Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "V = I R",
      "chartScript": {
        "script": "-I*R + V",
        "variables": [
          "I",
          "R",
          "V"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "I R",
      "chartScript": {
        "script": "I*R",
        "variables": [
          "I",
          "R"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "R",
      "type": "scalar",
      "latex": "R",
      "subexpr": "R",
      "chartScript": {
        "script": "R",
        "variables": [
          "R"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "V",
      "to": "__equals_1"
    },
    {
      "from": "I",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "R",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  V["$V$"]:::scalar
  __multiply_2(("$\times$")):::operator
  I["$I$"]:::scalar
  R["$R$"]:::scalar
  V --> __equals_1
  I --> __multiply_2
  R --> __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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "P = I V",
      "chartScript": {
        "script": "-I*V + P",
        "variables": [
          "I",
          "P",
          "V"
        ]
      }
    },
    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
          "P"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "I V",
      "chartScript": {
        "script": "I*V",
        "variables": [
          "I",
          "V"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "P",
      "to": "__equals_1"
    },
    {
      "from": "I",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "V",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  P["$P$"]:::scalar
  __multiply_2(("$\times$")):::operator
  I["$I$"]:::scalar
  V["$V$"]:::scalar
  P --> __equals_1
  I --> __multiply_2
  V --> __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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "R = R_1 + R_2 + R_3",
      "chartScript": {
        "script": "R - R_1 - R_2 - R_3",
        "variables": [
          "R",
          "R_1",
          "R_2",
          "R_3"
        ]
      }
    },
    {
      "id": "R",
      "type": "scalar",
      "latex": "R",
      "subexpr": "R",
      "chartScript": {
        "script": "R",
        "variables": [
          "R"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "R_{3} + R_{1} + R_{2}",
      "chartScript": {
        "script": "R_1 + R_2 + R_3",
        "variables": [
          "R_1",
          "R_2",
          "R_3"
        ]
      }
    },
    {
      "id": "__add_3",
      "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": "R_3",
      "type": "scalar",
      "latex": "R_{3}",
      "subexpr": "R_{3}",
      "chartScript": {
        "script": "R_3",
        "variables": [
          "R_3"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "R",
      "to": "__equals_1"
    },
    {
      "from": "R_1",
      "to": "__add_3"
    },
    {
      "from": "R_2",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__add_2"
    },
    {
      "from": "R_3",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  R["$R$"]:::scalar
  __add_2(("$+$")):::operator
  __add_3(("$+$")):::operator
  R_1["$R_{1}$"]:::scalar
  R_2["$R_{2}$"]:::scalar
  R_3["$R_{3}$"]:::scalar
  R --> __equals_1
  R_1 --> __add_3
  R_2 --> __add_3
  __add_3 --> __add_2
  R_3 --> __add_2
  __add_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "C = \\frac{Q}{V}",
      "chartScript": {
        "script": "C - Q/V",
        "variables": [
          "C",
          "Q",
          "V"
        ]
      }
    },
    {
      "id": "C",
      "type": "scalar",
      "latex": "C",
      "subexpr": "C",
      "chartScript": {
        "script": "C",
        "variables": [
          "C"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "Q \\frac{1}{V}",
      "chartScript": {
        "script": "Q/V",
        "variables": [
          "Q",
          "V"
        ]
      }
    },
    {
      "id": "Q",
      "type": "scalar",
      "latex": "Q",
      "subexpr": "Q",
      "chartScript": {
        "script": "Q",
        "variables": [
          "Q"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{V}",
      "chartScript": {
        "script": "1/V",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "C",
      "to": "__equals_1"
    },
    {
      "from": "Q",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "V",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "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
  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
  C["$C$"]:::scalar
  __multiply_2(("$\times$")):::operator
  Q["$Q$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  V["$V$"]:::scalar
  C --> __equals_1
  Q --> __multiply_2
  V --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#42a5f5,stroke-width:1px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "U = \\frac{1}{2} C V^2",
      "chartScript": {
        "script": "-1/2*C*pow(V, 2) + U",
        "variables": [
          "C",
          "U",
          "V"
        ]
      }
