Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "(x + 1)(x - 1) = x^2 - 1",
      "chartScript": {
        "script": "-pow(x, 2) + (x - 1)*(x + 1) + 1",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(x + 1\\right) \\left(x - 1\\right)",
      "chartScript": {
        "script": "(x - 1)*(x + 1)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "x + 1",
      "chartScript": {
        "script": "x + 1",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
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      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "__add_5",
      "type": "operator",
      "op": "add",
      "subexpr": "x - 1",
      "chartScript": {
        "script": "x - 1",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "-1",
      "subexpr": "-1",
      "chartScript": {
        "script": "-1",
        "variables": []
      }
    },
    {
      "id": "__add_7",
      "type": "operator",
      "op": "add",
      "subexpr": "x^{2} - 1",
      "chartScript": {
        "script": "pow(x, 2) - 1",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__power_8",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "x^{2}",
      "chartScript": {
        "script": "pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__num_9",
      "type": "number",
      "label": "-1",
      "subexpr": "-1",
      "chartScript": {
        "script": "-1",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__add_3"
    },
    {
      "from": "__num_4",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__add_5"
    },
    {
      "from": "__num_6",
      "to": "__add_5"
    },
    {
      "from": "__add_5",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "x",
      "to": "__power_8"
    },
    {
      "from": "__power_8",
      "to": "__add_7"
    },
    {
      "from": "__num_9",
      "to": "__add_7"
    },
    {
      "from": "__add_7",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
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  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
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  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
  __add_3(("$+$")):::operator
  x["$x$"]:::scalar
  __num_4["$1$"]:::number
  __add_5(("$+$")):::operator
  __num_6["$-1$"]:::number
  __add_7(("$+$")):::operator
  __power_8(("${(\cdot)}^{2}$")):::operator
  __num_9["$-1$"]:::number
  x --> __add_3
  __num_4 --> __add_3
  __add_3 --> __multiply_2
  x --> __add_5
  __num_6 --> __add_5
  __add_5 --> __multiply_2
  __multiply_2 --> __equals_1
  x --> __power_8
  __power_8 --> __add_7
  __num_9 --> __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:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#ef5350,stroke-width:6px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "ax^2 + bx + c = 0",
      "chartScript": {
        "script": "a*pow(x, 2) + b*x + c",
        "variables": [
          "a",
          "b",
          "c",
          "x"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "c + a x^{2} + x b",
      "chartScript": {
        "script": "a*pow(x, 2) + b*x + c",
        "variables": [
          "a",
          "b",
          "c",
          "x"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "a x^{2} + x b",
      "chartScript": {
        "script": "a*pow(x, 2) + b*x",
        "variables": [
          "a",
          "b",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a x^{2}",
      "chartScript": {
        "script": "a*pow(x, 2)",
        "variables": [
          "a",
          "x"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "x^{2}",
      "chartScript": {
        "script": "pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x b",
      "chartScript": {
        "script": "b*x",
        "variables": [
          "b",
          "x"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__num_7",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "a",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__add_3"
    },
    {
      "from": "b",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__add_2"
    },
    {
      "from": "c",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_7",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
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  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
  __add_3(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  a["$a$"]:::scalar
  __power_5(("${(\cdot)}^{2}$")):::operator
  x["$x$"]:::scalar
  __multiply_6(("$\times$")):::operator
  b["$b$"]:::scalar
  c["$c$"]:::scalar
  __num_7["$0$"]:::number
  a --> __multiply_4
  x --> __power_5
  __power_5 --> __multiply_4
  __multiply_4 --> __add_3
  b --> __multiply_6
  x --> __multiply_6
  __multiply_6 --> __add_3
  __add_3 --> __add_2
  c --> __add_2
  __add_2 --> __equals_1
  __num_7 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  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:#ef5350,stroke-width:3px
  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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}",
      "chartScript": {
        "script": "x + (1/2)*b*pm*sqrt(-4*a*c + pow(b, 2))/a",
