Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "e^{i\\theta} = \\cos\\theta + i \\sin\\theta",
      "chartScript": {
        "script": "-i*sin(theta) + exp(i*theta) - cos(theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{i \\theta}",
      "chartScript": {
        "script": "exp(i*theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "e",
      "type": "scalar",
      "latex": "e",
      "subexpr": "e",
      "chartScript": {
        "script": "e",
        "variables": []
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\theta",
      "chartScript": {
        "script": "i*theta",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "i \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "i*sin(theta) + cos(theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "__cos_5",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "cos(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "i*sin(theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "__sin_7",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "sin(theta)",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "e",
      "to": "__power_2"
    },
    {
      "from": "i",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__power_2",
      "role": "exp"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    },
    {
      "from": "theta",
      "to": "__cos_5"
    },
    {
      "from": "__cos_5",
      "to": "__add_4"
    },
    {
      "from": "i",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_7"
    },
    {
      "from": "__sin_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __power_2(("$(\cdot)^{\cdot}$")):::operator
  e["$e$"]:::scalar
  __multiply_3(("$\times$")):::operator
  i["$i$"]:::scalar
  theta["$\theta$"]:::scalar
  __add_4(("$+$")):::operator
  __cos_5{{"$\cos(\cdot)$"}}:::function
  __multiply_6(("$\times$")):::operator
  __sin_7{{"$\sin(\cdot)$"}}:::function
  e --> __power_2
  i --> __multiply_3
  theta --> __multiply_3
  __multiply_3 -->|exp| __power_2
  __power_2 --> __equals_1
  theta --> __cos_5
  __cos_5 --> __add_4
  i --> __multiply_6
  theta --> __sin_7
  __sin_7 --> __multiply_6
  __multiply_6 --> __add_4
  __add_4 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#ef5350,stroke-width:3px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#ef5350,stroke-width:3px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "e^{i\\pi} + 1 = 0",
      "chartScript": {
        "script": "exp(pi*i) + 1",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "e^{i \\pi} + 1",
      "chartScript": {
        "script": "exp(pi*i) + 1",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{i \\pi}",
      "chartScript": {
        "script": "exp(pi*i)",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "e",
      "type": "scalar",
      "latex": "e",
      "subexpr": "e",
      "chartScript": {
        "script": "e",
        "variables": []
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\pi",
      "chartScript": {
        "script": "pi*i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    },
    {
      "id": "__num_5",
      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "e",
      "to": "__power_3"
    },
    {
      "from": "i",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pi",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__power_3",
      "role": "exp"
    },
    {
      "from": "__power_3",
      "to": "__add_2"
    },
    {
      "from": "__num_5",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_6",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __add_2(("$+$")):::operator
  __power_3(("$(\cdot)^{\cdot}$")):::operator
  e["$e$"]:::scalar
  __multiply_4(("$\times$")):::operator
  i["$i$"]:::scalar
  pi["$\pi$"]:::constant
  __num_5["$1$"]:::number
  __num_6["$0$"]:::number
  e --> __power_3
  i --> __multiply_4
  pi --> __multiply_4
  __multiply_4 -->|exp| __power_3
  __power_3 --> __add_2
  __num_5 --> __add_2
  __add_2 --> __equals_1
  __num_6 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "|z| = \\sqrt{a^2 + b^2}",
      "chartScript": {
        "script": "-sqrt(pow(a, 2) + pow(b, 2)) + abs(z)",