    },
    {
      "id": "U",
      "type": "scalar",
      "latex": "U",
      "subexpr": "U",
      "chartScript": {
        "script": "U",
        "variables": [
          "U"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{2} C V^{2}",
      "chartScript": {
        "script": "(1/2)*C*pow(V, 2)",
        "variables": [
          "C",
          "V"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2}",
      "chartScript": {
        "script": "1/2",
        "variables": []
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "C V^{2}",
      "chartScript": {
        "script": "C*pow(V, 2)",
        "variables": [
          "C",
          "V"
        ]
      }
    },
    {
      "id": "C",
      "type": "scalar",
      "latex": "C",
      "subexpr": "C",
      "chartScript": {
        "script": "C",
        "variables": [
          "C"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "V^{2}",
      "chartScript": {
        "script": "pow(V, 2)",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "U",
      "to": "__equals_1"
    },
    {
      "from": "__num_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "C",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "V",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  U["$U$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  __num_4["$2$"]:::number
  __multiply_5(("$\times$")):::operator
  C["$C$"]:::scalar
  __power_6(("${(\cdot)}^{2}$")):::operator
  V["$V$"]:::scalar
  U --> __equals_1
  __num_4 --> __power_3
  __power_3 -.-> __multiply_2
  C --> __multiply_5
  V --> __power_6
  __power_6 --> __multiply_5
  __multiply_5 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#42a5f5,stroke-width:1px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "V = -L \\frac{d}{d t} I",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "V",
      "type": "scalar",
      "latex": "V",
      "subexpr": "V",
      "chartScript": {
        "script": "V",
        "variables": [
          "V"
        ]
      }
    },
    {
      "id": "__negation_2",
      "type": "operator",
      "op": "negation",
      "subexpr": "-L \\frac{d}{d t} I",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "L \\frac{d}{d t} I",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "__deriv_4",
      "type": "operator",
      "op": "derivative",
      "with_respect_to": "t",
      "subexpr": "\\frac{d}{d t} I",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "V",
      "to": "__equals_1"
    },
    {
      "from": "L",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "I",
      "to": "__deriv_4"
    },
    {
      "from": "t",
      "to": "__deriv_4",
      "role": "wrt"
    },
    {
      "from": "__deriv_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__negation_2"
    },
    {
      "from": "__negation_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "ODE",
    "order": 1,
    "dependent_variables": [
      "I"
    ],
    "independent_variables": [
      "t"
    ],
    "sympy_hints": [
      "factorable",
      "nth_algebraic",
      "separable",
      "1st_exact",
      "1st_linear",
      "Bernoulli",
      "1st_power_series",
      "lie_group",
      "nth_linear_constant_coeff_undetermined_coefficients",
      "nth_linear_euler_eq_nonhomogeneous_undetermined_coefficients",
      "nth_linear_constant_coeff_variation_of_parameters",
      "nth_linear_euler_eq_nonhomogeneous_variation_of_parameters"
    ],
    "linear": true,
    "homogeneous": true,
    "constant_coefficients": true
  }
}

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
  V["$V$"]:::scalar
  __negation_2@{ shape: "flip-tri", label: "$-$" }
  __multiply_3(("$\times$")):::operator
  L["$L$"]:::scalar
  I["$I$"]:::scalar
  t["$t$"]:::scalar
  __deriv_4(("$\dfrac{d}{d t}$")):::operator
  class __negation_2 operator
  V --> __equals_1
  L --> __multiply_3
  I --> __deriv_4
  t -->|wrt| __deriv_4
  __deriv_4 --> __multiply_3
  __multiply_3 --> __negation_2
  __negation_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = k_e \\frac{q_1 q_2}{r^2}",
      "chartScript": {
        "script": "F - k_e*q_1*q_2/pow(r, 2)",
        "variables": [
          "F",
          "k_e",
          "q_1",
          "q_2",
          "r"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "k_{e} q_{1} q_{2} \\frac{1}{r^{2}}",
      "chartScript": {
        "script": "k_e*q_1*q_2/pow(r, 2)",
        "variables": [
          "k_e",
          "q_1",
          "q_2",
          "r"
        ]
      }
    },
    {
      "id": "k_e",
      "type": "scalar",
      "latex": "k_{e}",
      "subexpr": "k_{e}",
      "chartScript": {
        "script": "k_e",
        "variables": [
          "k_e"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "q_{1} q_{2} \\frac{1}{r^{2}}",
      "chartScript": {
        "script": "q_1*q_2/pow(r, 2)",
        "variables": [
          "q_1",
          "q_2",
          "r"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "q_{1} q_{2}",
      "chartScript": {
        "script": "q_1*q_2",
        "variables": [