        "variables": [
          "a",
          "b",
          "c",
          "pm",
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "-b \\pm \\sqrt{b^{2} - 4 a c} \\frac{1}{2 a}",
      "chartScript": {
        "script": "-1/2*b*pm*sqrt(-4*a*c + pow(b, 2))/a",
        "variables": [
          "a",
          "b",
          "c",
          "pm"
        ]
      }
    },
    {
      "id": "__negation_3",
      "type": "operator",
      "op": "negation",
      "subexpr": "-b \\pm \\sqrt{b^{2} - 4 a c}",
      "chartScript": {
        "script": "-b*pm*sqrt(-4*a*c + pow(b, 2))",
        "variables": [
          "a",
          "b",
          "c",
          "pm"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "b \\pm \\sqrt{b^{2} - 4 a c}",
      "chartScript": {
        "script": "b*pm*sqrt(-4*a*c + pow(b, 2))",
        "variables": [
          "a",
          "b",
          "c",
          "pm"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "pm",
      "type": "scalar",
      "latex": "\\pm",
      "subexpr": "\\pm",
      "chartScript": {
        "script": "pm",
        "variables": [
          "pm"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "exponent": "1/2",
      "subexpr": "\\sqrt{b^{2} - 4 a c}",
      "chartScript": {
        "script": "sqrt(-4*a*c + pow(b, 2))",
        "variables": [
          "a",
          "b",
          "c"
        ]
      }
    },
    {
      "id": "__add_6",
      "type": "operator",
      "op": "add",
      "subexpr": "b^{2} - 4 a c",
      "chartScript": {
        "script": "-4*a*c + pow(b, 2)",
        "variables": [
          "a",
          "b",
          "c"
        ]
      }
    },
    {
      "id": "__power_7",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "b^{2}",
      "chartScript": {
        "script": "pow(b, 2)",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__negation_8",
      "type": "operator",
      "op": "negation",
      "subexpr": "-4 a c",
      "chartScript": {
        "script": "-4*a*c",
        "variables": [
          "a",
          "c"
        ]
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "4 a c",
      "chartScript": {
        "script": "4*a*c",
        "variables": [
          "a",
          "c"
        ]
      }
    },
    {
      "id": "__num_10",
      "type": "number",
      "label": "4",
      "subexpr": "4",
      "chartScript": {
        "script": "4",
        "variables": []
      }
    },
    {
      "id": "__multiply_11",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a c",
      "chartScript": {
        "script": "a*c",
        "variables": [
          "a",
          "c"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__power_12",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2 a}",
      "chartScript": {
        "script": "(1/2)/a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__multiply_13",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a 2",
      "chartScript": {
        "script": "2*a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__num_14",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__equals_1"
    },
    {
      "from": "b",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pm",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "b",
      "to": "__power_7"
    },
    {
      "from": "__power_7",
      "to": "__add_6"
    },
    {
      "from": "__num_10",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "c",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_11",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_9",
      "to": "__negation_8"
    },
    {
      "from": "__negation_8",
      "to": "__add_6"
    },
    {
      "from": "__add_6",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__negation_3"
    },
    {
      "from": "__negation_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__num_14",
      "to": "__multiply_13",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__multiply_13",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_13",
      "to": "__power_12"
    },
    {
      "from": "__power_12",
      "to": "__multiply_2"
    },
    {
      "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
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  x["$x$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __negation_3@{ shape: "flip-tri", label: "$-$" }
  __multiply_4(("$\times$")):::operator
  b["$b$"]:::scalar
  pm["$\pm$"]:::scalar
  __power_5(("${(\cdot)}^{1/2}$")):::operator
  __add_6(("$+$")):::operator
  __power_7(("${(\cdot)}^{2}$")):::operator
  __negation_8@{ shape: "flip-tri", label: "$-$" }
  __multiply_9(("$\times$")):::operator
  __num_10["$4$"]:::number
  __multiply_11(("$\times$")):::operator
  a["$a$"]:::scalar
  c["$c$"]:::scalar
  __power_12(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_13(("$\times$")):::operator
  __num_14["$2$"]:::number
  class __negation_3 operator
  class __negation_8 operator
  x --> __equals_1
  b --> __multiply_4
  pm --> __multiply_4
  b --> __power_7
  __power_7 --> __add_6
  __num_10 --> __multiply_9
  a --> __multiply_11
  c --> __multiply_11
