Semantic Graph — Visual Examination Report

{
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      "type": "relation",
      "op": "equals",
      "subexpr": "\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{x} \\sin{\\left(x \\right)}",
      "chartScript": {
        "script": "sin(x)/x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__sin_4",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(x \\right)}",
      "chartScript": {
        "script": "sin(x)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
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        "variables": [
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        ]
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    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{x}",
      "chartScript": {
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        "variables": [
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    },
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      "chartScript": {
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        "variables": []
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    },
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      "type": "operator",
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      "subexpr": "x \\to 0",
      "chartScript": {
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        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__limit_2",
      "type": "operator",
      "op": "limit",
      "subexpr": "\\lim_{x \\to 0}\\left(\\frac{\\sin{\\left(x \\right)}}{x}\\right)",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "__num_8",
      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
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    }
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  "edges": [
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      "to": "__sin_4"
    },
    {
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      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3"
    },
    {
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      "to": "__limit_2"
    },
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      "to": "__tends_to_7",
      "role": "lhs"
    },
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      "to": "__tends_to_7",
      "role": "rhs"
    },
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      "to": "__limit_2"
    },
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      "to": "__equals_1"
    },
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      "to": "__equals_1"
    }
  ],
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    "kind": "algebraic"
  }
}

flowchart RL
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  __multiply_3(("$\times$")):::operator
  __sin_4{{"$\sin(\cdot)$"}}:::function
  x["$x$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __num_6["$0$"]:::number
  __tends_to_7(("$\to$")):::operator
  __limit_2(("$\lim$")):::operator
  __num_8["$1$"]:::number
  x --> __sin_4
  __sin_4 --> __multiply_3
  x --> __power_5
  __power_5 -.-> __multiply_3
  __multiply_3 --> __limit_2
  x -->|lhs| __tends_to_7
  __num_6 -->|rhs| __tends_to_7
  __tends_to_7 --> __limit_2
  __limit_2 --> __equals_1
  __num_8 --> __equals_1
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{
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    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\lim_{x \\to a} \\frac{f(x)}{g(x)} = \\lim_{x \\to a} \\frac{f'(x)}{g'(x)}",
      "chartScript": {
        "script": "Limit(f(x)/g(x), x, a, dir='+-') - Limit(f_prime(x)/g_prime(x), x, a, dir='+-')",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "f{\\left(x \\right)} \\frac{1}{g{\\left(x \\right)}}",
      "chartScript": {
        "script": "f/g",
        "variables": [
          "f",
          "g"
        ]
      }
    },
    {
      "id": "__f_4",
      "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": [
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        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{g{\\left(x \\right)}}",
      "chartScript": {
        "script": "1/(g*x)",
        "variables": [
          "g",
          "x"
        ]
      }
    },
    {
      "id": "__g_6",
      "type": "function",
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      "subexpr": "g{\\left(x \\right)}",
      "chartScript": {
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        "variables": [
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        ]
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    },
    {
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      "type": "scalar",
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      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
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      }
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      "id": "__tends_to_7",
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      "op": "tends_to",
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      "limit_point": "a",
      "subexpr": "x \\to a",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__limit_2",
      "type": "operator",
      "op": "limit",
      "subexpr": "\\lim_{x \\to a}\\left(\\frac{f{\\left(x \\right)}}{g{\\left(x \\right)}}\\right)",
