一元三次方程解

cubic_equations.coffee

class @CubicEquations #加入 @ 跨作用域 绑定外层 this
  constructor: (@a, @b, @c, @d) ->
    @init()
    @calc()
    @result()

  get_cube_root = (value) ->
    if value < 0
      -Math.pow(-value, 1/3)
    else if value > 0
      Math.pow(value, 1/3)
    else
      0

  init: ->
    @A = @b * @b - 3 * @a * @c
    @B = @b * @c - 9 * @a * @d
    @C = @c * @c - 3 * @b * @d
    @delta = @B * @B - 4 * @A * @C

  A_and_B_equal_zero: ->
    @x1 = -@b / (3*@a)
    @x2 = @x1
    @x3 = @x1

  delta_equal_zero: ->
    k = @B / @A
    @x1 = -@b / @a + k
    @x2 = @x1
    @x3 = @x1

  delta_greater_zero: ->
    Y1 = @A * @b + 3 * @a * ( ( -@B + Math.sqrt(@delta) ) / 2 )
    Y2 = @A * @b + 3 * @a * ( ( -@B - Math.sqrt(@delta) ) / 2 )

    @x1 = ( -@b - ( get_cube_root(Y1) + get_cube_root(Y2) ) ) / (3 * @a)

    @x2 = 0
    @x3 = 0
    # @x2 @x3 是复数

  delta_less_zero: ->
    T = (2 * @A * @b - 3 * @a * @B) / (2 * Math.sqrt(@A * @A * @A))
    angle = Math.acos(T) / 3
    @x1 = (-@b - 2 * Math.sqrt(@A) * Math.cos(angle/3)) / (3 * @a);
    @x2 = (-@b + Math.sqrt(@A) * (Math.cos(angle/3) + Math.sqrt(3) * Math.sin(angle/3))) / (3 * @a)
    @x3 = (-@b + Math.sqrt(@A) * (Math.cos(angle/3) - Math.sqrt(3) * Math.sin(angle/3))) / (3 * @a)

  calc: ->
    if @A == 0 && @B== 0
      @A_and_B_equal_zero()
    else if @delta ==  0
      @delta_equal_zero()
    else if @delta > 0
      @delta_greater_zero()
    else
      @delta_less_zero()

  result: ->
    @result = Math.max(@x1, @x2, @x3)