Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "v = f \\lambda",
      "chartScript": {
        "script": "-f*lambda + v",
        "variables": [
          "f",
          "lambda",
          "v"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "f \\lambda",
      "chartScript": {
        "script": "f*lambda",
        "variables": [
          "f",
          "lambda"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "lambda",
      "type": "scalar",
      "latex": "\\lambda",
      "subexpr": "\\lambda",
      "chartScript": {
        "script": "lambda",
        "variables": [
          "lambda"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "v",
      "to": "__equals_1"
    },
    {
      "from": "f",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "lambda",
      "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
  f["$f$"]:::scalar
  lambda["$\lambda$"]:::scalar
  v --> __equals_1
  f --> __multiply_2
  lambda --> __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": "f = \\frac{1}{T}",
      "chartScript": {
        "script": "f - 1/T",
        "variables": [
          "T",
          "f"
        ]
      }
    },
    {
      "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}{T}",
      "chartScript": {
        "script": "1/T",
        "variables": [
          "T"
        ]
      }
    },
    {
      "id": "T",
      "type": "scalar",
      "latex": "T",
      "subexpr": "T",
      "chartScript": {
        "script": "T",
        "variables": [
          "T"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "f",
      "to": "__equals_1"
    },
    {
      "from": "T",
      "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
  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
  __power_2(("$\dfrac{1}{(\cdot)}$")):::operator
  T["$T$"]:::scalar
  f --> __equals_1
  T --> __power_2
  __power_2 -.-> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#42a5f5,stroke-width:1px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\omega = 2 \\pi f",
      "chartScript": {
        "script": "-2*pi*f + omega",
        "variables": [
          "f",
          "omega"
        ]
      }
    },
    {
      "id": "omega",
      "type": "scalar",
      "latex": "\\omega",
      "subexpr": "\\omega",
      "chartScript": {
        "script": "omega",
        "variables": [
          "omega"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "2 \\pi f",
      "chartScript": {
        "script": "2*pi*f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "__num_3",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\pi f",
      "chartScript": {
        "script": "pi*f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "omega",
      "to": "__equals_1"
    },
    {
      "from": "__num_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pi",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "f",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "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
  omega["$\omega$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __num_3["$2$"]:::number
  __multiply_4(("$\times$")):::operator
  pi["$\pi$"]:::constant
  f["$f$"]:::scalar
  omega --> __equals_1
  __num_3 --> __multiply_2
  pi --> __multiply_4
  f --> __multiply_4
  __multiply_4 --> __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

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "k = \\frac{2 \\pi}{\\lambda}",
      "chartScript": {
        "script": "k - 2*pi/lambda",
        "variables": [
          "k",
          "lambda"
        ]
      }
    },
    {
      "id": "k",
      "type": "scalar",
      "latex": "k",
      "subexpr": "k",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{\\lambda} \\pi 2",
      "chartScript": {
        "script": "2*pi/lambda",
        "variables": [
          "lambda"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\pi 2",
      "chartScript": {
        "script": "2*pi",
        "variables": []
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\lambda}",
      "chartScript": {
        "script": "1/lambda",
        "variables": [
          "lambda"
        ]
      }
    },
    {
      "id": "lambda",
      "type": "scalar",
      "latex": "\\lambda",
      "subexpr": "\\lambda",
      "chartScript": {
        "script": "lambda",
        "variables": [
          "lambda"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "k",
      "to": "__equals_1"
    },
    {
      "from": "__num_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "pi",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "lambda",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "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
  k["$k$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __multiply_3(("$\times$")):::operator
  __num_4["$2$"]:::number
  pi["$\pi$"]:::constant
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  lambda["$\lambda$"]:::scalar
  k --> __equals_1
  __num_4 --> __multiply_3
  pi --> __multiply_3
  __multiply_3 --> __multiply_2
  lambda --> __power_5
  __power_5 -.-> __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:#42a5f5,stroke-width:1px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E = \\frac{1}{2} k A^2",
      "chartScript": {