        "variables": [
          "a",
          "b",
          "z"
        ]
      }
    },
    {
      "id": "__abs_2",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{z}\\right|"
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "exponent": "1/2",
      "subexpr": "\\sqrt{a^{2} + b^{2}}",
      "chartScript": {
        "script": "sqrt(pow(a, 2) + pow(b, 2))",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "a^{2} + b^{2}",
      "chartScript": {
        "script": "pow(a, 2) + pow(b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "a^{2}",
      "chartScript": {
        "script": "pow(a, 2)",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "b^{2}",
      "chartScript": {
        "script": "pow(b, 2)",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "z",
      "to": "__abs_2"
    },
    {
      "from": "__abs_2",
      "to": "__equals_1"
    },
    {
      "from": "a",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__add_4"
    },
    {
      "from": "b",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __abs_2{{"$|\cdot|$"}}:::function
  z["$z$"]:::scalar
  __power_3(("${(\cdot)}^{1/2}$")):::operator
  __add_4(("$+$")):::operator
  __power_5(("${(\cdot)}^{2}$")):::operator
  a["$a$"]:::scalar
  __power_6(("${(\cdot)}^{2}$")):::operator
  b["$b$"]:::scalar
  z --> __abs_2
  __abs_2 --> __equals_1
  a --> __power_5
  __power_5 --> __add_4
  b --> __power_6
  __power_6 --> __add_4
  __add_4 --> __power_3
  __power_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:6px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:6px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "z = r e^{i\\theta}",
      "chartScript": {
        "script": "-r*exp(i*theta) + z",
        "variables": [
          "i",
          "r",
          "theta",
          "z"
        ]
      }
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "r e^{i \\theta}",
      "chartScript": {
        "script": "r*exp(i*theta)",
        "variables": [
          "i",
          "r",
          "theta"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{i \\theta}",
      "chartScript": {
        "script": "exp(i*theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "e",
      "type": "scalar",
      "latex": "e",
      "subexpr": "e",
      "chartScript": {
        "script": "e",
        "variables": []
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\theta",
      "chartScript": {
        "script": "i*theta",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "z",
      "to": "__equals_1"
    },
    {
      "from": "r",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "e",
      "to": "__power_3"
    },
    {
      "from": "i",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__power_3",
      "role": "exp"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  z["$z$"]:::scalar
  __multiply_2(("$\times$")):::operator
  r["$r$"]:::scalar
  __power_3(("$(\cdot)^{\cdot}$")):::operator
  e["$e$"]:::scalar
  __multiply_4(("$\times$")):::operator
  i["$i$"]:::scalar
  theta["$\theta$"]:::scalar
  z --> __equals_1
  r --> __multiply_2
  e --> __power_3
  i --> __multiply_4
  theta --> __multiply_4
  __multiply_4 -->|exp| __power_3
  __power_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "z \\overline{z} = |z|^2",
      "chartScript": {
        "script": "z*conjugate(z) - pow(abs(z), 2)",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "z \\overline{z}",
      "chartScript": {
        "script": "z*conjugate(z)",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "overlinez",
      "type": "scalar",
      "label": "\\overline{z}",
      "latex": "\\overline{z}",
      "subexpr": "\\overline{z}",
      "chartScript": {
        "script": "conjugate(z)",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "\\left|{z}\\right|^{2}"
    },
    {
      "id": "__abs_4",
      "type": "function",
      "op": "abs",
      "subexpr": "\\left|{z}\\right|"
    }
  ],
  "edges": [
    {
      "from": "z",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "overlinez",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "z",