  __multiply_11 --> __multiply_9
  __multiply_9 --> __negation_8
  __negation_8 --> __add_6
  __add_6 --> __power_5
  __power_5 --> __multiply_4
  __multiply_4 --> __negation_3
  __negation_3 --> __multiply_2
  __num_14 --> __multiply_13
  a --> __multiply_13
  __multiply_13 --> __power_12
  __power_12 -.-> __multiply_2
  __multiply_2 --> __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:#ef5350,stroke-width:6px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#ef5350,stroke-width:3px
  linkStyle 8 stroke:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#ef5350,stroke-width:3px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#ef5350,stroke-width:3px
  linkStyle 15 stroke:#ef5350,stroke-width:3px
  linkStyle 16 stroke:#ef5350,stroke-width:3px
  linkStyle 17 stroke:#aaa,stroke-width:2px
  linkStyle 18 stroke:#42a5f5,stroke-width:1px
  linkStyle 19 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "t^3 + pt + q = 0",
      "chartScript": {
        "script": "p*t + q + pow(t, 3)",
        "variables": [
          "p",
          "q",
          "t"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "q + t^{3} + t p",
      "chartScript": {
        "script": "p*t + q + pow(t, 3)",
        "variables": [
          "p",
          "q",
          "t"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "t^{3} + t p",
      "chartScript": {
        "script": "p*t + pow(t, 3)",
        "variables": [
          "p",
          "t"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "op": "power",
      "exponent": "3",
      "subexpr": "t^{3}",
      "chartScript": {
        "script": "pow(t, 3)",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "t p",
      "chartScript": {
        "script": "p*t",
        "variables": [
          "p",
          "t"
        ]
      }
    },
    {
      "id": "p",
      "type": "scalar",
      "latex": "p",
      "subexpr": "p",
      "chartScript": {
        "script": "p",
        "variables": [
          "p"
        ]
      }
    },
    {
      "id": "q",
      "type": "scalar",
      "latex": "q",
      "subexpr": "q",
      "chartScript": {
        "script": "q",
        "variables": [
          "q"
        ]
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "t",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__add_3"
    },
    {
      "from": "p",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "t",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__add_2"
    },
    {
      "from": "q",
      "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
  __add_3(("$+$")):::operator
  __power_4(("${(\cdot)}^{3}$")):::operator
  t["$t$"]:::scalar
  __multiply_5(("$\times$")):::operator
  p["$p$"]:::scalar
  q["$q$"]:::scalar
  __num_6["$0$"]:::number
  t --> __power_4
  __power_4 --> __add_3
  p --> __multiply_5
  t --> __multiply_5
  __multiply_5 --> __add_3
  __add_3 --> __add_2
  q --> __add_2
  __add_2 --> __equals_1
  __num_6 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:8px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "x^3 - 6x^2 + 11x - 6 = 0",
      "chartScript": {
        "script": "pow(x, 3) - 6*pow(x, 2) + 11*x - 6",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "x 11 + x^{3} - x^{2} 6 - 6",
      "chartScript": {
        "script": "pow(x, 3) - 6*pow(x, 2) + 11*x - 6",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "x 11 + x^{3} - x^{2} 6",
      "chartScript": {
        "script": "pow(x, 3) - 6*pow(x, 2) + 11*x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "x^{3} - x^{2} 6",
      "chartScript": {
        "script": "pow(x, 3) - 6*pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "exponent": "3",
      "subexpr": "x^{3}",
      "chartScript": {
        "script": "pow(x, 3)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__negation_6",
      "type": "operator",
      "op": "negation",
      "subexpr": "-x^{2} 6",
      "chartScript": {
        "script": "-6*pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x^{2} 6",
      "chartScript": {
        "script": "6*pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__num_8",
      "type": "number",
      "label": "6",
      "subexpr": "6",
      "chartScript": {
        "script": "6",
        "variables": []
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "x^{2}",
      "chartScript": {
        "script": "pow(x, 2)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_10",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x 11",
      "chartScript": {
        "script": "11*x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__num_11",
      "type": "number",
      "label": "11",
      "subexpr": "11",
      "chartScript": {
        "script": "11",
        "variables": []
      }
    },
    {
      "id": "__num_12",
      "type": "number",
      "label": "-6",
      "subexpr": "-6",
      "chartScript": {
        "script": "-6",
        "variables": []
      }
    },
    {
      "id": "__num_13",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__add_4"
    },
    {
      "from": "__num_8",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__power_9"
    },
    {
      "from": "__power_9",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__negation_6"
    },
    {
