require "#{File.dirname(File.expand_path(__FILE__))}/test_helper"

Infinity = 1.0/0
class TestPolynomial < MiniTest::Unit::TestCase
  include Polynomials
  def test_to_s
    polynomial = Polynomial.parse('5x + 2x^2 + 20')
    assert_equal '2x^2 + 5x + 20', polynomial.to_s
    polynomial = Polynomial.parse('6.5435x^234 + 5.0 + 20x')
    assert_equal '6.5435x^234 + 20x + 5', polynomial.to_s
    polynomial = Polynomial.parse('0x^0')
    assert_equal "0", polynomial.to_s
  end

  def test_derivative_of_linear_functions
    polynomial = Polynomial.parse('5x + 2')
    assert_equal Polynomial.parse('5') ,polynomial.derivative
  end

  def test_derivative_functions_with_higher_degree
    polynomial = Polynomial.parse('5.5x^4 + 3.5x^3 + 2x^2 + 2x + 50')
    assert_equal Polynomial.parse('22x^3 + 10.5x^2 + 4x + 2'), polynomial.derivative
  end

  def test_calculation
    polynomial = Polynomial.parse('2x^4 - 1 x')
    assert_equal 1245, polynomial.calculate(5)
  end

  def test_parsing
    assert_equal 0, Polynomial.parse('2').terms.values.first.exponent
    assert_equal 2, Polynomial.parse('2').terms.values.first.coefficient

    terms = Polynomial.parse('2x^2 + 5.5x^1 - 20').terms.values.sort_by(&:exponent).reverse
    assert_equal [2,1,0], terms.map(&:exponent)
    assert_equal [2,5.5,-20], terms.map(&:coefficient)
  end

  def test_equality
    assert_equal Polynomial.parse('3x^1 + 5'), Polynomial.parse('3x + 5 x^0')
  end

  def test_degree
    assert_equal 5,Polynomial.parse('3x^5 - 5 x + 3').degree
  end

  def test_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)
    polynomial = Polynomial.parse('5x^3 - 5x^2 + 2x - 2')
  end

  def test_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)
    assert_set_eql(Set[*[Infinity,-Infinity].map { |x| Extremum.new(x,nil, :maximum)}, Extremum.new(0.0,polynomial.calculate(0.0), :minimum) ], polynomial.extrema)
  end

  def test_no_local_extrema
    polynomial = Polynomial.parse('6x^6 - 5x + 50')
    assert_equal(Set[], polynomial.local_extrema)
    assert_set_eql(Set[*[ -1.0/0, 1.0/0 ].map { |x| Extremum.new(x, nil, :maximum)}], polynomial.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_extremums
    polynomial = Polynomial.parse('5')
    assert_equal(Set[], polynomial.extrema)
  end

  def test_no_curvature
    polynomials = []
    polynomials << Polynomial.parse('5 x + 4')
    polynomials << Polynomial.parse('4')
    polynomials.each do |polynomial|
      assert_equal({}, polynomial.curvature_behaviour)
    end
  end

  def test_local_extrema_of_derivative_leads_to_no_curvature
    polynomial = Polynomial.parse('50x^10 - 20x^2')
    assert_equal({}, 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_efficient_roots_calculation
    polynomial = Polynomial.parse('200x^2342435 + 6x^20')
    assert_set_eql(Set[Root.new(0.0)], polynomial.roots)
  end

  def test_lt
    polynomial = Polynomial.parse('1x^2342435 + 5x')
    assert_euqal Term.new(5,1), polynomial.lt
  end

  def test_lt
    polynomial = Polynomial.parse('1x^2342435 + 5x')
    assert_equal Term.new(2342435,1), polynomial.gt
  end

  def test_initalizer
    polynomial = Polynomial.new(5,0,2,-1)
    assert_equal '5x^3 + 2x - 1', polynomial.to_s
  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
end