mvw · January 17, 2020 01:37 · Sep 4, 2015 · Sep 4, 2015 · Sep 4, 2015
diff --git a/cuberots.rb b/cuberots.rb
@@ -174,7 +174,7 @@ def number_to_names(s)
   p
 end
 
-n = 8
+n = 5
 k_show = 20
 k_last = 4**n - 1 - k_show
 
@@ -188,13 +188,17 @@ def number_to_names(s)
   a = p.split('').reverse
   a.each do |c|
     rot = Rotation.from_name(c) * rot
+    # add (and normalize) intermediate results
     known, rot_n = $rots.add(rot)
     if known
       rot = rot_n
     else
       show = true
     end
   end
+  # try to add the original alias
+  rot_orig = Rotation.new(p, rot.perm.s)
+  $rots.add(rot_orig)
   puts "k = #{k+1}: #{s} #{p} -> #{rot}" if show || k >= k_last
 end
 

diff --git a/cuberots.rb b/cuberots.rb
@@ -0,0 +1,201 @@
+#!/usr/bin/ruby
+# cuberots.rb
+
+class Permutation
+  attr_accessor :s
+  attr_accessor :h
+
+  def initialize(s = '12345678')
+    @s = s
+
+    a = @s.split('')
+    @h = Hash.new
+    i = '1'
+    a.each do |c|
+      @h[i] = c
+      i.next!
+    end
+  end
+
+  def to_s
+    return @s
+  end
+
+  # composition f*g means (f*g)(x) = f(g(x))
+  def *(g)
+    s = ''
+    c = '1'
+    8.times do
+      s += @h[g.h[c]]
+      c.next!
+    end
+    Permutation.new(s)
+  end
+
+end
+
+
+class Rotation
+  attr_accessor :name
+  attr_accessor :perm
+
+  def initialize(name = 'e', perm_s = '12345678')
+    @name = name
+    @perm = Permutation.new(perm_s)
+  end
+
+  def to_s
+    @name + '=' + @perm.to_s
+  end
+
+  # composition f*g means (f*g)(x) = f(g(x))
+  def *(g)
+    Rotation.new(@name + g.name, (@perm * g.perm).s)
+  end
+
+  # exponentiation
+  def **(k)
+    case
+    when k < 0
+      nil  # TODO find out inverse
+    when k == 0
+      $e
+    when k == 1
+      self
+    else
+      self * (self**(k-1))
+    end
+  end
+
+  # name to rotation
+  def self.from_name(c)
+    case
+    when c == 'e'
+      $e
+    when c == 'x'
+      $x
+    when c == 'y'
+      $y
+    when c == 'z'
+      $z
+    else
+      nil
+    end
+  end
+
+end
+
+
+class Rots
+  def initialize
+    @h = Hash.new
+  end
+
+  def to_s
+    s = "[\n"
+    k = 0
+    @h.each do |name, value|
+      k += 1
+      rot, aliases = value
+      s += "  k = #{k}: #{rot} #{aliases}\n"
+    end
+    s += "]\n"
+    s
+  end
+
+  # returns if known (and normalized version)
+  def add(rot)
+    rot_s = rot.perm.s
+    entry = @h[rot_s]
+    if entry.nil?
+      @h[rot_s] = [rot, []]
+      return false, nil
+    end
+    name = rot.name
+    rot_n, aliases = entry
+    if name == rot_n.name
+      return true, rot_n
+    end
+    if aliases.member?(name)
+      return true, rot_n
+    end
+    # new alias
+    aliases << name
+    @h[rot_s] = [rot_n, aliases]
+    return true, rot_n
+  end
+
+end
+
+
+# base rotations
+
+#    / 8 7       / 8 7
+#   /  5 6      /  5 6
+#   4 3 /   ->  4 3 /
+#   1 2/        1 2/
+$e = Rotation.new('e', '12345678')
+
+#    / 8 7       / 5 6
+#   /  5 6      /  1 2
+#   4 3 /   ->  8 7 /
+#   1 2/        4 3/
+$x = Rotation.new('x', '56218734')
+
+#    / 8 7       / 5 8
+#   /  5 6      /  6 7
+#   4 3 /   ->  1 4 /
+#   1 2/        2 3/
+$y = Rotation.new('y', '41238567')
+
+#    / 8 7       / 7 3
+#   /  5 6      /  6 2
+#   4 3 /   ->  8 4 /
+#   1 2/        5 1/
+$z = Rotation.new('z', '26731584')
+
+$rots = Rots.new
+
+$rots.add($e)
+$rots.add($x)
+$rots.add($y)
+$rots.add($z)
+
+puts "rots = #{$rots}"
+
+
+# translate digits into base rotations
+def number_to_names(s)
+  p = s.dup
+  p.gsub!(/0/, 'e')
+  p.gsub!(/1/, 'x')
+  p.gsub!(/2/, 'y')
+  p.gsub!(/3/, 'z')
+  p
+end
+
+n = 8
+k_show = 20
+k_last = 4**n - 1 - k_show
+
+# iterate in base 4 up to length n
+(4**n).times do |k|
+  s = k.to_s(4)
+  p = number_to_names(s)
+  # parse string, compose rotations
+  rot = $e
+  show = k < k_show ? true : false
+  a = p.split('').reverse
+  a.each do |c|
+    rot = Rotation.from_name(c) * rot
+    known, rot_n = $rots.add(rot)
+    if known
+      rot = rot_n
+    else
+      show = true
+    end
+  end
+  puts "k = #{k+1}: #{s} #{p} -> #{rot}" if show || k >= k_last
+end
+
+puts "rots = #{$rots}"