          "q_1",
          "q_2"
        ]
      }
    },
    {
      "id": "q_1",
      "type": "scalar",
      "latex": "q_{1}",
      "subexpr": "q_{1}",
      "chartScript": {
        "script": "q_1",
        "variables": [
          "q_1"
        ]
      }
    },
    {
      "id": "q_2",
      "type": "scalar",
      "latex": "q_{2}",
      "subexpr": "q_{2}",
      "chartScript": {
        "script": "q_2",
        "variables": [
          "q_2"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{r^{2}}",
      "chartScript": {
        "script": "pow(r, -2)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "r^{2}",
      "chartScript": {
        "script": "pow(r, 2)",
        "variables": [
          "r"
        ]
      }
    },
    {
      "id": "r",
      "type": "scalar",
      "latex": "r",
      "subexpr": "r",
      "chartScript": {
        "script": "r",
        "variables": [
          "r"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "k_e",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "q_1",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "q_2",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "r",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3"
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __multiply_2(("$\times$")):::operator
  k_e["$k_{e}$"]:::scalar
  __multiply_3(("$\times$")):::operator
  __multiply_4(("$\times$")):::operator
  q_1["$q_{1}$"]:::scalar
  q_2["$q_{2}$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __power_6(("${(\cdot)}^{2}$")):::operator
  r["$r$"]:::scalar
  F --> __equals_1
  k_e --> __multiply_2
  q_1 --> __multiply_4
  q_2 --> __multiply_4
  __multiply_4 --> __multiply_3
  r --> __power_6
  __power_6 --> __power_5
  __power_5 -.-> __multiply_3
  __multiply_3 --> __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:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#ef5350,stroke-width:6px
  linkStyle 7 stroke:#42a5f5,stroke-width:1px
  linkStyle 8 stroke:#ef5350,stroke-width:3px
  linkStyle 9 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E = \\frac{F}{q}",
      "chartScript": {
        "script": "E - F/q",
        "variables": [
          "E",
          "F",
          "q"
        ]
      }
    },
    {
      "id": "E",
      "type": "scalar",
      "latex": "E",
      "subexpr": "E",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "F \\frac{1}{q}",
      "chartScript": {
        "script": "F/q",
        "variables": [
          "F",
          "q"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{q}",
      "chartScript": {
        "script": "1/q",
        "variables": [
          "q"
        ]
      }
    },
    {
      "id": "q",
      "type": "scalar",
      "latex": "q",
      "subexpr": "q",
      "chartScript": {
        "script": "q",
        "variables": [
          "q"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E",
      "to": "__equals_1"
    },
    {
      "from": "F",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "q",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "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
  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
  E["$E$"]:::scalar
  __multiply_2(("$\times$")):::operator
  F["$F$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  q["$q$"]:::scalar
  E --> __equals_1
  F --> __multiply_2
  q --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#42a5f5,stroke-width:1px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "F = q v B \\sin\\theta",
      "chartScript": {
        "script": "-B*q*v*sin(theta) + F",
        "variables": [
          "B",
          "F",
          "q",
          "theta",
          "v"
        ]
      }
    },
    {
      "id": "F",
      "type": "scalar",
      "latex": "F",
      "subexpr": "F",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "q v B \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "B*q*v*sin(theta)",
        "variables": [
          "B",
          "q",
          "theta",
          "v"
        ]
      }
    },
    {
      "id": "q",
      "type": "scalar",
      "latex": "q",
      "subexpr": "q",
      "chartScript": {
        "script": "q",
        "variables": [
          "q"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "v B \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "B*v*sin(theta)",
        "variables": [
          "B",
          "theta",
          "v"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "B \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "B*sin(theta)",
        "variables": [
          "B",
          "theta"
        ]
      }
    },
    {
      "id": "B",
      "type": "scalar",
      "latex": "B",
      "subexpr": "B",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    },
    {
      "id": "__sin_5",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "sin(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
      "from": "q",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "B",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_5"
