Class: Prime
Relationships & Source Files | |
Namespace Children | |
Classes:
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Super Chains via Extension / Inclusion / Inheritance | |
Class Chain:
self,
Enumerable,
Forwardable
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Instance Chain:
self,
Singleton,
Enumerable
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Inherits: | Object |
Defined in: | lib/prime.rb |
Overview
The set of all prime numbers.
Example
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]
Retrieving the 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
Generators
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? .
Instance Method Summary
-
#each(ubound = nil, generator = EratosthenesGenerator.new, &block)
Iterates the given block over all prime numbers.
-
#int_from_prime_division(pd)
Re-composes a prime factorization and returns the product.
-
#prime?(value, generator = Prime::Generator23.new) ⇒ Boolean
Returns true if
value
is a prime number, else returns false. -
#prime_division(value, generator = Prime::Generator23.new)
Returns the factorization of
value
.
Instance Method Details
#each(ubound = nil, generator = EratosthenesGenerator.new, &block)
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 it yields all prime numbers p <=
ubound
.
# File 'lib/prime.rb', line 135
def each(ubound = nil, generator = EratosthenesGenerator.new, &block) generator.upper_bound = ubound generator.each(&block) end
#int_from_prime_division(pd)
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 'lib/prime.rb', line 171
def int_from_prime_division(pd) pd.inject(1){|value, (prime, index)| value * prime**index } end
#prime?(value, generator = Prime::Generator23.new) ⇒ Boolean
Returns true if value
is a prime number, else returns false.
Parameters
value
-
an arbitrary integer to be checked.
generator
-
optional. A pseudo-prime generator.
# File 'lib/prime.rb', line 147
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
#prime_division(value, generator = Prime::Generator23.new)
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 ascending order. It must generate all prime numbers, but may also generate non prime numbers too.
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 'lib/prime.rb', line 201
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