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Object
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]
Prime
.new is obsolete. Now Prime
has the default
instance and you can access it as Prime
.instance.
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 a external iterator of prime enumeration which is compatible to an Enumerator.
Prime
::PseudoPrimeGenerator
is the base class for
generators. There are few implementations of generator.
Prime
::EratosthenesGenerator
Uses eratosthenes’s sieve.
Prime
::TrialDivisionGenerator
Uses the trial division method.
Prime
::Generator23
Generates all positive integers which is not divided by 2 nor 3. This sequence is very bad as a pseudo-prime sequence. But this is faster and uses much less memory than other generators. So, it is suitable for factorizing an integer which is not large but has many prime factors. e.g. for #prime? .
Returns the default instance of Prime.
# File prime.rb, line 106 def instance; @the_instance 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 yields all prime
numbers p <= ubound
.
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.
pd
Array of pairs of integers. The each internal pair consists of a prime number – a prime factor – and a natural number – an exponent.
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.
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
.
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.
ZeroDivisionError
when value
is zero.
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
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