      "to": "__abs_4"
    },
    {
      "from": "__abs_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  z["$z$"]:::scalar
  overlinez["$\overline{z}$"]:::scalar
  __power_3(("${(\cdot)}^{2}$")):::operator
  __abs_4{{"$|\cdot|$"}}:::function
  z --> __multiply_2
  overlinez --> __multiply_2
  __multiply_2 --> __equals_1
  z --> __abs_4
  __abs_4 --> __power_3
  __power_3 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:6px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "f(a) = \\frac{1}{2\\pi i} \\oint \\frac{f(z)}{z - a} dz",
      "chartScript": {
        "script": "-1/2*dz*oint*f(z)/(pi*i*(-a + z)) + f(a)",
        "variables": [
          "a",
          "dz",
          "i",
          "oint",
          "z"
        ]
      }
    },
    {
      "id": "__f_2",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(a \\right)}",
      "chartScript": {
        "script": "a*f",
        "variables": [
          "a",
          "f"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{2 i \\pi} \\int \\frac{f{\\left(z \\right)}}{- a + z}\\, dz",
      "chartScript": {
        "script": "(1/2)*f*(a*log(-a + z) + z)/(pi*i)",
        "variables": [
          "a",
          "f",
          "i",
          "z"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2 i \\pi}",
      "chartScript": {
        "script": "(1/2)/(pi*i)",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "2 \\pi i",
      "chartScript": {
        "script": "2*pi*i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\pi i",
      "chartScript": {
        "script": "pi*i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__closed_integral_8",
      "type": "operator",
      "op": "closed_integral",
      "with_respect_to": "z",
      "subexpr": "\\int \\frac{f{\\left(z \\right)}}{- a + z}\\, dz",
      "chartScript": {
        "script": "f*(a*log(-a + z) + z)",
        "variables": [
          "a",
          "f",
          "z"
        ]
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "f{\\left(z \\right)} \\frac{1}{- a + z}",
      "chartScript": {
        "script": "f*z/(-a + z)",
        "variables": [
          "a",
          "f",
          "z"
        ]
      }
    },
    {
      "id": "__f_10",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(z \\right)}",
      "chartScript": {
        "script": "f*z",
        "variables": [
          "f",
          "z"
        ]
      }
    },
    {
      "id": "__power_11",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{- a + z}",
      "chartScript": {
        "script": "1/(-a + z)",
        "variables": [
          "a",
          "z"
        ]
      }
    },
    {
      "id": "__add_12",
      "type": "operator",
      "op": "add",
      "subexpr": "z - a",
      "chartScript": {
        "script": "-a + z",
        "variables": [
          "a",
          "z"
        ]
      }
    },
    {
      "id": "__negation_13",
      "type": "operator",
      "op": "negation",
      "subexpr": "-a",
      "chartScript": {
        "script": "-a",
        "variables": [
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "a",
      "to": "__f_2"
    },
    {
      "from": "__f_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pi",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "i",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3"
    },
    {
      "from": "z",
      "to": "__closed_integral_8",
      "role": "wrt"
    },
    {
      "from": "z",
      "to": "__f_10"
    },
    {
      "from": "__f_10",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "z",
      "to": "__add_12"
    },
    {
      "from": "a",
      "to": "__negation_13"
    },
    {
      "from": "__negation_13",
      "to": "__add_12"
    },
    {
      "from": "__add_12",
      "to": "__power_11"
    },
    {
      "from": "__power_11",
      "to": "__multiply_9"
    },
    {
      "from": "__multiply_9",
      "to": "__closed_integral_8"
    },
    {
      "from": "__closed_integral_8",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __f_2{{"$f(\cdot)$"}}:::function
  a["$a$"]:::scalar
