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diff --git a/spec/ruby/library/matrix/lup_decomposition/to_a_spec.rb b/spec/ruby/library/matrix/lup_decomposition/to_a_spec.rb
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+++ b/spec/ruby/library/matrix/lup_decomposition/to_a_spec.rb
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+require File.expand_path('../../../../spec_helper', __FILE__)
+require 'matrix'
+
+describe "Matrix::LUPDecomposition#to_a" do
+  before :each do
+    @a = Matrix[[7, 8, 9], [14, 46, 51], [28, 82, 163]]
+    @lu = Matrix::LUPDecomposition.new(@a)
+    @to_a = @lu.to_a
+    @l, @u, @p = @to_a
+  end
+
+  it "returns an array of three matrices" do
+    @to_a.should be_kind_of(Array)
+    @to_a.length.should == 3
+    @to_a.each{|m| m.should be_kind_of(Matrix)}
+  end
+
+  it "returns [l, u, p] such that l*u == a*p" do
+    (@l * @u).should == (@p * @a)
+  end
+
+  it "returns the right values for rectangular matrices" do
+    [
+      Matrix[[7, 8, 9], [14, 46, 51]],
+      Matrix[[4, 11], [5, 8], [3, 4]],
+    ].each do |a|
+      l, u, p = Matrix::LUPDecomposition.new(a).to_a
+      (l * u).should == (p * a)
+    end
+  end
+
+  it "has other properties implied by the specs of #l, #u and #p"
+end