      "chartScript": {
        "script": "f/g",
        "variables": [
          "f",
          "g"
        ]
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\operatorname{f'}{\\left(x \\right)} \\frac{1}{\\operatorname{g'}{\\left(x \\right)}}",
      "chartScript": {
        "script": "f_prime/g_prime",
        "variables": [
          "f_prime",
          "g_prime"
        ]
      }
    },
    {
      "id": "__f_10",
      "type": "function",
      "op": "f'",
      "subexpr": "\\operatorname{f'}{\\left(x \\right)}",
      "chartScript": {
        "script": "f_prime*operatorname*x",
        "variables": [
          "f_prime",
          "operatorname",
          "x"
        ]
      }
    },
    {
      "id": "__power_11",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\operatorname{g'}{\\left(x \\right)}}",
      "chartScript": {
        "script": "1/(g_prime*operatorname*x)",
        "variables": [
          "g_prime",
          "operatorname",
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      }
    },
    {
      "id": "__g_12",
      "type": "function",
      "op": "g'",
      "subexpr": "\\operatorname{g'}{\\left(x \\right)}",
      "chartScript": {
        "script": "g_prime*operatorname*x",
        "variables": [
          "g_prime",
          "operatorname",
          "x"
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      }
    },
    {
      "id": "__tends_to_13",
      "type": "operator",
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      "limit_point": "a",
      "subexpr": "x \\to a",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__limit_8",
      "type": "operator",
      "op": "limit",
      "subexpr": "\\lim_{x \\to a}\\left(\\frac{\\operatorname{f'}{\\left(x \\right)}}{\\operatorname{g'}{\\left(x \\right)}}\\right)",
      "chartScript": {
        "script": "f_prime/g_prime",
        "variables": [
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          "g_prime"
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      "to": "__f_4"
    },
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      "semantic": "direct",
      "weight": 1.0
    },
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    },
    {
      "from": "__g_6",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3"
    },
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      "to": "__limit_2"
    },
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      "to": "__tends_to_7",
      "role": "lhs"
    },
    {
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      "to": "__tends_to_7",
      "role": "rhs"
    },
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      "to": "__limit_2"
    },
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      "from": "__limit_2",
      "to": "__equals_1"
    },
    {
      "from": "x",
      "to": "__f_10"
    },
    {
      "from": "__f_10",
      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__g_12"
    },
    {
      "from": "__g_12",
      "to": "__power_11"
    },
    {
      "from": "__power_11",
      "to": "__multiply_9"
    },
    {
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      "to": "__limit_8"
    },
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      "role": "lhs"
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    {
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      "role": "rhs"
    },
    {
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      "to": "__limit_8"
    },
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      "to": "__equals_1"
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    "kind": "algebraic"
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}

flowchart RL
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  __multiply_3(("$\times$")):::operator
  __f_4{{"$f(\cdot)$"}}:::function
  x["$x$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __g_6{{"$g(\cdot)$"}}:::function
  a["$a$"]:::scalar
  __tends_to_7(("$\to$")):::operator
  __limit_2(("$\lim$")):::operator
  __multiply_9(("$\times$")):::operator
  __f_10{{"$f'(\cdot)$"}}:::function
  __power_11(("$\dfrac{1}{(\cdot)}$")):::operator
  __g_12{{"$g'(\cdot)$"}}:::function
  __tends_to_13(("$\to$")):::operator
  __limit_8(("$\lim$")):::operator
  x --> __f_4
  __f_4 --> __multiply_3
  x --> __g_6
  __g_6 --> __power_5
  __power_5 -.-> __multiply_3
  __multiply_3 --> __limit_2
  x -->|lhs| __tends_to_7
  a -->|rhs| __tends_to_7
  __tends_to_7 --> __limit_2
  __limit_2 --> __equals_1
  x --> __f_10
  __f_10 --> __multiply_9
  x --> __g_12
  __g_12 --> __power_11
  __power_11 -.-> __multiply_9
  __multiply_9 --> __limit_8
  x -->|lhs| __tends_to_13
  a -->|rhs| __tends_to_13
  __tends_to_13 --> __limit_8
  __limit_8 --> __equals_1
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{
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    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\lim_{x \\to \\infty} \\frac{1}{x} = 0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{x}",
      "chartScript": {
        "script": "1/x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
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      "chartScript": {
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        "variables": [