  __multiply_3(("$\times$")):::operator
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_5(("$\times$")):::operator
  __num_6["$2$"]:::number
  __multiply_7(("$\times$")):::operator
  pi["$\pi$"]:::constant
  i["$i$"]:::scalar
  z["$z$"]:::scalar
  __closed_integral_8(("$\oint dz$")):::operator
  __multiply_9(("$\times$")):::operator
  __f_10{{"$f(\cdot)$"}}:::function
  __power_11(("$\dfrac{1}{(\cdot)}$")):::operator
  __add_12(("$+$")):::operator
  __negation_13@{ shape: "flip-tri", label: "$-$" }
  class __negation_13 operator
  a --> __f_2
  __f_2 --> __equals_1
  __num_6 --> __multiply_5
  pi --> __multiply_7
  i --> __multiply_7
  __multiply_7 --> __multiply_5
  __multiply_5 --> __power_4
  __power_4 -.-> __multiply_3
  z -->|wrt| __closed_integral_8
  z --> __f_10
  __f_10 --> __multiply_9
  z --> __add_12
  a --> __negation_13
  __negation_13 --> __add_12
  __add_12 --> __power_11
  __power_11 -.-> __multiply_9
  __multiply_9 --> __closed_integral_8
  __closed_integral_8 --> __multiply_3
  __multiply_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#42a5f5,stroke-width:1px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#42a5f5,stroke-width:1px
  linkStyle 16 stroke:#aaa,stroke-width:2px
  linkStyle 17 stroke:#ef5350,stroke-width:3px
  linkStyle 18 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\oint f(z) dz = 2\\pi i \\sum_{\\iota=0}^{\\infty} \\text{Res}(f, z_k)",
      "chartScript": {
        "script": "-Number.POSITIVE_INFINITY*R*i*s*text + dz*oint*f(z)",
        "variables": [
          "R",
          "dz",
          "i",
          "oint",
          "s",
          "text",
          "z"
        ]
      }
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "__closed_integral_2",
      "type": "operator",
      "op": "closed_integral",
      "with_respect_to": "z",
      "subexpr": "\\int f{\\left(z \\right)}\\, dz",
      "chartScript": {
        "script": "(1/2)*f*pow(z, 2)",
        "variables": [
          "f",
          "z"
        ]
      }
    },
    {
      "id": "__f_3",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(z \\right)}",
      "chartScript": {
        "script": "f*z",
        "variables": [
          "f",
          "z"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "2 \\pi i \\sum \\text{Res}{\\left(f,z_{k} \\right)}",
      "chartScript": {
        "script": "2*pi*i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__num_5",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\pi i \\sum \\text{Res}{\\left(f,z_{k} \\right)}",
      "chartScript": {
        "script": "pi*i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\sum \\text{Res}{\\left(f,z_{k} \\right)}",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__sum_8",
      "type": "operator",
      "op": "sum",
      "subexpr": "\\sum \\text{Res}{\\left(f,z_{k} \\right)}"
    },
    {
      "id": "Res_9",
      "type": "function",
      "latex": "\\text{Res}",
      "op": "alpha",
      "subexpr": "\\text{Res}{\\left(f,z_{k} \\right)}",
      "chartScript": {
        "script": "e*R*s*text",
        "variables": [
          "R",
          "s",
          "text"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "z_k",
      "type": "scalar",
      "latex": "z_{k}",
      "subexpr": "z_{k}",
      "chartScript": {
        "script": "z_k",
        "variables": [
          "z_k"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "z",
      "to": "__closed_integral_2",
      "role": "wrt"
    },
    {
      "from": "z",
      "to": "__f_3"
    },
    {
      "from": "__f_3",
      "to": "__closed_integral_2"
    },
    {
      "from": "__closed_integral_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pi",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "i",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "f",
      "to": "Res_9"
    },
    {
      "from": "z_k",
      "to": "Res_9"
    },
    {
      "from": "Res_9",
      "to": "__sum_8"
    },
    {
      "from": "__sum_8",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  z["$z$"]:::scalar
