{
  "exercise": "complex-numbers",
  "version": "1.2.0",
  "comments": [
    " The canonical data assumes mathematically correct real   ",
    " numbers. The testsuites should consider rounding errors  ",
    " instead of testing for exact values for any non-integer  ",
    " tests.                                                   ",
    " Complex numbers z are represented as arrays [x, y] so    ",
    " that z = x + i * y.                                      ",
    " Pi is represented as a string \"pi\", euler's number is  ",
    " represented as \"e\".                                    "
  ],
  "cases": [
    {
      "description": "Real part",
      "cases": [
        {
          "description": "Real part of a purely real number",
          "property": "real",
          "input": {
            "z": [1, 0]
          },
          "expected": 1
        },
        {
          "description": "Real part of a purely imaginary number",
          "property": "real",
          "input": {
            "z": [0, 1]
          },
          "expected": 0
        },
        {
          "description": "Real part of a number with real and imaginary part",
          "property": "real",
          "input": {
            "z": [1, 2]
          },
          "expected": 1
        }
      ]
    },
    {
      "description": "Imaginary part",
      "cases": [
        {
          "description": "Imaginary part of a purely real number",
          "property": "imaginary",
          "input": {
            "z": [1, 0]
          },
          "expected": 0
        },
        {
          "description": "Imaginary part of a purely imaginary number",
          "property": "imaginary",
          "input": {
            "z": [0, 1]
          },
          "expected": 1
        },
        {
          "description": "Imaginary part of a number with real and imaginary part",
          "property": "imaginary",
          "input":  {
            "z": [1, 2]
          },
          "expected": 2
        }
      ]
    },
    {
      "description": "Imaginary unit",
      "property": "mul",
      "input": {
        "z1": [0, 1],
        "z2": [0, 1]
      },
      "expected": [-1, 0]
    },
    {
      "description": "Arithmetic",
      "cases": [
        {
          "description": "Addition",
          "cases": [
            {
              "description": "Add purely real numbers",
              "property": "add",
              "input": {
                "z1": [1, 0],
                "z2": [2, 0]
              },
              "expected": [3, 0]
            },
            {
              "description": "Add purely imaginary numbers",
              "property": "add",
              "input": {
                "z1": [0, 1],
                "z2": [0, 2]
              },
              "expected": [0, 3]
            },
            {
              "description": "Add numbers with real and imaginary part",
              "property": "add",
              "input": {
                "z1": [1, 2],
                "z2": [3, 4]
              },
              "expected": [4, 6]
            }
          ]
        },
        {
          "description": "Subtraction",
          "cases": [
            {
              "description": "Subtract purely real numbers",
              "property": "sub",
              "input": {
                "z1": [1, 0],
                "z2": [2, 0]
              },
              "expected": [-1, 0]
            },
            {
              "description": "Subtract purely imaginary numbers",
              "property": "sub",
              "input": {
                "z1": [0, 1],
                "z2": [0, 2]
              },
              "expected": [0, -1]
            },
            {
              "description": "Subtract numbers with real and imaginary part",
              "property": "sub",
              "input": {
                "z1": [1, 2],
                "z2": [3, 4]
              },
              "expected": [-2, -2]
            }
          ]
        },
        {
          "description": "Multiplication",
          "cases": [
            {
              "description": "Multiply purely real numbers",
              "property": "mul",
              "input": {
                "z1": [1, 0],
                "z2": [2, 0]
              },
              "expected": [2, 0]
            },
            {
              "description": "Multiply purely imaginary numbers",
              "property": "mul",
              "input": {
                "z1": [0, 1],
                "z2": [0, 2]
              },
              "expected": [-2, 0]
            },
            {
              "description": "Multiply numbers with real and imaginary part",
              "property": "mul",
              "input": {
                "z1": [1, 2],
                "z2": [3, 4]
              },
              "expected": [-5, 10]
            }
          ]
        },
        {
          "description": "Division",
          "cases": [
            {
              "description": "Divide purely real numbers",
              "property": "div",
              "input": {
                "z1": [1, 0],
                "z2": [2, 0]
              },
              "expected": [0.5, 0]
            },
            {
              "description": "Divide purely imaginary numbers",
              "property": "div",
              "input": {
                "z1": [0, 1],
                "z2": [0, 2]
              },
              "expected": [0.5, 0]
            },
            {
              "description": "Divide numbers with real and imaginary part",
              "property": "div",
              "input": {
                "z1": [1, 2],
                "z2": [3, 4]
              },
              "expected": [0.44, 0.08]
            }
          ]
        }
      ]
    },
    {
      "description": "Absolute value",
      "cases": [
        {
          "description": "Absolute value of a positive purely real number",
          "property": "abs",
          "input": {
            "z": [5, 0]
          },
          "expected": 5
        },
        {
          "description": "Absolute value of a negative purely real number",
          "property": "abs",
          "input": {
            "z": [-5, 0]
          },
          "expected": 5
        },
        {
          "description": "Absolute value of a purely imaginary number with positive imaginary part",
          "property": "abs",
          "input": {
            "z": [0, 5]
          },
          "expected": 5
        },
        {
          "description": "Absolute value of a purely imaginary number with negative imaginary part",
          "property": "abs",
          "input": {
            "z": [0, -5]
          },
          "expected": 5
        },
        {
          "description": "Absolute value of a number with real and imaginary part",
          "property": "abs",
          "input": {
            "z": [3, 4]
          },
          "expected": 5
        }
      ]
    },
    {
      "description": "Complex conjugate",
      "cases": [
        {
          "description": "Conjugate a purely real number",
          "property": "conjugate",
          "input": {
            "z": [5, 0]
          },
          "expected": [5, 0]
        },
        {
          "description": "Conjugate a purely imaginary number",
          "property": "conjugate",
          "input": {
            "z": [0, 5]
          },
          "expected": [0, -5]
        },
        {
          "description": "Conjugate a number with real and imaginary part",
          "property": "conjugate",
          "input": {
            "z": [1, 1]
          },
          "expected": [1, -1]
        }
      ]
    },
    {
      "description": "Complex exponential function",
      "comments": [
        " Defining the exponential function can be optional.       ",
        " If the language used does not have sine and cosine       ",
        " functions in the standard library, this will be          ",
        " significantly more difficult than the rest of the exer-  ",
        " cise and should probably not be part of the problem.     ",
        " The recommended implementation uses Euler's formula      ",
        " exp(ix) = cos(x) + i * sin(x). This is not an ideal sol- ",
        " ution but works for the purpose of teaching complex      ",
        " numbers.                                                 "
      ],
      "cases": [
        {
          "description": "Euler's identity/formula",
          "property": "exp",
          "input":  {
            "z": [0, "pi"]
          },
          "expected": [-1, 0]
        },
        {
          "description": "Exponential of 0",
          "property": "exp",
          "input": {
            "z": [0, 0]
          },
          "expected": [1, 0]
        },
        {
          "description": "Exponential of a purely real number",
          "property": "exp",
          "input": {
            "z": [1, 0]
          },
          "expected": ["e", 0]
        }
      ]
    }
  ]
}