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

class TestMath < MiniTest::Unit::TestCase
  include Polynomials
  def test_roots_for_constant_functions
    polynomial = Polynomial.parse('5')
    assert_set_eql Set[],polynomial.roots
  end

  def test_roots_for_linear_functions
    polynomial = Polynomial.parse('5x + 2')
    assert_set_eql Set[Root.new(-2.0/5.0)],polynomial.roots
  end

  def test_roots_quadratic_functions
    polynomial = Polynomial.parse('3x^2 + 2x - 40')
    p = 2.0/3.0
    q = -40.0/3.0
    root = Math.sqrt((p/2)**2 - q)
    fraction = -(p/2)
    assert_set_eql Set[Root.new((fraction - root).round(10)), Root.new((fraction + root).round(10))],polynomial.roots

    polynomial = Polynomial.parse('3x^2 - 40')
    assert_set_eql Set[Root.new(Math.sqrt(40.0/3).round(10)), Root.new(-Math.sqrt(40.0/3).round(10))], polynomial.roots
  end

  def test_roots_for_cubic_functions
    polynomial = Polynomial.parse('1x^3  + 1x^2  + 2x - 1')
    assert_equal(1, polynomial.roots.size)
    assert_set_eql Set[Root.new(0.3926467817)], polynomial.roots

    polynomial = Polynomial.parse('2x^3  - 4x^2  - 22x + 24')
    assert_set_eql Set[Root.new(4.0),Root.new(-3.0),Root.new(1.0)], polynomial.roots
  end

  def test_roots_for_cubic_functions_with_complex
    coefficients = Polynomial.parse('3x^3   - 10x^2   + 14x + 27').terms.first(4).map{ |t| t.last.coefficient }
    assert_equal Set[-1.0, Complex(2.1666666666666634,2.0749832663314605), Complex(2.1666666666666634,-2.0749832663314605)],Formulas.roots_of_cubic_function(*coefficients, true)
  end

  def test_roots_for_cubic_functions_one_real_all_equal
    polynomial = Polynomial.parse('1x^3   + 6x^2   + 12x + 8')
    assert_equal(1, polynomial.roots.size)
    assert_equal(Root.new(-2), polynomial.roots.first)
  end

  def test_roots_for_quartic_functions
    polynomial = Polynomial.parse('3x^4   + 6x^3   - 123x^2   - 126x + 1080')
    assert_set_eql Set[Root.new(5.0), Root.new(3.0), Root.new(-4.0), Root.new(-6.0)], polynomial.roots

    polynomial = Polynomial.parse('-20x^4   + 5x^3   + 17x^2   - 29x + 87')
    assert_set_eql Set[Root.new(-1.6820039266),Root.new(1.4875831103)], polynomial.roots
  end

  def test_roots_without_term_with_exponent_of_zero
    polynomial = Polynomial.parse('3x^3 + 3x^2')
    assert_set_eql Set[Root.new(0.0),Root.new(-1.0)], polynomial.roots

    polynomial = Polynomial.parse('1 x^4')
    assert_set_eql Set[Root.new(0.0)], polynomial.roots
  end

  def test_roots_biquadratic_equation
    polynomial = Polynomial.parse('4x^4 + 2x^2 - 1')
    assert_set_eql Set[Root.new(0.5558929703), Root.new(-0.5558929703)], polynomial.roots
  end
end