  __closed_integral_2(("$\oint dz$")):::operator
  __f_3{{"$f(\cdot)$"}}:::function
  __multiply_4(("$\times$")):::operator
  __num_5["$2$"]:::number
  __multiply_6(("$\times$")):::operator
  pi["$\pi$"]:::constant
  __multiply_7(("$\times$")):::operator
  i["$i$"]:::scalar
  __sum_8(("$\sum$")):::operator
  Res_9{{"$\text{Res}(\cdot, \cdot)$"}}:::function
  f["$f$"]:::scalar
  z_k["$z_{k}$"]:::scalar
  z -->|wrt| __closed_integral_2
  z --> __f_3
  __f_3 --> __closed_integral_2
  __closed_integral_2 --> __equals_1
  __num_5 --> __multiply_4
  pi --> __multiply_6
  i --> __multiply_7
  f --> Res_9
  z_k --> Res_9
  Res_9 --> __sum_8
  __sum_8 --> __multiply_7
  __multiply_7 --> __multiply_6
  __multiply_6 --> __multiply_4
  __multiply_4 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#ef5350,stroke-width:3px
  linkStyle 12 stroke:#ef5350,stroke-width:3px
  linkStyle 13 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "(\\cos\\theta + i\\sin\\theta)^n = \\cos(n\\theta) + i\\sin(n\\theta)",
      "chartScript": {
        "script": "-i*sin(n*theta) + pow(i*sin(theta) + cos(theta), n) - cos(n*theta)",
        "variables": [
          "i",
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "subexpr": "\\left(i \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)}\\right)^{n}",
      "chartScript": {
        "script": "pow(i*sin(theta) + cos(theta), n)",
        "variables": [
          "i",
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "i \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "i*sin(theta) + cos(theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "__cos_4",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "cos(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "i*sin(theta)",
        "variables": [
          "i",
          "theta"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__sin_6",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "sin(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__add_7",
      "type": "operator",
      "op": "add",
      "subexpr": "i \\sin{\\left(n \\theta \\right)} + \\cos{\\left(n \\theta \\right)}",
      "chartScript": {
        "script": "i*sin(n*theta) + cos(n*theta)",
        "variables": [
          "i",
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__cos_8",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(n \\theta \\right)}",
      "chartScript": {
        "script": "cos(n*theta)",
        "variables": [
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\theta n",
      "chartScript": {
        "script": "n*theta",
        "variables": [
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_10",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\sin{\\left(n \\theta \\right)}",
      "chartScript": {
        "script": "i*sin(n*theta)",
        "variables": [
          "i",
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__sin_11",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(n \\theta \\right)}",
      "chartScript": {
        "script": "sin(n*theta)",
        "variables": [
          "n",
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_12",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\theta n",
      "chartScript": {
        "script": "n*theta",
        "variables": [
          "n",
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "theta",
      "to": "__cos_4"
    },
    {
      "from": "__cos_4",
      "to": "__add_3"
    },
    {
      "from": "i",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_6"
    },
    {
      "from": "__sin_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__power_2"
    },
    {
      "from": "n",
      "to": "__power_2",
      "role": "exp"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    },
    {
      "from": "n",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_9",
      "to": "__cos_8"
    },
    {
      "from": "__cos_8",
      "to": "__add_7"
    },
    {
      "from": "i",
      "to": "__multiply_10",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "n",
      "to": "__multiply_12",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__multiply_12",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_12",
      "to": "__sin_11"
    },