      "from": "__negation_6",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__add_3"
    },
    {
      "from": "__num_11",
      "to": "__multiply_10",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__multiply_10",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_10",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__add_2"
    },
    {
      "from": "__num_12",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_13",
      "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
  __add_3(("$+$")):::operator
  __add_4(("$+$")):::operator
  __power_5(("${(\cdot)}^{3}$")):::operator
  x["$x$"]:::scalar
  __negation_6@{ shape: "flip-tri", label: "$-$" }
  __multiply_7(("$\times$")):::operator
  __num_8["$6$"]:::number
  __power_9(("${(\cdot)}^{2}$")):::operator
  __multiply_10(("$\times$")):::operator
  __num_11["$11$"]:::number
  __num_12["$-6$"]:::number
  __num_13["$0$"]:::number
  class __negation_6 operator
  x --> __power_5
  __power_5 --> __add_4
  __num_8 --> __multiply_7
  x --> __power_9
  __power_9 --> __multiply_7
  __multiply_7 --> __negation_6
  __negation_6 --> __add_4
  __add_4 --> __add_3
  __num_11 --> __multiply_10
  x --> __multiply_10
  __multiply_10 --> __add_3
  __add_3 --> __add_2
  __num_12 --> __add_2
  __add_2 --> __equals_1
  __num_13 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:8px
  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:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#ef5350,stroke-width:3px
  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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "a^2 - b^2 = (a + b)(a - b)",
      "chartScript": {
        "script": "pow(a, 2) - pow(b, 2) - (a - b)*(a + b)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "a^{2} - b^{2}",
      "chartScript": {
        "script": "pow(a, 2) - pow(b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_3",
      "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": "__negation_4",
      "type": "operator",
      "op": "negation",
      "subexpr": "-b^{2}",
      "chartScript": {
        "script": "-pow(b, 2)",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__power_5",
      "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"
        ]
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(a + b\\right) \\left(a - b\\right)",
      "chartScript": {
        "script": "(a - b)*(a + b)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_7",
      "type": "operator",
      "op": "add",
      "subexpr": "a + b",
      "chartScript": {
        "script": "a + b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_8",
      "type": "operator",
      "op": "add",
      "subexpr": "a - b",
      "chartScript": {
        "script": "a - b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__negation_9",
      "type": "operator",
      "op": "negation",
      "subexpr": "-b",
      "chartScript": {
        "script": "-b",
        "variables": [
          "b"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "a",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__add_2"
    },
    {
      "from": "b",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__negation_4"
    },
    {
      "from": "__negation_4",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "a",
      "to": "__add_7"
    },
    {
      "from": "b",
      "to": "__add_7"
    },
    {
      "from": "__add_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__add_8"
    },
    {
      "from": "b",
      "to": "__negation_9"
    },
    {
      "from": "__negation_9",
      "to": "__add_8"
    },
    {
      "from": "__add_8",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_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(("${(\cdot)}^{2}$")):::operator
  a["$a$"]:::scalar
  __negation_4@{ shape: "flip-tri", label: "$-$" }
  __power_5(("${(\cdot)}^{2}$")):::operator
  b["$b$"]:::scalar
  __multiply_6(("$\times$")):::operator
  __add_7(("$+$")):::operator
  __add_8(("$+$")):::operator
  __negation_9@{ shape: "flip-tri", label: "$-$" }
  class __negation_4 operator
  class __negation_9 operator
  a --> __power_3
  __power_3 --> __add_2
  b --> __power_5
  __power_5 --> __negation_4
  __negation_4 --> __add_2
  __add_2 --> __equals_1
  a --> __add_7
  b --> __add_7
  __add_7 --> __multiply_6
  a --> __add_8
  b --> __negation_9
  __negation_9 --> __add_8
  __add_8 --> __multiply_6
  __multiply_6 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:6px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:6px
  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:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#ef5350,stroke-width:3px
  linkStyle 13 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "a^2 + 2ab + b^2 = (a + b)^2",
      "chartScript": {
        "script": "pow(a, 2) + 2*a*b + pow(b, 2) - pow(a + b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "b^{2} + a^{2} + 2 a b",
      "chartScript": {
        "script": "pow(a, 2) + 2*a*b + pow(b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "a^{2} + 2 a b",
      "chartScript": {
        "script": "pow(a, 2) + 2*a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_4",
