The set of all prime numbers.
Prime.each(100) do |prime| p prime #=> 2, 3, 5, 7, 11, ...., 97 end
Prime is Enumerable:
Prime.first 5 # => [2, 3, 5, 7, 11]
For convenience, each instance method of Prime.instance can be accessed as a class method of Prime.
e.g.
Prime.instance.prime?(2) #=> true Prime.prime?(2) #=> true
A “generator” provides an implementation of enumerating pseudo-prime numbers and it remembers the position of enumeration and upper bound. Furthermore, it is an external iterator of prime enumeration which is compatible with an Enumerator.
Prime::PseudoPrimeGenerator is the base class for generators. There are few implementations of generator.
Prime::EratosthenesGenerator Uses Eratosthenes' sieve.
Prime::TrialDivisionGenerator Uses the trial division method.
Prime::Generator23 Generates all positive integers which are not divisible by either 2 or 3. This sequence is very bad as a pseudo-prime sequence. But this is faster and uses much less memory than the other generators. So, it is suitable for factorizing an integer which is not large but has many prime factors. e.g. for Prime#prime? .
# File lib/prime.rb, line 212 def each(ubound = nil, generator = EratosthenesGenerator.new, &block) generator.upper_bound = ubound generator.each(&block) end
Iterates the given block over all prime numbers.
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.
An evaluated value of the given block at the last time. Or an enumerator which is compatible to an Enumerator if no block given.
Calls block once for each prime number, passing the prime as a parameter.
ubound Upper bound of prime numbers. The iterator stops after it yields all prime numbers p <= ubound.
# File lib/prime.rb, line 220
def include?(obj)
case obj
when Integer
prime?(obj)
when Module
Module.instance_method(:include?).bind(Prime).call(obj)
else
false
end
end Returns true if obj is an Integer and is prime. Also returns true if obj is a Module that is an ancestor of Prime. Otherwise returns false.
# File lib/prime.rb, line 268
def int_from_prime_division(pd)
pd.inject(1){|value, (prime, index)|
value * prime**index
}
end Re-composes a prime factorization and returns the product.
For the decomposition:
[[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.
pd Array of pairs of integers. Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).
Prime.int_from_prime_division([[3, 2], [5, 1]]) #=> 45 3**2 * 5 #=> 45
# File lib/prime.rb, line 238
def prime?(value, generator = Prime::Generator23.new)
raise ArgumentError, "Expected a prime generator, got #{generator}" unless generator.respond_to? :each
raise ArgumentError, "Expected an integer, got #{value}" unless value.respond_to?(:integer?) && value.integer?
return false if value < 2
generator.each do |num|
q,r = value.divmod num
return true if q < num
return false if r == 0
end
end Returns true if value is a prime number, else returns false. Integer#prime? is much more performant.
value an arbitrary integer to be checked.
generator optional. A pseudo-prime generator.
# File lib/prime.rb, line 303
def prime_division(value, generator = Prime::Generator23.new)
raise ZeroDivisionError if value == 0
if value < 0
value = -value
pv = [[-1, 1]]
else
pv = []
end
generator.each do |prime|
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
pv
end Returns the factorization of value.
For an arbitrary integer:
p_1**e_1 * p_2**e_2 * ... * p_n**e_n,
prime_division returns an array of pairs of integers:
[[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]].
Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).
value An arbitrary integer.
generator Optional. A pseudo-prime generator. generator.succ must return the next pseudo-prime number in ascending order. It must generate all prime numbers, but may also generate non-prime numbers, too.
ZeroDivisionError when value is zero.
Prime.prime_division(45) #=> [[3, 2], [5, 1]] 3**2 * 5 #=> 45
Ruby Core © 1993–2020 Yukihiro Matsumoto
Licensed under the Ruby License.
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Licensed under their own licenses.