    {
      "from": "__sin_11",
      "to": "__multiply_10",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_10",
      "to": "__add_7"
    },
    {
      "from": "__add_7",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __power_2(("$(\cdot)^{\cdot}$")):::operator
  __add_3(("$+$")):::operator
  __cos_4{{"$\cos(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  __multiply_5(("$\times$")):::operator
  i["$i$"]:::scalar
  __sin_6{{"$\sin(\cdot)$"}}:::function
  n["$n$"]:::scalar
  __add_7(("$+$")):::operator
  __cos_8{{"$\cos(\cdot)$"}}:::function
  __multiply_9(("$\times$")):::operator
  __multiply_10(("$\times$")):::operator
  __sin_11{{"$\sin(\cdot)$"}}:::function
  __multiply_12(("$\times$")):::operator
  theta --> __cos_4
  __cos_4 --> __add_3
  i --> __multiply_5
  theta --> __sin_6
  __sin_6 --> __multiply_5
  __multiply_5 --> __add_3
  __add_3 --> __power_2
  n -->|exp| __power_2
  __power_2 --> __equals_1
  n --> __multiply_9
  theta --> __multiply_9
  __multiply_9 --> __cos_8
  __cos_8 --> __add_7
  i --> __multiply_10
  n --> __multiply_12
  theta --> __multiply_12
  __multiply_12 --> __sin_11
  __sin_11 --> __multiply_10
  __multiply_10 --> __add_7
  __add_7 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#ef5350,stroke-width:3px
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#ef5350,stroke-width:3px
  linkStyle 14 stroke:#ef5350,stroke-width:3px
  linkStyle 15 stroke:#ef5350,stroke-width:3px
  linkStyle 16 stroke:#aaa,stroke-width:2px
  linkStyle 17 stroke:#ef5350,stroke-width:3px
  linkStyle 18 stroke:#aaa,stroke-width:2px
  linkStyle 19 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\frac{\\partial u}{\\partial x} = \\frac{\\partial v}{\\partial y}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "u",
      "type": "scalar",
      "latex": "u",
      "subexpr": "u",
      "chartScript": {
        "script": "u",
        "variables": [
          "u"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__deriv_2",
      "type": "operator",
      "op": "partial_derivative",
      "with_respect_to": "x",
      "subexpr": "\\frac{\\partial u}{\\partial x}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "y",
      "type": "scalar",
      "latex": "y",
      "subexpr": "y",
      "chartScript": {
        "script": "y",
        "variables": [
          "y"
        ]
      }
    },
    {
      "id": "__deriv_3",
      "type": "operator",
      "op": "partial_derivative",
      "with_respect_to": "y",
      "subexpr": "\\frac{\\partial v}{\\partial y}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "u",
      "to": "__deriv_2"
    },
    {
      "from": "x",
      "to": "__deriv_2",
      "role": "wrt"
    },
    {
      "from": "__deriv_2",
      "to": "__equals_1"
    },
    {
      "from": "v",
      "to": "__deriv_3"
    },
    {
      "from": "y",
      "to": "__deriv_3",
      "role": "wrt"
    },
    {
      "from": "__deriv_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "PDE",
    "order": 1,
    "dependent_variables": [
      "u",
      "v"
    ],
    "independent_variables": [
      "x",
      "y"
    ]
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  u["$u$"]:::scalar
  x["$x$"]:::scalar
  __deriv_2(("$\dfrac{\partial}{\partial x}$")):::operator
  v["$v$"]:::scalar
  y["$y$"]:::scalar
  __deriv_3(("$\dfrac{\partial}{\partial y}$")):::operator
  u --> __deriv_2
  x -->|wrt| __deriv_2
  __deriv_2 --> __equals_1
  v --> __deriv_3
  y -->|wrt| __deriv_3
  __deriv_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "f(z) = \\sum_{n=-\\infty}^{\\infty} a_n (z - z_0)^n"
    },
    {
      "id": "__f_2",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(z \\right)}",
      "chartScript": {
        "script": "f*z",
        "variables": [
          "f",
          "z"
        ]
      }
    },
    {
      "id": "z",
      "type": "scalar",
      "latex": "z",
      "subexpr": "z",
      "chartScript": {
        "script": "z",
        "variables": [
          "z"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "-oo",
      "subexpr": "-\\infty",
      "chartScript": {