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        ]
      }
    },
    {
      "id": "__const_4",
      "type": "constant",
      "label": "infinity",
      "latex": "\\infty",
      "subexpr": "\\infty",
      "chartScript": {
        "script": "Number.POSITIVE_INFINITY",
        "variables": []
      }
    },
    {
      "id": "__tends_to_5",
      "type": "operator",
      "op": "tends_to",
      "with_respect_to": "x",
      "limit_point": "__const_4",
      "limit_direction": "-",
      "subexpr": "x \\to \\infty",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__limit_2",
      "type": "operator",
      "op": "limit",
      "subexpr": "\\lim_{x \\to \\infty} \\frac{1}{x}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__num_6",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
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  "edges": [
    {
      "from": "x",
      "to": "__power_3"
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      "from": "__power_3",
      "to": "__limit_2"
    },
    {
      "from": "x",
      "to": "__tends_to_5",
      "role": "lhs"
    },
    {
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      "to": "__tends_to_5",
      "role": "rhs"
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      "to": "__limit_2"
    },
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      "to": "__equals_1"
    },
    {
      "from": "__num_6",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
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  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  x["$x$"]:::scalar
  __const_4["$\infty$"]:::constant
  __tends_to_5(("$\to$")):::operator
  __limit_2(("$\lim$")):::operator
  __num_6["$0$"]:::number
  x --> __power_3
  __power_3 -.-> __limit_2
  x -->|lhs| __tends_to_5
  __const_4 -->|rhs| __tends_to_5
  __tends_to_5 --> __limit_2
  __limit_2 --> __equals_1
  __num_6 --> __equals_1
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{
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    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\frac{d}{dx} x^n = n x^{n-1}",
      "chartScript": {
        "script": "-n*pow(x, n - 1) + n*pow(x, n)/x",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{n}",
      "chartScript": {
        "script": "pow(x, n)",
        "variables": [
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          "x"
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      }
    },
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      "id": "x",
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      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__deriv_2",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "x",
      "subexpr": "\\frac{\\partial}{\\partial x} x^{n}",
      "chartScript": {
        "script": "n*pow(x, n)/x",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x^{n - 1} n",
      "chartScript": {
        "script": "n*pow(x, n - 1)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{n - 1}",
      "chartScript": {
        "script": "pow(x, n - 1)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__add_6",
      "type": "operator",
      "op": "add",
      "subexpr": "n - 1",
      "chartScript": {
        "script": "n - 1",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_7",
      "type": "number",
      "label": "-1",
      "subexpr": "-1",
      "chartScript": {
        "script": "-1",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__power_3"
    },
    {
      "from": "n",
      "to": "__power_3",
      "role": "exp"
    },
    {
      "from": "__power_3",
      "to": "__deriv_2"
    },
    {
      "from": "x",
      "to": "__deriv_2",
      "role": "wrt"
    },
    {
      "from": "__deriv_2",
      "to": "__equals_1"
    },
    {
      "from": "n",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__power_5"
    },
    {
      "from": "n",
      "to": "__add_6"
    },
    {
      "from": "__num_7",
      "to": "__add_6"
    },
    {
      "from": "__add_6",
      "to": "__power_5",
      "role": "exp"
    },
    {
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      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "ODE",
    "order": 1,
    "dependent_variables": [],
    "independent_variables": [
      "x"
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  }
}

flowchart RL
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  __equals_1{"="}:::relation
  __power_3(("$(\cdot)^{\cdot}$")):::operator
  x["$x$"]:::scalar
  n["$n$"]:::scalar
  __deriv_2(("$\dfrac{d}{d x}$")):::operator
  __multiply_4(("$\times$")):::operator
  __power_5(("$(\cdot)^{\cdot}$")):::operator
  __add_6(("$+$")):::operator
  __num_7["$-1$"]:::number
  x --> __power_3
  n -->|exp| __power_3
  __power_3 --> __deriv_2
  x -->|wrt| __deriv_2
  __deriv_2 --> __equals_1
  n --> __multiply_4
  x --> __power_5
  n --> __add_6
  __num_7 --> __add_6
  __add_6 -->|exp| __power_5
  __power_5 --> __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:#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
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\frac{dy}{dx} = \\frac{dy}{du} \\cdot \\frac{du}{dx}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "y",
      "type": "scalar",
      "latex": "y",
      "subexpr": "y",
      "chartScript": {
        "script": "y",
