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Stored size: 1.6 KB
Contents
# coding: utf-8
describe Integer, "#mobius" do
# http://www.research.att.com/~njas/sequences/A008683
MOBIUS = [1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,-1,0,
1,1,-1,0,0,1,0,0,-1,-1,-1,0,1,1,1,0,-1,1,1,0,-1,
-1,-1,0,0,1,-1,0,0,0,1,0,-1,0,1,0,1,1,-1,0,-1,1,0,
0,1,-1,-1,0,1,-1,-1,0,-1,1,0,0,1]
it "returns 1 if n is a square-free positive integer with an even number of distinct prime factors" do
MOBIUS.each_with_index do |value, idx|
next unless value == 1
(idx + 1).mobius.should == 1
end
end
it "returns −1 if n is a square-free positive integer with an odd number of distinct prime factors" do
MOBIUS.each_with_index do |value, idx|
next unless value == -1
(idx + 1).mobius.should == -1
end
end
it "returns −1 if n is prime" do
Prime.each(200).each do |prime|
next if MOBIUS.size < prime
prime.mobius.should == -1
end
end
it "returns 0 iff n is not square-free." do
MOBIUS.each_with_index do |value, idx|
next unless value == 0
(idx + 1).mobius.should == 0
end
# http://www.research.att.com/~njas/sequences/A013929
[4,8,9,12,16,18,20,24,25,27,28,32,36,40,44,45,48,
49,50,52,54,56,60,63,64,68,72,75,76,80,81,84,88,
90,92,96,98,99,100,104,108,112,116,117,120,121,
124,125,126,128,132,135,136,140,144,147,148,150,
152,153,156,160].each do |number|
next if MOBIUS.size < number
number.mobius.should == 0
end
end
it "returns nil if n is not a positive integer" do
(0..25).each do |number|
(-number).mobius.should be_nil
end
end
end
Version data entries
16 entries across 16 versions & 1 rubygems