        "script": "-1/2*pow(A, 2)*k + E",
        "variables": [
          "A",
          "E",
          "k"
        ]
      }
    },
    {
      "id": "E",
      "type": "scalar",
      "latex": "E",
      "subexpr": "E",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{2} k A^{2}",
      "chartScript": {
        "script": "(1/2)*pow(A, 2)*k",
        "variables": [
          "A",
          "k"
        ]
      }
    },
    {
      "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": "k A^{2}",
      "chartScript": {
        "script": "pow(A, 2)*k",
        "variables": [
          "A",
          "k"
        ]
      }
    },
    {
      "id": "k",
      "type": "scalar",
      "latex": "k",
      "subexpr": "k",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "A^{2}",
      "chartScript": {
        "script": "pow(A, 2)",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E",
      "to": "__equals_1"
    },
    {
      "from": "__num_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "k",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "A",
      "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
  E["$E$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  __num_4["$2$"]:::number
  __multiply_5(("$\times$")):::operator
  k["$k$"]:::scalar
  __power_6(("${(\cdot)}^{2}$")):::operator
  A["$A$"]:::scalar
  E --> __equals_1
  __num_4 --> __power_3
  __power_3 -.-> __multiply_2
  k --> __multiply_5
  A --> __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": "I = \\frac{P}{A}",
      "chartScript": {
        "script": "I - P/A",
        "variables": [
          "A",
          "I",
          "P"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "P \\frac{1}{A}",
      "chartScript": {
        "script": "P/A",
        "variables": [
          "A",
          "P"
        ]
      }
    },
    {
      "id": "P",
      "type": "scalar",
      "latex": "P",
      "subexpr": "P",
      "chartScript": {
        "script": "P",
        "variables": [
          "P"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{A}",
      "chartScript": {
        "script": "1/A",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "I",
      "to": "__equals_1"
    },
    {
      "from": "P",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "A",
      "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
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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
  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
  I["$I$"]:::scalar
  __multiply_2(("$\times$")):::operator
  P["$P$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  A["$A$"]:::scalar
  I --> __equals_1
  P --> __multiply_2
  A --> __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": "n_1 \\sin\\theta_1 = n_2 \\sin\\theta_2",
      "chartScript": {
        "script": "n_1*sin(theta_1) - n_2*sin(theta_2)",
        "variables": [
          "n_1",
          "n_2",
          "theta_1",
          "theta_2"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "n_{1} \\sin{\\left(\\theta_{1} \\right)}",
      "chartScript": {
        "script": "n_1*sin(theta_1)",
        "variables": [
          "n_1",
          "theta_1"
        ]
      }
    },
    {
      "id": "n_1",
      "type": "scalar",
      "latex": "n_{1}",
      "subexpr": "n_{1}",
      "chartScript": {
        "script": "n_1",
        "variables": [
          "n_1"
        ]
      }
    },
    {
      "id": "__sin_3",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta_{1} \\right)}",
      "chartScript": {
        "script": "sin(theta_1)",
        "variables": [
          "theta_1"
        ]
      }
    },
    {
      "id": "theta_1",
      "type": "scalar",
      "latex": "\\theta_{1}",
      "subexpr": "\\theta_{1}",
      "chartScript": {
        "script": "theta_1",
        "variables": [
          "theta_1"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "n_{2} \\sin{\\left(\\theta_{2} \\right)}",
      "chartScript": {
        "script": "n_2*sin(theta_2)",
        "variables": [
          "n_2",
          "theta_2"
        ]
      }
    },
    {
      "id": "n_2",
      "type": "scalar",
      "latex": "n_{2}",
      "subexpr": "n_{2}",
      "chartScript": {
        "script": "n_2",
        "variables": [
          "n_2"
        ]
      }
    },
    {
      "id": "__sin_5",
      "type": "function",
      "latex": "\\sin",
      "op": "sin",
      "subexpr": "\\sin{\\left(\\theta_{2} \\right)}",
      "chartScript": {
        "script": "sin(theta_2)",
        "variables": [
          "theta_2"
        ]
      }
    },
    {
      "id": "theta_2",
      "type": "scalar",
      "latex": "\\theta_{2}",
      "subexpr": "\\theta_{2}",
      "chartScript": {
        "script": "theta_2",
        "variables": [
          "theta_2"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "n_1",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta_1",
      "to": "__sin_3"
    },
    {
      "from": "__sin_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "n_2",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta_2",
      "to": "__sin_5"
    },
    {
      "from": "__sin_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  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