        "variables": [
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        ]
      }
    },
    {
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      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__deriv_2",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "x",
      "subexpr": "\\frac{d}{d x} y",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{d}{d u} y \\frac{d}{d x} u",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "u",
      "type": "scalar",
      "latex": "u",
      "subexpr": "u",
      "chartScript": {
        "script": "u",
        "variables": [
          "u"
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      }
    },
    {
      "id": "__deriv_4",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "u",
      "subexpr": "\\frac{d}{d u} y",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__deriv_5",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "x",
      "subexpr": "\\frac{d}{d x} u",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "y",
      "to": "__deriv_2"
    },
    {
      "from": "x",
      "to": "__deriv_2",
      "role": "wrt"
    },
    {
      "from": "__deriv_2",
      "to": "__equals_1"
    },
    {
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      "to": "__deriv_4"
    },
    {
      "from": "u",
      "to": "__deriv_4",
      "role": "wrt"
    },
    {
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      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__deriv_5"
    },
    {
      "from": "x",
      "to": "__deriv_5",
      "role": "wrt"
    },
    {
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      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "PDE",
    "order": 1,
    "dependent_variables": [
      "u",
      "y"
    ],
    "independent_variables": [
      "u",
      "x"
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  }
}

flowchart RL
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  __equals_1{"="}:::relation
  y["$y$"]:::scalar
  x["$x$"]:::scalar
  __deriv_2(("$\dfrac{d}{d x}$")):::operator
  __multiply_3(("$\times$")):::operator
  u["$u$"]:::scalar
  __deriv_4(("$\dfrac{d}{d u}$")):::operator
  __deriv_5(("$\dfrac{d}{d x}$")):::operator
  y --> __deriv_2
  x -->|wrt| __deriv_2
  __deriv_2 --> __equals_1
  y --> __deriv_4
  u -->|wrt| __deriv_4
  __deriv_4 --> __multiply_3
  u --> __deriv_5
  x -->|wrt| __deriv_5
  __deriv_5 --> __multiply_3
  __multiply_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
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  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "(fg)' = f'g + fg'",
      "chartScript": {
        "script": "f*g",
        "variables": [
          "f",
          "g"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "g",
      "type": "scalar",
      "latex": "g",
      "subexpr": "g",
      "chartScript": {
        "script": "g",
        "variables": [
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        ]
      }
    }
  ],
  "edges": [
    {
      "from": "f",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "g",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    }
  ],
  "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
  __multiply_1(("$\times$")):::operator
  f["$f$"]:::scalar
  g["$g$"]:::scalar
  f --> __multiply_1
  g --> __multiply_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(\\frac{f}{g}\\right)' = \\frac{f'g - fg'}{g^2}",
      "chartScript": {
        "script": "f/g",
        "variables": [
          "f",
          "g"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{g}",
      "chartScript": {
        "script": "1/g",
        "variables": [
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        ]
      }
    },
    {
      "id": "g",
      "type": "scalar",
      "latex": "g",
      "subexpr": "g",
      "chartScript": {
        "script": "g",
        "variables": [
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        ]
      }
    }
  ],
  "edges": [
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      "semantic": "direct",
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    },
    {
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      "to": "__power_2"
    },
    {
      "from": "__power_2",
      "to": "__multiply_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  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
  __multiply_1(("$\times$")):::operator
  f["$f$"]:::scalar
  __power_2(("$\dfrac{1}{(\cdot)}$")):::operator
  g["$g$"]:::scalar
  f --> __multiply_1
  g --> __power_2
  __power_2 -.-> __multiply_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#42a5f5,stroke-width:1px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "f'(c) = \\frac{f(b) - f(a)}{b - a}",
      "chartScript": {
        "script": "f_prime(c) - (-f(a) + f(b))/(-a + b)",
        "variables": [
          "a",
          "b",
          "c"
        ]
      }
    },
    {
      "id": "__f_2",
      "type": "function",
      "op": "f'",
      "subexpr": "\\operatorname{f'}{\\left(c \\right)}",
      "chartScript": {
        "script": "c*f_prime*operatorname",
        "variables": [
          "c",
          "f_prime",
          "operatorname"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(-f{\\left(a \\right)} + f{\\left(b \\right)}\\right) \\frac{1}{- a + b}",
