require "#{File.dirname(File.expand_path(__FILE__))}/test_helper"
Infinity = 1.0/0
class TestAnalyzable < MiniTest::Unit::TestCase
  include Polynomials

  def test_local_extrema
    polynomial = Polynomial.parse('3x^2 + 2x + 1')
    assert_set_eql(Set[ Extremum.new(-2.0/6.0,polynomial.calculate(-2.0/6.0), :minimum) ], polynomial.local_extrema)
  end

  def test_local_extrema_with_slope_of_derivative_equal_to_zero
    polynomial = Polynomial.parse('1x^4')
    assert_set_eql(Set[ Extremum.new(0.0,polynomial.calculate(0.0), :minimum) ], polynomial.local_extrema)
  end

  def test_no_local_extrema
    polynomial = Polynomial.parse('6x^6 - 5x + 50')
    assert_equal(Set[], polynomial.local_extrema)
  end

  def test_curvature_behaviour_no_inflection_points
    polynomial = Polynomial.parse('1 x^4')
    assert_equal({ left: [[-1.0/0,+1.0/0]] }, polynomial.curvature_behaviour)

    polynomial = Polynomial.parse('-1 x^4')
    assert_equal({ right: [[-1.0/0,+1.0/0]] }, polynomial.curvature_behaviour)

    polynomial = Polynomial.parse('5x^2')
    assert_equal({ left: [[-1.0/0,+1.0/0]] }, polynomial.curvature_behaviour)
  end

  def test_no_curvature
    polynomials = []
    polynomials << Polynomial.parse('0')
    polynomials << Polynomial.parse('4')
    polynomials.each do |polynomial|
      assert_equal(nil, polynomial.curvature_behaviour)
    end
  end

  def test_no_local_extrema_of_derivative_leads_to_no_curvature
    polynomial = Polynomial.parse('50x^10 - 20x^2')
    assert_equal({:left=>[[-Infinity, Infinity]]}, polynomial.curvature_behaviour)
  end

  def test_curvature_behaviour_two_inflection_points
    polynomial = Polynomial.parse('+ 1.0 x^4 + 5.0 x^3 - 1.0 x^2 + 3.0 x + 5.0')
    assert_equal({left:[[-1.0/0,-2.5649778198], [0.0649778198,1.0/0]], right: [[-2.5649778198,0.0649778198]] } , polynomial.curvature_behaviour)
  end

  def test_curvature_behaviour_three_inflection_points
    polynomial = Polynomial.new(20,4,0,-1,-200)
    assert_equal( {:right=>[[(-1/10),0.0]], :left=>[[-Infinity,(-1/10)], [0.0,Infinity]]}, polynomial.curvature_behaviour)
  end

  def test_inflection_points
    polynomial = Polynomial.new(20,4,0,-1,-200)
    assert_set_eql Set[InflectionPoint.new(-1/10,polynomial.(-1/10)),InflectionPoint.new(0,polynomial.(0))], polynomial.inflection_points
  end

  def test_strives_for
    polynomial = Polynomial.new(2,0,0)
    assert_equal [Infinity,Infinity], polynomial.strives_for
    polynomial = Polynomial.new(-2,0,0)
    assert_equal [-Infinity,-Infinity], polynomial.strives_for
    polynomial = Polynomial.new(2,0,0,0)
    assert_equal [-Infinity,Infinity], polynomial.strives_for
    polynomial = Polynomial.new(-2,0,0,0)
    assert_equal [Infinity,-Infinity], polynomial.strives_for
    polynomial = Polynomial.new(2)
    assert_equal nil, polynomial.strives_for

    polynomial = Polynomial.parse('+ 1.0 x^4 + 5.0 x^3 - 1.0 x^2 + 3.0 x + 5.0').derivative
    assert_equal [-Infinity,Infinity], polynomial.strives_for
  end
end