    },
    {
      "from": "__sin_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  F["$F$"]:::scalar
  __multiply_2(("$\times$")):::operator
  q["$q$"]:::scalar
  __multiply_3(("$\times$")):::operator
  v["$v$"]:::scalar
  __multiply_4(("$\times$")):::operator
  B["$B$"]:::scalar
  __sin_5{{"$\sin(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  F --> __equals_1
  q --> __multiply_2
  v --> __multiply_3
  B --> __multiply_4
  theta --> __sin_5
  __sin_5 --> __multiply_4
  __multiply_4 --> __multiply_3
  __multiply_3 --> __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:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#ef5350,stroke-width:3px
  linkStyle 8 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "c = \\frac{1}{\\sqrt{\\mu_0 \\epsilon_0}}",
      "chartScript": {
        "script": "c - 1/sqrt(epsilon_0*mu_0)",
        "variables": [
          "c",
          "epsilon_0",
          "mu_0"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\sqrt{\\mu_{0} \\epsilon_{0}}}",
      "chartScript": {
        "script": "pow(epsilon_0*mu_0, -1/2)",
        "variables": [
          "epsilon_0",
          "mu_0"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "exponent": "1/2",
      "subexpr": "\\sqrt{\\mu_{0} \\epsilon_{0}}",
      "chartScript": {
        "script": "sqrt(epsilon_0*mu_0)",
        "variables": [
          "epsilon_0",
          "mu_0"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\mu_{0} \\epsilon_{0}",
      "chartScript": {
        "script": "epsilon_0*mu_0",
        "variables": [
          "epsilon_0",
          "mu_0"
        ]
      }
    },
    {
      "id": "mu_0",
      "type": "scalar",
      "latex": "\\mu_{0}",
      "subexpr": "\\mu_{0}",
      "chartScript": {
        "script": "mu_0",
        "variables": [
          "mu_0"
        ]
      }
    },
    {
      "id": "epsilon_0",
      "type": "scalar",
      "latex": "\\epsilon_{0}",
      "subexpr": "\\epsilon_{0}",
      "chartScript": {
        "script": "epsilon_0",
        "variables": [
          "epsilon_0"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "c",
      "to": "__equals_1"
    },
    {
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      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__power_2"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar 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 result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  c["$c$"]:::scalar
  __power_2(("$\dfrac{1}{(\cdot)}$")):::operator
  __power_3(("${(\cdot)}^{1/2}$")):::operator
  __multiply_4(("$\times$")):::operator
  mu_0["$\mu_{0}$"]:::scalar
  epsilon_0["$\epsilon_{0}$"]:::scalar
  c --> __equals_1
  mu_0 --> __multiply_4
  epsilon_0 --> __multiply_4
  __multiply_4 --> __power_3
  __power_3 --> __power_2
  __power_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:#aaa,stroke-width:2px
  linkStyle 5 stroke:#42a5f5,stroke-width:1px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\oint \\vec{E} \\cdot d \\vec{A} = \\frac{Q}{\\epsilon_0}",
      "chartScript": {
        "script": "E*dA*oint - Q/epsilon_0",
        "variables": [
          "E",
          "Q",
          "dA",
          "epsilon_0",
          "oint"
        ]
      }
    },
    {
      "id": "__closed_integral_2",
      "type": "operator",
      "op": "closed_integral",
      "with_respect_to": "A",
      "subexpr": "\\int \\vec{E}\\, dA",
      "chartScript": {
        "script": "A*E",
        "variables": [
          "A",
          "E"
        ]
      }
    },
    {
      "id": "dA",
      "type": "differential",
      "latex": "dA",
      "with_respect_to": "A"
    },
    {
      "id": "E",
      "type": "vector",
      "latex": "\\vec{E}",
      "subexpr": "\\vec{E}",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "Q \\frac{1}{\\epsilon_{0}}",
      "chartScript": {
        "script": "Q/epsilon_0",
        "variables": [
          "Q",
          "epsilon_0"
        ]
      }
    },
    {
      "id": "Q",
      "type": "scalar",
      "latex": "Q",
      "subexpr": "Q",
      "chartScript": {
        "script": "Q",
        "variables": [
          "Q"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\epsilon_{0}}",
      "chartScript": {
        "script": "1/epsilon_0",
        "variables": [
          "epsilon_0"
        ]
      }
    },
    {
      "id": "epsilon_0",
      "type": "scalar",
      "latex": "\\epsilon_{0}",
      "subexpr": "\\epsilon_{0}",
      "chartScript": {
        "script": "epsilon_0",
        "variables": [
          "epsilon_0"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "dA",
      "to": "__closed_integral_2",
      "role": "wrt"
    },
    {
      "from": "E",
      "to": "__closed_integral_2"
    },
    {
      "from": "__closed_integral_2",
      "to": "__equals_1"
    },
    {
      "from": "Q",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "epsilon_0",
      "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
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __closed_integral_2(("$\oint$")):::operator