      "chartScript": {
        "script": "(-a*f + b*f)/(-a + b)",
        "variables": [
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          "b",
          "f"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "-f{\\left(a \\right)} + f{\\left(b \\right)}",
      "chartScript": {
        "script": "-a*f + b*f",
        "variables": [
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          "b",
          "f"
        ]
      }
    },
    {
      "id": "__f_5",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(b \\right)}",
      "chartScript": {
        "script": "b*f",
        "variables": [
          "b",
          "f"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__negation_6",
      "type": "operator",
      "op": "negation",
      "subexpr": "-f{\\left(a \\right)}",
      "chartScript": {
        "script": "-a*f",
        "variables": [
          "a",
          "f"
        ]
      }
    },
    {
      "id": "__f_7",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(a \\right)}",
      "chartScript": {
        "script": "a*f",
        "variables": [
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          "f"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
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        ]
      }
    },
    {
      "id": "__power_8",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{- a + b}",
      "chartScript": {
        "script": "1/(-a + b)",
        "variables": [
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          "b"
        ]
      }
    },
    {
      "id": "__add_9",
      "type": "operator",
      "op": "add",
      "subexpr": "b - a",
      "chartScript": {
        "script": "-a + b",
        "variables": [
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          "b"
        ]
      }
    },
    {
      "id": "__negation_10",
      "type": "operator",
      "op": "negation",
      "subexpr": "-a",
      "chartScript": {
        "script": "-a",
        "variables": [
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    }
  ],
  "edges": [
    {
      "from": "c",
      "to": "__f_2"
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      "to": "__equals_1"
    },
    {
      "from": "b",
      "to": "__f_5"
    },
    {
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      "to": "__add_4"
    },
    {
      "from": "a",
      "to": "__f_7"
    },
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      "to": "__negation_6"
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    {
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      "to": "__add_4"
    },
    {
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      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__add_9"
    },
    {
      "from": "a",
      "to": "__negation_10"
    },
    {
      "from": "__negation_10",
      "to": "__add_9"
    },
    {
      "from": "__add_9",
      "to": "__power_8"
    },
    {
      "from": "__power_8",
      "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
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  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
  __f_2{{"$f'(\cdot)$"}}:::function
  c["$c$"]:::scalar
  __multiply_3(("$\times$")):::operator
  __add_4(("$+$")):::operator
  __f_5{{"$f(\cdot)$"}}:::function
  b["$b$"]:::scalar
  __negation_6@{ shape: "flip-tri", label: "$-$" }
  __f_7{{"$f(\cdot)$"}}:::function
  a["$a$"]:::scalar
  __power_8(("$\dfrac{1}{(\cdot)}$")):::operator
  __add_9(("$+$")):::operator
  __negation_10@{ shape: "flip-tri", label: "$-$" }
  class __negation_6 operator
  class __negation_10 operator
  c --> __f_2
  __f_2 --> __equals_1
  b --> __f_5
  __f_5 --> __add_4
  a --> __f_7
  __f_7 --> __negation_6
  __negation_6 --> __add_4
  __add_4 --> __multiply_3
  b --> __add_9
  a --> __negation_10
  __negation_10 --> __add_9
  __add_9 --> __power_8
  __power_8 -.-> __multiply_3
  __multiply_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:#ef5350,stroke-width:3px
  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:#42a5f5,stroke-width:1px
  linkStyle 13 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\int x^n \\, dx = \\frac{x^{n+1}}{n+1} + C",
      "chartScript": {
        "script": "-C - pow(x, n + 1)/(n + 1) + ((n != -1) ? (\n   pow(x, n + 1)/(n + 1)\n)\n: (\n   log(x)\n))",
        "variables": [
          "C",
          "n",
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__integral_2",
      "type": "operator",
      "op": "integral",
      "with_respect_to": "x",
      "subexpr": "\\int x^{n}\\, dx",
      "chartScript": {
        "script": "((n != -1) ? (\n   pow(x, n + 1)/(n + 1)\n)\n: (\n   log(x)\n))",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{n}",
      "chartScript": {
        "script": "pow(x, n)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "C + x^{n + 1} \\frac{1}{n + 1}",
      "chartScript": {
        "script": "C + pow(x, n + 1)/(n + 1)",
        "variables": [
          "C",
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x^{n + 1} \\frac{1}{n + 1}",
      "chartScript": {
        "script": "pow(x, n + 1)/(n + 1)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{n + 1}",
      "chartScript": {
        "script": "pow(x, n + 1)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__add_7",