      "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": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "2 a b",
      "chartScript": {
        "script": "2*a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a b",
      "chartScript": {
        "script": "a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__power_8",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "b^{2}",
      "chartScript": {
        "script": "pow(b, 2)",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "\\left(a + b\\right)^{2}",
      "chartScript": {
        "script": "pow(a + b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_10",
      "type": "operator",
      "op": "add",
      "subexpr": "a + b",
      "chartScript": {
        "script": "a + b",
        "variables": [
          "a",
          "b"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "a",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__add_3"
    },
    {
      "from": "__num_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "b",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__add_2"
    },
    {
      "from": "b",
      "to": "__power_8"
    },
    {
      "from": "__power_8",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "a",
      "to": "__add_10"
    },
    {
      "from": "b",
      "to": "__add_10"
    },
    {
      "from": "__add_10",
      "to": "__power_9"
    },
    {
      "from": "__power_9",
      "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
  __add_3(("$+$")):::operator
  __power_4(("${(\cdot)}^{2}$")):::operator
  a["$a$"]:::scalar
  __multiply_5(("$\times$")):::operator
  __num_6["$2$"]:::number
  __multiply_7(("$\times$")):::operator
  b["$b$"]:::scalar
  __power_8(("${(\cdot)}^{2}$")):::operator
  __power_9(("${(\cdot)}^{2}$")):::operator
  __add_10(("$+$")):::operator
  a --> __power_4
  __power_4 --> __add_3
  __num_6 --> __multiply_5
  a --> __multiply_7
  b --> __multiply_7
  __multiply_7 --> __multiply_5
  __multiply_5 --> __add_3
  __add_3 --> __add_2
  b --> __power_8
  __power_8 --> __add_2
  __add_2 --> __equals_1
  a --> __add_10
  b --> __add_10
  __add_10 --> __power_9
  __power_9 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:6px
  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:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#ef5350,stroke-width:6px
  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:#ef5350,stroke-width:6px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "a^3 + b^3 = (a + b)(a^2 - ab + b^2)",
      "chartScript": {
        "script": "pow(a, 3) + pow(b, 3) - (a + b)*(pow(a, 2) - a*b + pow(b, 2))",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "a^{3} + b^{3}",
      "chartScript": {
        "script": "pow(a, 3) + pow(b, 3)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "exponent": "3",
      "subexpr": "a^{3}",
      "chartScript": {
        "script": "pow(a, 3)",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "op": "power",
      "exponent": "3",
      "subexpr": "b^{3}",
      "chartScript": {
        "script": "pow(b, 3)",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(a + b\\right) \\left(b^{2} + a^{2} - a b\\right)",
      "chartScript": {
        "script": "(a + b)*(pow(a, 2) - a*b + pow(b, 2))",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_6",
      "type": "operator",
      "op": "add",
      "subexpr": "a + b",
      "chartScript": {
        "script": "a + b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_7",
      "type": "operator",
      "op": "add",
      "subexpr": "b^{2} + a^{2} - a b",
      "chartScript": {
        "script": "pow(a, 2) - a*b + pow(b, 2)",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__add_8",
      "type": "operator",
      "op": "add",
      "subexpr": "a^{2} - a b",
      "chartScript": {
        "script": "pow(a, 2) - a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "a^{2}",
      "chartScript": {
        "script": "pow(a, 2)",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__negation_10",
      "type": "operator",
      "op": "negation",
      "subexpr": "-a b",
      "chartScript": {
        "script": "-a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__multiply_11",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a b",
      "chartScript": {
        "script": "a*b",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__power_12",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "b^{2}",
      "chartScript": {
        "script": "pow(b, 2)",
        "variables": [
          "b"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "a",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__add_2"
    },
    {
      "from": "b",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "a",
      "to": "__add_6"
    },
    {
      "from": "b",
      "to": "__add_6"
    },
    {
      "from": "__add_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__power_9"
    },
    {
      "from": "__power_9",
      "to": "__add_8"
    },
    {
      "from": "a",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "b",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_11",