  __multiply_2(("$\times$")):::operator
  n_1["$n_{1}$"]:::scalar
  __sin_3{{"$\sin(\cdot)$"}}:::function
  theta_1["$\theta_{1}$"]:::scalar
  __multiply_4(("$\times$")):::operator
  n_2["$n_{2}$"]:::scalar
  __sin_5{{"$\sin(\cdot)$"}}:::function
  theta_2["$\theta_{2}$"]:::scalar
  n_1 --> __multiply_2
  theta_1 --> __sin_3
  __sin_3 --> __multiply_2
  __multiply_2 --> __equals_1
  n_2 --> __multiply_4
  theta_2 --> __sin_5
  __sin_5 --> __multiply_4
  __multiply_4 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#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": "\\frac{1}{f} = \\frac{1}{d_o} + \\frac{1}{d_i}",
      "chartScript": {
        "script": "1/f - 1/d_o - 1/d_i",
        "variables": [
          "d_i",
          "d_o",
          "f"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{f}",
      "chartScript": {
        "script": "1/f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "\\frac{1}{d_{o}} + \\frac{1}{d_{i}}",
      "chartScript": {
        "script": "1/d_o + 1/d_i",
        "variables": [
          "d_i",
          "d_o"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{d_{o}}",
      "chartScript": {
        "script": "1/d_o",
        "variables": [
          "d_o"
        ]
      }
    },
    {
      "id": "d_o",
      "type": "scalar",
      "latex": "d_{o}",
      "subexpr": "d_{o}",
      "chartScript": {
        "script": "d_o",
        "variables": [
          "d_o"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{d_{i}}",
      "chartScript": {
        "script": "1/d_i",
        "variables": [
          "d_i"
        ]
      }
    },
    {
      "id": "d_i",
      "type": "scalar",
      "latex": "d_{i}",
      "subexpr": "d_{i}",
      "chartScript": {
        "script": "d_i",
        "variables": [
          "d_i"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "f",
      "to": "__power_2"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    },
    {
      "from": "d_o",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__add_3"
    },
    {
      "from": "d_i",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __power_2(("$\dfrac{1}{(\cdot)}$")):::operator
  f["$f$"]:::scalar
  __add_3(("$+$")):::operator
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  d_o["$d_{o}$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  d_i["$d_{i}$"]:::scalar
  f --> __power_2
  __power_2 -.-> __equals_1
  d_o --> __power_4
  __power_4 -.-> __add_3
  d_i --> __power_5
  __power_5 -.-> __add_3
  __add_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#42a5f5,stroke-width:1px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#42a5f5,stroke-width:1px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#42a5f5,stroke-width:1px
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{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\tan\\theta_B = \\frac{n_2}{n_1}",
      "chartScript": {
        "script": "tan(theta_B) - n_2/n_1",
        "variables": [
          "n_1",
          "n_2",
          "theta_B"
        ]
      }
    },
    {
      "id": "__tan_2",
      "type": "function",
      "latex": "\\tan",
      "op": "tan",
      "subexpr": "\\tan{\\left(\\theta_{B} \\right)}",
      "chartScript": {
        "script": "tan(theta_B)",
        "variables": [
          "theta_B"
        ]
      }
    },
    {
      "id": "theta_B",
      "type": "scalar",
      "latex": "\\theta_{B}",
      "subexpr": "\\theta_{B}",
      "chartScript": {
        "script": "theta_B",
        "variables": [
          "theta_B"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "n_{2} \\frac{1}{n_{1}}",
      "chartScript": {
        "script": "n_2/n_1",
        "variables": [
          "n_1",
          "n_2"
        ]
      }
    },
    {
      "id": "n_2",
      "type": "scalar",
      "latex": "n_{2}",
      "subexpr": "n_{2}",
      "chartScript": {
        "script": "n_2",
        "variables": [
          "n_2"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{n_{1}}",
      "chartScript": {
        "script": "1/n_1",
        "variables": [
          "n_1"
        ]
      }
    },
    {
      "id": "n_1",
      "type": "scalar",
      "latex": "n_{1}",
      "subexpr": "n_{1}",
      "chartScript": {
        "script": "n_1",
        "variables": [
          "n_1"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "theta_B",
      "to": "__tan_2"
    },
    {
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      "to": "__equals_1"
    },
    {
      "from": "n_2",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "n_1",
      "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 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 annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __tan_2{{"$\tan(\cdot)$"}}:::function
  theta_B["$\theta_{B}$"]:::scalar
  __multiply_3(("$\times$")):::operator
  n_2["$n_{2}$"]:::scalar
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  n_1["$n_{1}$"]:::scalar
  theta_B --> __tan_2
  __tan_2 --> __equals_1
  n_2 --> __multiply_3
  n_1 --> __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:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#42a5f5,stroke-width:1px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "I = I_0 \\cos^2\\theta",