  dA["$dA$"]
  E["$\vec{E}$"]:::vector
  __multiply_3(("$\times$")):::operator
  Q["$Q$"]:::scalar
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  epsilon_0["$\epsilon_{0}$"]:::scalar
  dA -->|wrt| __closed_integral_2
  E --> __closed_integral_2
  __closed_integral_2 --> __equals_1
  Q --> __multiply_3
  epsilon_0 --> __power_4
  __power_4 -.-> __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:#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": "\\nabla \\times \\vec{E} = -\\frac{\\partial \\vec{B}}{\\partial t}",
      "chartScript": {
        "script": "E*nabla",
        "variables": [
          "E",
          "nabla"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\nabla \\times \\vec{E}",
      "chartScript": {
        "script": "E*nabla",
        "variables": [
          "E",
          "nabla"
        ]
      }
    },
    {
      "id": "nabla",
      "type": "scalar",
      "latex": "\\nabla",
      "subexpr": "\\nabla",
      "chartScript": {
        "script": "nabla",
        "variables": [
          "nabla"
        ]
      }
    },
    {
      "id": "E",
      "type": "vector",
      "latex": "\\vec{E}",
      "subexpr": "\\vec{E}",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__negation_3",
      "type": "operator",
      "op": "negation",
      "subexpr": "-\\frac{\\partial \\vec{B}}{\\partial t}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "B",
      "type": "vector",
      "latex": "\\vec{B}",
      "subexpr": "\\vec{B}",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
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      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "__deriv_4",
      "type": "operator",
      "op": "partial_derivative",
      "with_respect_to": "t",
      "subexpr": "\\frac{\\partial \\vec{B}}{\\partial t}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "nabla",
      "to": "__multiply_2",
      "semantic": "direct",
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    },
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      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "B",
      "to": "__deriv_4"
    },
    {
      "from": "t",
      "to": "__deriv_4",
      "role": "wrt"
    },
    {
      "from": "__deriv_4",
      "to": "__negation_3"
    },
    {
      "from": "__negation_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "ODE",
    "order": 1,
    "dependent_variables": [
      "B"
    ],
    "independent_variables": [
      "t"
    ],
    "sympy_hints": [
      "factorable",
      "nth_algebraic",
      "separable",
      "1st_exact",
      "1st_linear",
      "Bernoulli",
      "1st_power_series",
      "lie_group",
      "nth_linear_constant_coeff_undetermined_coefficients",
      "nth_linear_euler_eq_nonhomogeneous_undetermined_coefficients",
      "nth_linear_constant_coeff_variation_of_parameters",
      "nth_linear_euler_eq_nonhomogeneous_variation_of_parameters"
    ],
    "linear": true,
    "homogeneous": true,
    "constant_coefficients": true
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  nabla["$\nabla$"]:::scalar
  E["$\vec{E}$"]:::vector
  __negation_3@{ shape: "flip-tri", label: "$-$" }
  B["$\vec{B}$"]:::vector
  t["$t$"]:::scalar
  __deriv_4(("$\dfrac{\partial}{\partial t}$")):::operator
  class __negation_3 operator
  nabla --> __multiply_2
  E --> __multiply_2
  __multiply_2 --> __equals_1
  B --> __deriv_4
  t -->|wrt| __deriv_4
  __deriv_4 --> __negation_3
  __negation_3 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
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  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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\vec{F} = q \\cdot (\\vec{E} + \\vec{v} \\times \\vec{B})",
      "chartScript": {
        "script": "F - q*(B*v + E)",
        "variables": [
          "B",
          "E",
          "F",
          "q",
          "v"
        ]
      }
    },
    {
      "id": "F",
      "type": "vector",
      "latex": "\\vec{F}",
      "subexpr": "\\vec{F}",
      "chartScript": {
        "script": "F",
        "variables": [
          "F"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "q \\left(\\vec{E} + \\vec{v} \\vec{B}\\right)",
      "chartScript": {
        "script": "q(B*v + E)",
        "variables": [
          "B",
          "E",
          "v"
        ]
      }
    },
    {
      "id": "q",
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      "latex": "q",
      "subexpr": "q",
      "chartScript": {
        "script": "q",
        "variables": [
          "q"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "\\vec{E} + \\vec{v} \\vec{B}",
      "chartScript": {
        "script": "B*v + E",
        "variables": [
          "B",
          "E",
          "v"
        ]
      }
    },
    {
      "id": "E",
      "type": "vector",
      "latex": "\\vec{E}",
      "subexpr": "\\vec{E}",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\vec{v} \\vec{B}",
      "chartScript": {