      "to": "__negation_10"
    },
    {
      "from": "__negation_10",
      "to": "__add_8"
    },
    {
      "from": "__add_8",
      "to": "__add_7"
    },
    {
      "from": "b",
      "to": "__power_12"
    },
    {
      "from": "__power_12",
      "to": "__add_7"
    },
    {
      "from": "__add_7",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "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(("${(\cdot)}^{3}$")):::operator
  a["$a$"]:::scalar
  __power_4(("${(\cdot)}^{3}$")):::operator
  b["$b$"]:::scalar
  __multiply_5(("$\times$")):::operator
  __add_6(("$+$")):::operator
  __add_7(("$+$")):::operator
  __add_8(("$+$")):::operator
  __power_9(("${(\cdot)}^{2}$")):::operator
  __negation_10@{ shape: "flip-tri", label: "$-$" }
  __multiply_11(("$\times$")):::operator
  __power_12(("${(\cdot)}^{2}$")):::operator
  class __negation_10 operator
  a --> __power_3
  __power_3 --> __add_2
  b --> __power_4
  __power_4 --> __add_2
  __add_2 --> __equals_1
  a --> __add_6
  b --> __add_6
  __add_6 --> __multiply_5
  a --> __power_9
  __power_9 --> __add_8
  a --> __multiply_11
  b --> __multiply_11
  __multiply_11 --> __negation_10
  __negation_10 --> __add_8
  __add_8 --> __add_7
  b --> __power_12
  __power_12 --> __add_7
  __add_7 --> __multiply_5
  __multiply_5 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:8px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:8px
  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:6px
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#ef5350,stroke-width:3px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#aaa,stroke-width:2px
  linkStyle 16 stroke:#ef5350,stroke-width:6px
  linkStyle 17 stroke:#ef5350,stroke-width:3px
  linkStyle 18 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "r_1 + r_2 = -\\frac{b}{a}",
      "chartScript": {
        "script": "r_1 + r_2 + b/a",
        "variables": [
          "a",
          "b",
          "r_1",
          "r_2"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "r_{1} + r_{2}",
      "chartScript": {
        "script": "r_1 + r_2",
        "variables": [
          "r_1",
          "r_2"
        ]
      }
    },
    {
      "id": "r_1",
      "type": "scalar",
      "latex": "r_{1}",
      "subexpr": "r_{1}",
      "chartScript": {
        "script": "r_1",
        "variables": [
          "r_1"
        ]
      }
    },
    {
      "id": "r_2",
      "type": "scalar",
      "latex": "r_{2}",
      "subexpr": "r_{2}",
      "chartScript": {
        "script": "r_2",
        "variables": [
          "r_2"
        ]
      }
    },
    {
      "id": "__negation_3",
      "type": "operator",
      "op": "negation",
      "subexpr": "-\\frac{1}{a} b",
      "chartScript": {
        "script": "-b/a",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{a} b",
      "chartScript": {
        "script": "b/a",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{a}",
      "chartScript": {
        "script": "1/a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "r_1",
      "to": "__add_2"
    },
    {
      "from": "r_2",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    },
    {
      "from": "b",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_4"
    },
    {
      "from": "__multiply_4",
      "to": "__negation_3"
    },
    {
      "from": "__negation_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
  __add_2(("$+$")):::operator
  r_1["$r_{1}$"]:::scalar
  r_2["$r_{2}$"]:::scalar
  __negation_3@{ shape: "flip-tri", label: "$-$" }
  __multiply_4(("$\times$")):::operator
  b["$b$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  a["$a$"]:::scalar
  class __negation_3 operator
  r_1 --> __add_2
  r_2 --> __add_2
  __add_2 --> __equals_1
  b --> __multiply_4
  a --> __power_5
  __power_5 -.-> __multiply_4
  __multiply_4 --> __negation_3
  __negation_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:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#42a5f5,stroke-width:1px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "r_1 r_2 = \\frac{c}{a}",
      "chartScript": {
        "script": "r_1*r_2 - c/a",
        "variables": [
          "a",
          "c",
          "r_1",
          "r_2"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "r_{1} r_{2}",
      "chartScript": {
        "script": "r_1*r_2",
        "variables": [
          "r_1",
          "r_2"
        ]
      }
    },
    {
      "id": "r_1",
      "type": "scalar",
      "latex": "r_{1}",
      "subexpr": "r_{1}",
      "chartScript": {
        "script": "r_1",
        "variables": [
          "r_1"
        ]
      }
    },
    {
      "id": "r_2",
      "type": "scalar",
      "latex": "r_{2}",
      "subexpr": "r_{2}",
      "chartScript": {
        "script": "r_2",
        "variables": [
          "r_2"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{a} c",
      "chartScript": {
        "script": "c/a",
        "variables": [
          "a",
          "c"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{a}",
      "chartScript": {
