 0
      value = value1
      count += 1
    end
    if count != 0
      pv.push [prime, count]
    end
    break if value1 <= prime
  end
  if value > 1
    pv.push [value, 1]
  end
  return pv
end