        "script": "B*v",
        "variables": [
          "B",
          "v"
        ]
      }
    },
    {
      "id": "v",
      "type": "vector",
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      "subexpr": "\\vec{v}",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "B",
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      "latex": "\\vec{B}",
      "subexpr": "\\vec{B}",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "F",
      "to": "__equals_1"
    },
    {
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      "to": "__multiply_2",
      "semantic": "direct",
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    },
    {
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      "to": "__add_3"
    },
    {
      "from": "v",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__multiply_4",
      "semantic": "direct",
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    },
    {
      "from": "__multiply_4",
      "to": "__add_3"
    },
    {
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      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
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}

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 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["$\vec{F}$"]:::vector
  __multiply_2(("$\times$")):::operator
  q["$q$"]:::scalar
  __add_3(("$+$")):::operator
  E["$\vec{E}$"]:::vector
  __multiply_4(("$\times$")):::operator
  v["$\vec{v}$"]:::vector
  B["$\vec{B}$"]:::vector
  F --> __equals_1
  q --> __multiply_2
  E --> __add_3
  v --> __multiply_4
  B --> __multiply_4
  __multiply_4 --> __add_3
  __add_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
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  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\vec{S} = \\frac{1}{\\mu_0} \\vec{E} \\times \\vec{B}",
      "chartScript": {
        "script": "-B*E/mu_0 + S",
        "variables": [
          "B",
          "E",
          "S",
          "mu_0"
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      }
    },
    {
      "id": "S",
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      "latex": "\\vec{S}",
      "subexpr": "\\vec{S}",
      "chartScript": {
        "script": "S",
        "variables": [
          "S"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\vec{B} \\vec{E} \\frac{1}{\\mu_{0}}",
      "chartScript": {
        "script": "B*E/mu_0",
        "variables": [
          "B",
          "E",
          "mu_0"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\vec{E} \\frac{1}{\\mu_{0}}",
      "chartScript": {
        "script": "E/mu_0",
        "variables": [
          "E",
          "mu_0"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\mu_{0}}",
      "chartScript": {
        "script": "1/mu_0",
        "variables": [
          "mu_0"
        ]
      }
    },
    {
      "id": "mu_0",
      "type": "scalar",
      "latex": "\\mu_{0}",
      "subexpr": "\\mu_{0}",
      "chartScript": {
        "script": "mu_0",
        "variables": [
          "mu_0"
        ]
      }
    },
    {
      "id": "E",
      "type": "vector",
      "latex": "\\vec{E}",
      "subexpr": "\\vec{E}",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "B",
      "type": "vector",
      "latex": "\\vec{B}",
      "subexpr": "\\vec{B}",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "S",
      "to": "__equals_1"
    },
    {
      "from": "mu_0",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3"
    },
    {
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      "to": "__multiply_3",
      "semantic": "direct",
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    },
    {
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      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "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
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  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
  S["$\vec{S}$"]:::vector
  __multiply_2(("$\times$")):::operator
  __multiply_3(("$\times$")):::operator
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  mu_0["$\mu_{0}$"]:::scalar
  E["$\vec{E}$"]:::vector
  B["$\vec{B}$"]:::vector
  S --> __equals_1
  mu_0 --> __power_4
  __power_4 -.-> __multiply_3
  E --> __multiply_3
  __multiply_3 --> __multiply_2
  B --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#42a5f5,stroke-width:1px
  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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\nabla \\times \\vec{B} = \\mu_0 \\vec{J} + \\mu_0 \\epsilon_0 \\frac{\\partial \\vec{E}}{\\partial t}",
      "chartScript": {
        "script": "B*nabla - J*mu_0",
        "variables": [
          "B",
          "J",
          "mu_0",
          "nabla"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\nabla \\times \\vec{B}",
      "chartScript": {
        "script": "B*nabla",
        "variables": [
          "B",
          "nabla"
        ]
      }
    },
    {
      "id": "nabla",
      "type": "scalar",