        "script": "1/a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "r_1",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "r_2",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "c",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "a",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3"
    },
    {
      "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
  __multiply_2(("$\times$")):::operator
  r_1["$r_{1}$"]:::scalar
  r_2["$r_{2}$"]:::scalar
  __multiply_3(("$\times$")):::operator
  c["$c$"]:::scalar
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  a["$a$"]:::scalar
  r_1 --> __multiply_2
  r_2 --> __multiply_2
  __multiply_2 --> __equals_1
  c --> __multiply_3
  a --> __power_4
  __power_4 -.-> __multiply_3
  __multiply_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:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#42a5f5,stroke-width:1px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "(x + y)^n = \\sum_{k=0}^{n} \\binom{n}{k} x^{n-k} y^k",
      "chartScript": {
        "script": "pow(x + y, n) - ((re(n) <= -1 && abs(y/x) < 1 || abs(y/x) <= 1 && re(n) > 0 || re(n) <= 0 && abs(y/x) <= 1 && re(n) > -1 && y/x != -1) ? (\n   pow(x, n)*pow(1 + y/x, n)\n)\n: (\n   Sum(pow(x, -k + n)*pow(y, k)*binomial(n, k), (k, 0, n))\n))",
        "variables": [
          "n",
          "x",
          "y"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "subexpr": "\\left(x + y\\right)^{n}",
      "chartScript": {
        "script": "pow(x + y, n)",
        "variables": [
          "n",
          "x",
          "y"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "x + y",
      "chartScript": {
        "script": "x + y",
        "variables": [
          "x",
          "y"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "y",
      "type": "scalar",
      "latex": "y",
      "subexpr": "y",
      "chartScript": {
        "script": "y",
        "variables": [
          "y"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "k",
      "type": "scalar",
      "latex": "k",
      "subexpr": "k",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__num_5",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__equals_6",
      "type": "relation",
      "op": "equals",
      "subexpr": "k = 0",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__sum_4",
      "type": "operator",
      "op": "sum",
      "with_respect_to": "k",
      "lower_bound": "__num_5",
      "upper_bound": "n",
      "subexpr": "\\sum_{k=0}^{n} x^{- k + n} y^{k} {\\binom{n}{k}}",
      "chartScript": {
        "script": "((re(n) <= -1 && abs(y/x) < 1 || abs(y/x) <= 1 && re(n) > 0 || re(n) <= 0 && abs(y/x) <= 1 && re(n) > -1 && y/x != -1) ? (\n   pow(x, n)*pow(1 + y/x, n)\n)\n: (\n   Sum(pow(x, -k + n)*pow(y, k)*binomial(n, k), (k, 0, n))\n))",
        "variables": [
          "n",
          "x",
          "y"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "{\\binom{n}{k}} x^{- k + n} y^{k}",
      "chartScript": {
        "script": "pow(x, -k + n)*pow(y, k)*binomial(n, k)",
        "variables": [
          "k",
          "n",
          "x",
          "y"
        ]
      }
    },
    {
      "id": "__choose_8",
      "type": "function",
      "op": "choose",
      "subexpr": "{\\binom{n}{k}}",
      "chartScript": {
        "script": "binomial(n, k)",
        "variables": [
          "k",
          "n"
        ]
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x^{- k + n} y^{k}",
      "chartScript": {
        "script": "pow(x, -k + n)*pow(y, k)",
        "variables": [
          "k",
          "n",
          "x",
          "y"
        ]
      }
    },
    {
      "id": "__power_10",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{- k + n}",
      "chartScript": {
        "script": "pow(x, -k + n)",
        "variables": [
          "k",
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__add_11",
      "type": "operator",
      "op": "add",
      "subexpr": "n - k",
      "chartScript": {
        "script": "-k + n",
        "variables": [
          "k",
          "n"
        ]
      }
    },
    {
      "id": "__negation_12",
      "type": "operator",
      "op": "negation",
      "subexpr": "-k",
      "chartScript": {
        "script": "-k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__power_13",
      "type": "operator",
      "op": "power",
      "subexpr": "y^{k}",
      "chartScript": {
        "script": "pow(y, k)",
        "variables": [
          "k",
          "y"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__add_3"
    },
    {
      "from": "y",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__power_2"
    },
    {
      "from": "n",
      "to": "__power_2",
      "role": "exp"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    },
    {
      "from": "k",
      "to": "__sum_4",
      "role": "wrt"
    },
    {
      "from": "k",
      "to": "__equals_6"
    },
    {
      "from": "__num_5",
      "to": "__equals_6"
    },
    {
      "from": "__equals_6",
      "to": "__sum_4",
      "role": "lb"
    },
    {
      "from": "n",
      "to": "__sum_4",
      "role": "ub"
    },
    {
      "from": "n",
      "to": "__choose_8"
    },
    {
      "from": "k",
      "to": "__choose_8"
    },
    {