      "type": "operator",
      "op": "add",
      "subexpr": "n + 1",
      "chartScript": {
        "script": "n + 1",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_8",
      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{n + 1}",
      "chartScript": {
        "script": "1/(n + 1)",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__add_10",
      "type": "operator",
      "op": "add",
      "subexpr": "n + 1",
      "chartScript": {
        "script": "n + 1",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_11",
      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "C",
      "type": "scalar",
      "latex": "C",
      "subexpr": "C",
      "chartScript": {
        "script": "C",
        "variables": [
          "C"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__integral_2",
      "role": "wrt"
    },
    {
      "from": "x",
      "to": "__power_3"
    },
    {
      "from": "n",
      "to": "__power_3",
      "role": "exp"
    },
    {
      "from": "__power_3",
      "to": "__integral_2"
    },
    {
      "from": "__integral_2",
      "to": "__equals_1"
    },
    {
      "from": "x",
      "to": "__power_6"
    },
    {
      "from": "n",
      "to": "__add_7"
    },
    {
      "from": "__num_8",
      "to": "__add_7"
    },
    {
      "from": "__add_7",
      "to": "__power_6",
      "role": "exp"
    },
    {
      "from": "__power_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "n",
      "to": "__add_10"
    },
    {
      "from": "__num_11",
      "to": "__add_10"
    },
    {
      "from": "__add_10",
      "to": "__power_9"
    },
    {
      "from": "__power_9",
      "to": "__multiply_5"
    },
    {
      "from": "__multiply_5",
      "to": "__add_4"
    },
    {
      "from": "C",
      "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
  x["$x$"]:::scalar
  __integral_2(("$\int dx$")):::operator
  __power_3(("$(\cdot)^{\cdot}$")):::operator
  n["$n$"]:::scalar
  __add_4(("$+$")):::operator
  __multiply_5(("$\times$")):::operator
  __power_6(("$(\cdot)^{\cdot}$")):::operator
  __add_7(("$+$")):::operator
  __num_8["$1$"]:::number
  __power_9(("$\dfrac{1}{(\cdot)}$")):::operator
  __add_10(("$+$")):::operator
  __num_11["$1$"]:::number
  C["$C$"]:::scalar
  x -->|wrt| __integral_2
  x --> __power_3
  n -->|exp| __power_3
  __power_3 --> __integral_2
  __integral_2 --> __equals_1
  x --> __power_6
  n --> __add_7
  __num_8 --> __add_7
  __add_7 -->|exp| __power_6
  __power_6 --> __multiply_5
  n --> __add_10
  __num_11 --> __add_10
  __add_10 --> __power_9
  __power_9 -.-> __multiply_5
  __multiply_5 --> __add_4
  C --> __add_4
  __add_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:#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:#42a5f5,stroke-width:1px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#aaa,stroke-width:2px
  linkStyle 16 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\int_a^b f(x) \\, dx = F(b) - F(a)",
      "chartScript": {
        "script": "F(a) - F(b) + Integral(f(x), (x, a, b))",
        "variables": [
          "a",
          "b"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "b",
      "type": "scalar",
      "latex": "b",
      "subexpr": "b",
      "chartScript": {
        "script": "b",
        "variables": [
          "b"
        ]
      }
    },
    {
      "id": "__integral_2",
      "type": "operator",
      "op": "integral",
      "with_respect_to": "x",
      "lower_bound": "a",
      "upper_bound": "b",
      "subexpr": "\\int\\limits_{a}^{b} f{\\left(x \\right)}\\, dx",
      "chartScript": {
        "script": "-1/2*pow(a, 2)*f + (1/2)*pow(b, 2)*f",
        "variables": [
          "a",
          "b",
          "f"
        ]
      }
    },
    {
      "id": "__f_3",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(x \\right)}",
      "chartScript": {
        "script": "f*x",
        "variables": [
          "f",
          "x"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "-F{\\left(a \\right)} + F{\\left(b \\right)}",
      "chartScript": {
        "script": "-F*a + F*b",
        "variables": [
          "F",
          "a",
          "b"
        ]
      }
    },
    {
      "id": "__F_5",
      "type": "function",
      "op": "F",
      "subexpr": "F{\\left(b \\right)}",
      "chartScript": {
        "script": "F*b",
        "variables": [
          "F",
          "b"
        ]
      }
    },
    {
      "id": "__negation_6",
      "type": "operator",
      "op": "negation",
      "subexpr": "-F{\\left(a \\right)}",
      "chartScript": {
        "script": "-F*a",
        "variables": [
          "F",
          "a"
        ]
      }
    },
    {
      "id": "__F_7",
      "type": "function",
      "op": "F",
      "subexpr": "F{\\left(a \\right)}",
      "chartScript": {
        "script": "F*a",
        "variables": [
          "F",
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__integral_2",
      "role": "wrt"
    },
    {
      "from": "a",
      "to": "__integral_2",
      "role": "lb"
    },
    {
      "from": "b",
      "to": "__integral_2",
      "role": "ub"
    },
    {
      "from": "x",
      "to": "__f_3"
    },
    {
      "from": "__f_3",
      "to": "__integral_2"
    },
    {
      "from": "__integral_2",
      "to": "__equals_1"
    },
    {
      "from": "b",