      "latex": "\\nabla",
      "subexpr": "\\nabla",
      "chartScript": {
        "script": "nabla",
        "variables": [
          "nabla"
        ]
      }
    },
    {
      "id": "B",
      "type": "vector",
      "latex": "\\vec{B}",
      "subexpr": "\\vec{B}",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "\\vec{J} \\mu_{0} + \\mu_{0} \\epsilon_{0} \\frac{\\partial \\vec{E}}{\\partial t}",
      "chartScript": {
        "script": "J*mu_0",
        "variables": [
          "J",
          "mu_0"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\vec{J} \\mu_{0}",
      "chartScript": {
        "script": "J*mu_0",
        "variables": [
          "J",
          "mu_0"
        ]
      }
    },
    {
      "id": "mu_0",
      "type": "scalar",
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      "subexpr": "\\mu_{0}",
      "chartScript": {
        "script": "mu_0",
        "variables": [
          "mu_0"
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      }
    },
    {
      "id": "J",
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      "subexpr": "\\vec{J}",
      "chartScript": {
        "script": "J",
        "variables": [
          "J"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\mu_{0} \\epsilon_{0} \\frac{\\partial \\vec{E}}{\\partial t}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\epsilon_{0} \\frac{\\partial \\vec{E}}{\\partial t}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    },
    {
      "id": "epsilon_0",
      "type": "scalar",
      "latex": "\\epsilon_{0}",
      "subexpr": "\\epsilon_{0}",
      "chartScript": {
        "script": "epsilon_0",
        "variables": [
          "epsilon_0"
        ]
      }
    },
    {
      "id": "E",
      "type": "vector",
      "latex": "\\vec{E}",
      "subexpr": "\\vec{E}",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "__deriv_7",
      "type": "operator",
      "op": "partial_derivative",
      "with_respect_to": "t",
      "subexpr": "\\frac{\\partial \\vec{E}}{\\partial t}",
      "chartScript": {
        "script": "0",
        "variables": []
      }
    }
  ],
  "edges": [
    {
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      "to": "__multiply_2",
      "semantic": "direct",
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    },
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    },
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      "to": "__equals_1"
    },
    {
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    },
    {
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      "to": "__multiply_5",
      "semantic": "direct",
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    },
    {
      "from": "epsilon_0",
      "to": "__multiply_6",
      "semantic": "direct",
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    },
    {
      "from": "E",
      "to": "__deriv_7"
    },
    {
      "from": "t",
      "to": "__deriv_7",
      "role": "wrt"
    },
    {
      "from": "__deriv_7",
      "to": "__multiply_6",
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    },
    {
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      "semantic": "direct",
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    },
    {
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    },
    {
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  "classification": {
    "kind": "ODE",
    "order": 1,
    "dependent_variables": [
      "E"
    ],
    "independent_variables": [
      "t"
    ],
    "sympy_hints": [
      "factorable",
      "nth_algebraic",
      "separable",
      "1st_exact",
      "1st_linear",
      "Bernoulli",
      "1st_power_series",
      "lie_group",
      "nth_linear_constant_coeff_undetermined_coefficients",
      "nth_linear_euler_eq_nonhomogeneous_undetermined_coefficients",
      "nth_linear_constant_coeff_variation_of_parameters",
      "nth_linear_euler_eq_nonhomogeneous_variation_of_parameters"
    ],
    "linear": true,
    "homogeneous": true,
    "constant_coefficients": true
  }
}

flowchart RL
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  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  nabla["$\nabla$"]:::scalar
  B["$\vec{B}$"]:::vector
  __add_3(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  mu_0["$\mu_{0}$"]:::scalar
  J["$\vec{J}$"]:::vector
  __multiply_5(("$\times$")):::operator
  __multiply_6(("$\times$")):::operator
  epsilon_0["$\epsilon_{0}$"]:::scalar
  E["$\vec{E}$"]:::vector
  t["$t$"]:::scalar
  __deriv_7(("$\dfrac{\partial}{\partial t}$")):::operator
  nabla --> __multiply_2
  B --> __multiply_2
  __multiply_2 --> __equals_1
  mu_0 --> __multiply_4
  J --> __multiply_4
  __multiply_4 --> __add_3
  mu_0 --> __multiply_5
  epsilon_0 --> __multiply_6
  E --> __deriv_7
  t -->|wrt| __deriv_7
  __deriv_7 --> __multiply_6
  __multiply_6 --> __multiply_5
  __multiply_5 --> __add_3
  __add_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
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