Integer#primitive_roots: Add

lib/numb/primitive_root.rb

@@ -1,6 +1,7 @@
 class Integer
   def primitive_root?(g=nil)
     if g
+      return true if g.zero? and self == 1
       coprime?(g) and g.modulo_order(self) == totient
     else
       return true if [1, 2, 4].include?(self)

lib/numb/primitive_roots.rb

@@ -0,0 +1,6 @@
+class Integer
+  def primitive_roots
+    return [] unless primitive_root?
+    (0..self).select{|n| primitive_root?(n)}
+  end
+end

spec/numb/primitive_root_spec.rb

@@ -67,4 +67,8 @@
       n.should be_primitive_root(7)
     end
   end
+
+  it "returns true when asked whether 0 is a primitive root of unity" do
+    1.should be_primitive_root(0)
+  end
 end

spec/numb/primitive_roots_spec.rb

@@ -0,0 +1,34 @@
+describe Integer, "#primitive_roots" do
+  # A046144
+  @seq = [1,1,1,1,2,1,2,0,2,2,4,0,4,2,0,0,8,2,6,0,0,4,10,0,
+          8,4,6,0,12,0,8,0,0,8,0,0,12,6,0,0,16,0,12,0,0,10,
+          22,0,12,8,0,0,24,6,0,0,0,12,28,0,16,8,0,0,0,0,20,
+          0,0,0,24,0,24,12,0,0,0,0,24,0,18,16,40,0,0,12,0,0,
+          40,0,0]
+
+  @seq.to_enum.with_index(1).each do |count,n|
+    pr = n.primitive_roots
+    it "returns #{count} primitive roots for #{n}" do
+      pr.size.should == count
+      pr.uniq.size.should == pr.size
+    end
+
+    pr.sample(2).each do |root|
+      it "returns actual primitive roots, e.g. #{root} for #{n}" do
+        n.primitive_root?(root)
+      end
+    end
+  end
+
+  # A046146 
+  @seq = [0,0,1,2,3,3,5,5,0,5,7,8,0,11,5,0,0,14,11,15,0,0,
+          19,21,0,23,19,23,0,27,0,24,0,0,31,0,0,35,33,0,0,
+          35,0,34,0,0,43,45,0,47,47,0,0,51,47,0,0,0,55,56,0,
+          59,55,0,0,0,0,63,0,0,0,69,0,68,69,0,0,0,0,77,0,77,
+          75,80,0,0].each_with_index.to_a.sample(15).each do |largest, n|
+    next if largest.zero?
+    it "returns #{largest} as the largest primitive root of #{n}" do
+      n.primitive_roots.max.should == largest
+    end
+  end
+end