      "chartScript": {
        "script": "I - I_0*pow(cos(theta), 2)",
        "variables": [
          "I",
          "I_0",
          "theta"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "I_{0} \\cos^{2}{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "I_0*pow(cos(theta), 2)",
        "variables": [
          "I_0",
          "theta"
        ]
      }
    },
    {
      "id": "I_0",
      "type": "scalar",
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      "subexpr": "I_{0}",
      "chartScript": {
        "script": "I_0",
        "variables": [
          "I_0"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "\\cos^{2}{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "pow(cos(theta), 2)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "__cos_4",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "cos(theta)",
        "variables": [
          "theta"
        ]
      }
    },
    {
      "id": "theta",
      "type": "scalar",
      "latex": "\\theta",
      "subexpr": "\\theta",
      "chartScript": {
        "script": "theta",
        "variables": [
          "theta"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "I",
      "to": "__equals_1"
    },
    {
      "from": "I_0",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__cos_4"
    },
    {
      "from": "__cos_4",
      "to": "__power_3"
    },
    {
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      "to": "__multiply_2",
      "semantic": "direct",
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    },
    {
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      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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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
  I["$I$"]:::scalar
  __multiply_2(("$\times$")):::operator
  I_0["$I_{0}$"]:::scalar
  __power_3(("${(\cdot)}^{2}$")):::operator
  __cos_4{{"$\cos(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  I --> __equals_1
  I_0 --> __multiply_2
  theta --> __cos_4
  __cos_4 --> __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:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "{d} \\sin\\theta = m \\lambda",
      "chartScript": {
        "script": "d*sin(theta) - lambda*m",
        "variables": [
          "d",
          "lambda",
          "m",
          "theta"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "d \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "dsin*theta",
        "variables": [
          "dsin",
          "theta"
        ]
      }
    },
    {
      "id": "d",
      "type": "scalar",
      "latex": "d",
      "subexpr": "d",
      "chartScript": {
        "script": "d",
        "variables": [
          "d"
        ]
      }
    },
    {
      "id": "__sin_3",
      "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"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m \\lambda",
      "chartScript": {
        "script": "lambda*m",
        "variables": [
          "lambda",
          "m"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "lambda",
      "type": "scalar",
      "latex": "\\lambda",
      "subexpr": "\\lambda",
      "chartScript": {
        "script": "lambda",
        "variables": [
          "lambda"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "d",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_3"
    },
    {
      "from": "__sin_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "m",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "lambda",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  }
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  d["$d$"]:::scalar
  __sin_3{{"$\sin(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  __multiply_4(("$\times$")):::operator
  m["$m$"]:::scalar
  lambda["$\lambda$"]:::scalar
  d --> __multiply_2
  theta --> __sin_3
  __sin_3 --> __multiply_2
  __multiply_2 --> __equals_1
  m --> __multiply_4
  lambda --> __multiply_4
  __multiply_4 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\Delta = {d} \\sin\\theta",
      "chartScript": {
        "script": "Delta - d*sin(theta)",
        "variables": [
          "Delta",
          "d",
          "theta"
        ]
      }
    },
    {
      "id": "Delta",
      "type": "scalar",
      "latex": "\\Delta",
      "subexpr": "\\Delta",
      "chartScript": {
        "script": "Delta",
        "variables": [
          "Delta"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "d \\sin{\\left(\\theta \\right)}",
      "chartScript": {
        "script": "dsin*theta",
        "variables": [
          "dsin",
          "theta"
        ]
      }
    },
    {
      "id": "d",
      "type": "scalar",
      "latex": "d",
      "subexpr": "d",
      "chartScript": {
        "script": "d",
        "variables": [
          "d"
        ]
      }
    },
    {
      "id": "__sin_3",
      "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": "Delta",
      "to": "__equals_1"
    },
    {
      "from": "d",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "theta",
      "to": "__sin_3"
    },
    {
      "from": "__sin_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
  Delta["$\Delta$"]:::scalar