      "from": "__choose_8",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__power_10"
    },
    {
      "from": "n",
      "to": "__add_11"
    },
    {
      "from": "k",
      "to": "__negation_12"
    },
    {
      "from": "__negation_12",
      "to": "__add_11"
    },
    {
      "from": "__add_11",
      "to": "__power_10",
      "role": "exp"
    },
    {
      "from": "__power_10",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "y",
      "to": "__power_13"
    },
    {
      "from": "k",
      "to": "__power_13",
      "role": "exp"
    },
    {
      "from": "__power_13",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_9",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__sum_4"
    },
    {
      "from": "__sum_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
  __add_3(("$+$")):::operator
  x["$x$"]:::scalar
  y["$y$"]:::scalar
  n["$n$"]:::scalar
  k["$k$"]:::scalar
  __num_5["$0$"]:::number
  __equals_6{"="}:::relation
  __sum_4(("$\sum_{k}$")):::operator
  __multiply_7(("$\times$")):::operator
  __choose_8{{"$\binom{\cdot}{\cdot}$"}}:::function
  __multiply_9(("$\times$")):::operator
  __power_10(("$(\cdot)^{\cdot}$")):::operator
  __add_11(("$+$")):::operator
  __negation_12@{ shape: "flip-tri", label: "$-$" }
  __power_13(("$(\cdot)^{\cdot}$")):::operator
  class __negation_12 operator
  x --> __add_3
  y --> __add_3
  __add_3 --> __power_2
  n -->|exp| __power_2
  __power_2 --> __equals_1
  k -->|wrt| __sum_4
  k --> __equals_6
  __num_5 --> __equals_6
  __equals_6 -->|lb| __sum_4
  n -->|ub| __sum_4
  n --> __choose_8
  k --> __choose_8
  __choose_8 --> __multiply_7
  x --> __power_10
  n --> __add_11
  k --> __negation_12
  __negation_12 --> __add_11
  __add_11 -->|exp| __power_10
  __power_10 --> __multiply_9
  y --> __power_13
  k -->|exp| __power_13
  __power_13 --> __multiply_9
  __multiply_9 --> __multiply_7
  __multiply_7 --> __sum_4
  __sum_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:#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:#ef5350,stroke-width:3px
  linkStyle 13 stroke:#aaa,stroke-width:2px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#aaa,stroke-width:2px
  linkStyle 16 stroke:#aaa,stroke-width:2px
  linkStyle 17 stroke:#aaa,stroke-width:2px
  linkStyle 18 stroke:#ef5350,stroke-width:3px
  linkStyle 19 stroke:#aaa,stroke-width:2px
  linkStyle 20 stroke:#aaa,stroke-width:2px
  linkStyle 21 stroke:#ef5350,stroke-width:3px
  linkStyle 22 stroke:#ef5350,stroke-width:3px
  linkStyle 23 stroke:#aaa,stroke-width:2px
  linkStyle 24 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "f(x) = q(x) \\cdot d(x) + r(x)",
      "chartScript": {
        "script": "-d(x)*q(x) + f(x) - r(x)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__f_2",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(x \\right)}",
      "chartScript": {
        "script": "f*x",
        "variables": [
          "f",
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "q{\\left(x \\right)} d{\\left(x \\right)} + r{\\left(x \\right)}",
      "chartScript": {
        "script": "d*q*pow(x, 2) + r*x",
        "variables": [
          "d",
          "q",
          "r",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "q{\\left(x \\right)} d{\\left(x \\right)}",
      "chartScript": {
        "script": "d*q*pow(x, 2)",
        "variables": [
          "d",
          "q",
          "x"
        ]
      }
    },
    {
      "id": "__q_5",
      "type": "function",
      "op": "q",
      "subexpr": "q{\\left(x \\right)}",
      "chartScript": {
        "script": "q*x",
        "variables": [
          "q",
          "x"
        ]
      }
    },
    {
      "id": "__d_6",
      "type": "function",
      "op": "d",
      "subexpr": "d{\\left(x \\right)}",
      "chartScript": {
        "script": "d*x",
        "variables": [
          "d",
          "x"
        ]
      }
    },
    {
      "id": "__r_7",
      "type": "function",
      "op": "r",
      "subexpr": "r{\\left(x \\right)}",
      "chartScript": {
        "script": "r*x",
        "variables": [
          "r",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__f_2"
    },
    {
      "from": "__f_2",
      "to": "__equals_1"
    },
    {
      "from": "x",
      "to": "__q_5"
    },
    {
      "from": "__q_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__d_6"
    },
    {
      "from": "__d_6",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__add_3"
    },
    {
      "from": "x",
      "to": "__r_7"
    },
    {
      "from": "__r_7",
      "to": "__add_3"
    },
    {
      "from": "__add_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
  x["$x$"]:::scalar
  __add_3(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  __q_5{{"$q(\cdot)$"}}:::function
  __d_6{{"$d(\cdot)$"}}:::function
  __r_7{{"$r(\cdot)$"}}:::function
  x --> __f_2
  __f_2 --> __equals_1
  x --> __q_5
  __q_5 --> __multiply_4
  x --> __d_6
  __d_6 --> __multiply_4
  __multiply_4 --> __add_3
  x --> __r_7
  __r_7 --> __add_3
  __add_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:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  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