        "script": "Number.NEGATIVE_INFINITY",
        "variables": []
      }
    },
    {
      "id": "__const_5",
      "type": "constant",
      "label": "infinity",
      "latex": "\\infty",
      "subexpr": "\\infty",
      "chartScript": {
        "script": "Number.POSITIVE_INFINITY",
        "variables": []
      }
    },
    {
      "id": "__equals_6",
      "type": "relation",
      "op": "equals",
      "subexpr": "n = -\\infty",
      "chartScript": {
        "script": "n + Number.POSITIVE_INFINITY",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__sum_3",
      "type": "operator",
      "op": "sum",
      "with_respect_to": "n",
      "lower_bound": "__num_4",
      "upper_bound": "__const_5",
      "subexpr": "\\sum_{n=-\\infty}^{\\infty} a_{n}^{n}{\\left(z - z_{0} \\right)}",
      "chartScript": {
        "script": "Sum(pow(a_n, n)*(z - z_0), (n, Number.NEGATIVE_INFINITY, Number.POSITIVE_INFINITY))",
        "variables": [
          "a_n",
          "z",
          "z_0"
        ]
      }
    },
    {
      "id": "__power_7",
      "type": "operator",
      "op": "power",
      "subexpr": "a_{n}^{n}{\\left(z - z_{0} \\right)}",
      "chartScript": {
        "script": "pow(a_n, n)*(z - z_0)",
        "variables": [
          "a_n",
          "n",
          "z",
          "z_0"
        ]
      }
    },
    {
      "id": "__a_n_8",
      "type": "function",
      "op": "a_{n}",
      "subexpr": "a_{n}{\\left(z - z_{0} \\right)}",
      "chartScript": {
        "script": "a_n*(z - z_0)",
        "variables": [
          "a_n",
          "z",
          "z_0"
        ]
      }
    },
    {
      "id": "__add_9",
      "type": "operator",
      "op": "add",
      "subexpr": "z - z_{0}",
      "chartScript": {
        "script": "z - z_0",
        "variables": [
          "z",
          "z_0"
        ]
      }
    },
    {
      "id": "__negation_10",
      "type": "operator",
      "op": "negation",
      "subexpr": "-z_{0}",
      "chartScript": {
        "script": "-z_0",
        "variables": [
          "z_0"
        ]
      }
    },
    {
      "id": "z_0",
      "type": "scalar",
      "latex": "z_{0}",
      "subexpr": "z_{0}",
      "chartScript": {
        "script": "z_0",
        "variables": [
          "z_0"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "z",
      "to": "__f_2"
    },
    {
      "from": "__f_2",
      "to": "__equals_1"
    },
    {
      "from": "n",
      "to": "__sum_3",
      "role": "wrt"
    },
    {
      "from": "n",
      "to": "__equals_6"
    },
    {
      "from": "__num_4",
      "to": "__equals_6"
    },
    {
      "from": "__equals_6",
      "to": "__sum_3",
      "role": "lb"
    },
    {
      "from": "__const_5",
      "to": "__sum_3",
      "role": "ub"
    },
    {
      "from": "z",
      "to": "__add_9"
    },
    {
      "from": "z_0",
      "to": "__negation_10"
    },
    {
      "from": "__negation_10",
      "to": "__add_9"
    },
    {
      "from": "__add_9",
      "to": "__a_n_8"
    },
    {
      "from": "__a_n_8",
      "to": "__power_7"
    },
    {
      "from": "n",
      "to": "__power_7",
      "role": "exp"
    },
    {
      "from": "__power_7",
      "to": "__sum_3"
    },
    {
      "from": "__sum_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __f_2{{"$f(\cdot)$"}}:::function
  z["$z$"]:::scalar
  n["$n$"]:::scalar
  __num_4["$-\infty$"]:::number
  __const_5["$\infty$"]:::constant
  __equals_6{"="}:::relation
  __sum_3(("$\sum_{n}$")):::operator
  __power_7(("$(\cdot)^{\cdot}$")):::operator
  __a_n_8{{"$a_{n}(\cdot)$"}}:::function
  __add_9(("$+$")):::operator
  __negation_10@{ shape: "flip-tri", label: "$-$" }
  z_0["$z_{0}$"]:::scalar
  class __negation_10 operator
  z --> __f_2
  __f_2 --> __equals_1
  n -->|wrt| __sum_3
  n --> __equals_6
  __num_4 --> __equals_6
  __equals_6 -->|lb| __sum_3
  __const_5 -->|ub| __sum_3
  z --> __add_9
  z_0 --> __negation_10
  __negation_10 --> __add_9
  __add_9 --> __a_n_8
  __a_n_8 --> __power_7
  n -->|exp| __power_7
  __power_7 --> __sum_3
  __sum_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px