Class: Algebra::PermutationGroup

Inherits:
Group show all
Defined in:
lib/algebra/permutation-group.rb

Instance Attribute Summary collapse

Attributes inherited from Group

#unity

Attributes inherited from Set

#body

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Group

#D, #K, #Z, #ascending_central_series, #center, #center?, #centralizer, #closed?, #commutator, #commutator_series, #complete, #complete!, #conjugacy_class, #conjugacy_classes, #descending_central_series, generate_strong, #nilpotency_class, #nilpotent?, #normal?, #normal_subgroups, #normalizer, #quotient_group, #semi_complete, #semi_complete!, #separate, #simple?, #solvable?, #subgroups, #to_a, #unit_group

Methods inherited from Set

#<, #>, [], #append, #append!, #bijections, #cast, #concat, #decreasing_series, #difference, #dup, #each, #each_member, #each_non_trivial_subset, #each_pair, #each_product, #each_subset, #empty?, #empty_set, empty_set, #eql?, #equiv_class, #hash, #identity_map, #include?, #increasing_series, #injections, #injections0, #inspect, #intersection, #map_s, new_a, new_h, null, phi, #pick, #power, #power_set, #product, #rehash, #separate, #shift, #singleton, singleton, #singleton?, #size, #sort, #subset?, #superset?, #surjections, #to_a, #to_ary, #to_s, #union

Methods included from OperatorDomain

#left_act, #left_orbit!, #left_quotient, #left_representatives, #right_act, #right_orbit!, #right_quotient, #right_representatives

Methods included from Enumerable

#all?, #any?, #collecti, #sum

Constructor Details

#initialize(u, *a) ⇒ PermutationGroup

Returns a new instance of PermutationGroup.



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# File 'lib/algebra/permutation-group.rb', line 37

def initialize(u, *a)
  @degree = u.degree
  super(u, *a)
end

Instance Attribute Details

#degree ⇒ Object (readonly)

Returns the value of attribute degree.



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# File 'lib/algebra/permutation-group.rb', line 42

def degree
  @degree
end

Class Method Details

.alternate(n) ⇒ Object 



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# File 'lib/algebra/permutation-group.rb', line 33

def self.alternate(n)
  symmetric(n).separate { |x| x.sign > 0 } # slow two times
end

.perm(a) ⇒ Object 



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# File 'lib/algebra/permutation-group.rb', line 21

def self.perm(a)
  Permutation.new(a)
end

.symmetric(n) ⇒ Object 



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# File 'lib/algebra/permutation-group.rb', line 25

def self.symmetric(n)
  s = new(unity(n))
  Combinatorial.perm(n) do |x|
    s << perm(x) # unity is not duplicated naturally
  end
  s
end

.unit_group(d) ⇒ Object 



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# File 'lib/algebra/permutation-group.rb', line 13

def self.unit_group(d)
  self[unity(d)]
end

.unity(n) ⇒ Object 



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# File 'lib/algebra/permutation-group.rb', line 17

def self.unity(n)
  Permutation.unity(n)
end