      "to": "__F_5"
    },
    {
      "from": "__F_5",
      "to": "__add_4"
    },
    {
      "from": "a",
      "to": "__F_7"
    },
    {
      "from": "__F_7",
      "to": "__negation_6"
    },
    {
      "from": "__negation_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
  x["$x$"]:::scalar
  a["$a$"]:::scalar
  b["$b$"]:::scalar
  __integral_2(("$\int_{a}^{b} dx$")):::operator
  __f_3{{"$f(\cdot)$"}}:::function
  __add_4(("$+$")):::operator
  __F_5{{"$F(\cdot)$"}}:::function
  __negation_6@{ shape: "flip-tri", label: "$-$" }
  __F_7{{"$F(\cdot)$"}}:::function
  class __negation_6 operator
  x -->|wrt| __integral_2
  a -->|lb| __integral_2
  b -->|ub| __integral_2
  x --> __f_3
  __f_3 --> __integral_2
  __integral_2 --> __equals_1
  b --> __F_5
  __F_5 --> __add_4
  a --> __F_7
  __F_7 --> __negation_6
  __negation_6 --> __add_4
  __add_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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\frac{d}{dx} \\int_a^x f(t) \\, dt = f(x)",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__integral_3",
      "type": "operator",
      "op": "integral",
      "with_respect_to": "t",
      "lower_bound": "a",
      "upper_bound": "x",
      "subexpr": "\\int\\limits_{a}^{x} f{\\left(t \\right)}\\, dt",
      "chartScript": {
        "script": "-1/2*pow(a, 2)*f + (1/2)*f*pow(x, 2)",
        "variables": [
          "a",
          "f",
          "x"
        ]
      }
    },
    {
      "id": "__f_4",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(t \\right)}",
      "chartScript": {
        "script": "f*t",
        "variables": [
          "f",
          "t"
        ]
      }
    },
    {
      "id": "__deriv_2",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "x",
      "subexpr": "\\frac{\\partial}{\\partial x} \\int\\limits_{a}^{x} f{\\left(t \\right)}\\, dt",
      "chartScript": {
        "script": "f*x",
        "variables": [
          "f",
          "x"
        ]
      }
    },
    {
      "id": "__f_5",
      "type": "function",
      "op": "f",
      "subexpr": "f{\\left(x \\right)}",
      "chartScript": {
        "script": "f*x",
        "variables": [
          "f",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "t",
      "to": "__integral_3",
      "role": "wrt"
    },
    {
      "from": "a",
      "to": "__integral_3",
      "role": "lb"
    },
    {
      "from": "x",
      "to": "__integral_3",
      "role": "ub"
    },
    {
      "from": "t",
      "to": "__f_4"
    },
    {
      "from": "__f_4",
      "to": "__integral_3"
    },
    {
      "from": "__integral_3",
      "to": "__deriv_2"
    },
    {
      "from": "x",
      "to": "__deriv_2",
      "role": "wrt"
    },
    {
      "from": "__deriv_2",
      "to": "__equals_1"
    },
    {
      "from": "x",
      "to": "__f_5"
    },
    {
      "from": "__f_5",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "ODE",
    "order": 1,
    "dependent_variables": [],
    "independent_variables": [
      "x"
    ]
  }
}

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
  t["$t$"]:::scalar
  a["$a$"]:::scalar
  x["$x$"]:::scalar
  __integral_3(("$\int_{a}^{x} dt$")):::operator
  __f_4{{"$f(\cdot)$"}}:::function
  __deriv_2(("$\dfrac{d}{d x}$")):::operator
  __f_5{{"$f(\cdot)$"}}:::function
  t -->|wrt| __integral_3
  a -->|lb| __integral_3
  x -->|ub| __integral_3
  t --> __f_4
  __f_4 --> __integral_3
  __integral_3 --> __deriv_2
  x -->|wrt| __deriv_2
  __deriv_2 --> __equals_1
  x --> __f_5
  __f_5 --> __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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "e^x = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{x}",
      "chartScript": {
        "script": "exp(x)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "e",
      "type": "scalar",
      "latex": "e",
      "subexpr": "e",
      "chartScript": {
        "script": "e",
        "variables": []
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "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 = 0",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__sum_3",
      "type": "operator",
      "op": "sum",
      "with_respect_to": "n",
      "lower_bound": "__num_4",
      "upper_bound": "__const_5",
      "subexpr": "\\sum_{n=0}^{\\infty} \\frac{x^{n}}{n!}",
      "chartScript": {
        "script": "exp(x)",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x^{n} \\frac{1}{n!}",
      "chartScript": {
        "script": "pow(x, n)/factorial(n)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_8",
      "type": "operator",
      "op": "power",
      "subexpr": "x^{n}",
      "chartScript": {
        "script": "pow(x, n)",
        "variables": [
          "n",
          "x"
        ]
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{n!}",
      "chartScript": {
        "script": "1/factorial(n)",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__factorial_10",
      "type": "operator",
      "op": "factorial",
      "subexpr": "n!",
      "chartScript": {
        "script": "factorial(n)",
        "variables": [
          "n"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "e",
      "to": "__power_2"
    },
    {
      "from": "x",
      "to": "__power_2",
      "role": "exp"
    },
    {
      "from": "__power_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": "x",
      "to": "__power_8"
    },
    {
      "from": "n",
      "to": "__power_8",
      "role": "exp"
    },
    {
      "from": "__power_8",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "n",
      "to": "__factorial_10"
    },
    {
      "from": "__factorial_10",
      "to": "__power_9"
    },
    {
      "from": "__power_9",
      "to": "__multiply_7"
    },
    {
      "from": "__multiply_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
  __power_2(("$(\cdot)^{\cdot}$")):::operator
  e["$e$"]:::scalar
  x["$x$"]:::scalar
  n["$n$"]:::scalar
  __num_4["$0$"]:::number
  __const_5["$\infty$"]:::constant
  __equals_6{"="}:::relation
  __sum_3(("$\sum_{n}$")):::operator
  __multiply_7(("$\times$")):::operator
  __power_8(("$(\cdot)^{\cdot}$")):::operator
  __power_9(("$\dfrac{1}{(\cdot)}$")):::operator
  __factorial_10(("$(\cdot)!$")):::operator
  e --> __power_2
  x -->|exp| __power_2
  __power_2 --> __equals_1
  n -->|wrt| __sum_3
  n --> __equals_6
  __num_4 --> __equals_6
  __equals_6 -->|lb| __sum_3
  __const_5 -->|ub| __sum_3
  x --> __power_8
  n -->|exp| __power_8
  __power_8 --> __multiply_7
  n --> __factorial_10
  __factorial_10 --> __power_9
  __power_9 -.-> __multiply_7
  __multiply_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:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#42a5f5,stroke-width:1px
  linkStyle 14 stroke:#aaa,stroke-width:2px
  linkStyle 15 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\sum_{n=0}^{\\infty} r^n = \\frac{1}{1 - r}",
      "chartScript": {
        "script": "((abs(r) < 1) ? (\n   1/(1 - r)\n)\n: (\n   Sum(pow(r, n), (n, 0, Number.POSITIVE_INFINITY))\n)) - 1/(1 - r)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__num_3",
      "type": "number",
      "label": "0",
      "subexpr": "0",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__const_4",
      "type": "constant",
      "label": "infinity",
      "latex": "\\infty",
      "subexpr": "\\infty",
      "chartScript": {
        "script": "Number.POSITIVE_INFINITY",
        "variables": []
      }
    },
    {
      "id": "__equals_5",
      "type": "relation",
      "op": "equals",
      "subexpr": "n = 0",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__sum_2",
      "type": "operator",
      "op": "sum",
      "with_respect_to": "n",
      "lower_bound": "__num_3",
      "upper_bound": "__const_4",
      "subexpr": "\\sum_{n=0}^{\\infty} r^{n}",
      "chartScript": {
        "script": "((abs(r) < 1) ? (\n   1/(1 - r)\n)\n: (\n   Sum(pow(r, n), (n, 0, Number.POSITIVE_INFINITY))\n))",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "subexpr": "r^{n}",
      "chartScript": {
        "script": "pow(r, n)",
        "variables": [
          "n",
          "r"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__power_7",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{1 - r}",
      "chartScript": {
        "script": "1/(1 - r)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__add_8",
      "type": "operator",
      "op": "add",
      "subexpr": "1 - r",
      "chartScript": {
        "script": "1 - r",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__num_9",
      "type": "number",
      "label": "1",
      "subexpr": "1",
      "chartScript": {
        "script": "1",
        "variables": []
      }
    },
    {
      "id": "__negation_10",
      "type": "operator",
      "op": "negation",
      "subexpr": "-r",
      "chartScript": {
        "script": "-r",
        "variables": [
          "r"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "n",
      "to": "__sum_2",
      "role": "wrt"
    },
    {
      "from": "n",
      "to": "__equals_5"
    },
    {
      "from": "__num_3",
      "to": "__equals_5"
    },
    {
      "from": "__equals_5",
      "to": "__sum_2",
      "role": "lb"
    },
    {
      "from": "__const_4",
      "to": "__sum_2",
      "role": "ub"
    },
    {
      "from": "r",
      "to": "__power_6"
    },
    {
      "from": "n",
      "to": "__power_6",
      "role": "exp"
    },
    {
      "from": "__power_6",
      "to": "__sum_2"
    },
    {
      "from": "__sum_2",
      "to": "__equals_1"
    },
    {
      "from": "__num_9",
      "to": "__add_8"
    },
    {
      "from": "r",
      "to": "__negation_10"
    },
    {
      "from": "__negation_10",
      "to": "__add_8"
    },
    {
      "from": "__add_8",
      "to": "__power_7"
    },
    {
      "from": "__power_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
  n["$n$"]:::scalar
  __num_3["$0$"]:::number
  __const_4["$\infty$"]:::constant
  __equals_5{"="}:::relation
  __sum_2(("$\sum_{n}$")):::operator
  __power_6(("$(\cdot)^{\cdot}$")):::operator
  r["$r$"]:::scalar
  __power_7(("$\dfrac{1}{(\cdot)}$")):::operator
  __add_8(("$+$")):::operator
  __num_9["$1$"]:::number
  __negation_10@{ shape: "flip-tri", label: "$-$" }
  class __negation_10 operator
  n -->|wrt| __sum_2
  n --> __equals_5
  __num_3 --> __equals_5
  __equals_5 -->|lb| __sum_2
  __const_4 -->|ub| __sum_2
  r --> __power_6
  n -->|exp| __power_6
  __power_6 --> __sum_2
  __sum_2 --> __equals_1
  __num_9 --> __add_8
  r --> __negation_10
  __negation_10 --> __add_8
  __add_8 --> __power_7
  __power_7 -.-> __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:#42a5f5,stroke-width:1px