  __multiply_2(("$\times$")):::operator
  d["$d$"]:::scalar
  __sin_3{{"$\sin(\cdot)$"}}:::function
  theta["$\theta$"]:::scalar
  Delta --> __equals_1
  d --> __multiply_2
  theta --> __sin_3
  __sin_3 --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\lambda_n = \\frac{2 L}{n}",
      "chartScript": {
        "script": "-2*L/n + lambda_n",
        "variables": [
          "L",
          "lambda_n",
          "n"
        ]
      }
    },
    {
      "id": "lambda_n",
      "type": "scalar",
      "latex": "\\lambda_{n}",
      "subexpr": "\\lambda_{n}",
      "chartScript": {
        "script": "lambda_n",
        "variables": [
          "lambda_n"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{n} L 2",
      "chartScript": {
        "script": "2*L/n",
        "variables": [
          "L",
          "n"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "L 2",
      "chartScript": {
        "script": "2*L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{n}",
      "chartScript": {
        "script": "1/n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "lambda_n",
      "to": "__equals_1"
    },
    {
      "from": "__num_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "L",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "n",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "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
  lambda_n["$\lambda_{n}$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __multiply_3(("$\times$")):::operator
  __num_4["$2$"]:::number
  L["$L$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  n["$n$"]:::scalar
  lambda_n --> __equals_1
  __num_4 --> __multiply_3
  L --> __multiply_3
  __multiply_3 --> __multiply_2
  n --> __power_5
  __power_5 -.-> __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:#42a5f5,stroke-width:1px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "f' = f \\frac{v + v_o}{v - v_s}",
      "chartScript": {
        "script": "-f*(v + v_o)/(v - v_s) + f_prime",
        "variables": [
          "f",
          "f_prime",
          "v",
          "v_o",
          "v_s"
        ]
      }
    },
    {
      "id": "f",
      "type": "scalar",
      "latex": "f'",
      "subexpr": "f'",
      "chartScript": {
        "script": "f_prime",
        "variables": [
          "f_prime"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "f \\left(v + v_{o}\\right) \\frac{1}{v - v_{s}}",
      "chartScript": {
        "script": "f(v + v_o)/(v - v_s)",
        "variables": [
          "v",
          "v_o",
          "v_s"
        ]
      }
    },
    {
      "id": "f_2",
      "type": "scalar",
      "latex": "f",
      "subexpr": "f",
      "chartScript": {
        "script": "f",
        "variables": [
          "f"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\left(v + v_{o}\\right) \\frac{1}{v - v_{s}}",
      "chartScript": {
        "script": "(v + v_o)/(v - v_s)",
        "variables": [
          "v",
          "v_o",
          "v_s"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "v + v_{o}",
      "chartScript": {
        "script": "v + v_o",
        "variables": [
          "v",
          "v_o"
        ]
      }
    },
    {
      "id": "v",
      "type": "scalar",
      "latex": "v",
      "subexpr": "v",
      "chartScript": {
        "script": "v",
        "variables": [
          "v"
        ]
      }
    },
    {
      "id": "v_o",
      "type": "scalar",
      "latex": "v_{o}",
      "subexpr": "v_{o}",
      "chartScript": {
        "script": "v_o",
        "variables": [
          "v_o"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{v - v_{s}}",
      "chartScript": {
        "script": "1/(v - v_s)",
        "variables": [
          "v",
          "v_s"
        ]
      }
    },
    {
      "id": "__add_6",
      "type": "operator",
      "op": "add",
      "subexpr": "v - v_{s}",
      "chartScript": {
        "script": "v - v_s",
        "variables": [
          "v",
          "v_s"
        ]
      }
    },
    {
      "id": "__negation_7",
      "type": "operator",
      "op": "negation",
      "subexpr": "-v_{s}",
      "chartScript": {
        "script": "-v_s",
        "variables": [
          "v_s"
        ]
      }
    },
    {
      "id": "v_s",
      "type": "scalar",
      "latex": "v_{s}",
      "subexpr": "v_{s}",
      "chartScript": {
        "script": "v_s",
        "variables": [
          "v_s"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "f",
      "to": "__equals_1"
    },
    {
      "from": "f_2",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__add_4"
    },
    {
      "from": "v_o",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "v",
      "to": "__add_6"
    },
    {
      "from": "v_s",
      "to": "__negation_7"
    },
    {
      "from": "__negation_7",
      "to": "__add_6"
    },
    {
      "from": "__add_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
  f_2["$f$"]:::scalar
  __multiply_3(("$\times$")):::operator
  __add_4(("$+$")):::operator
  v["$v$"]:::scalar
  v_o["$v_{o}$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __add_6(("$+$")):::operator
  __negation_7@{ shape: "flip-tri", label: "$-$" }
  v_s["$v_{s}$"]:::scalar
  class __negation_7 operator
  f --> __equals_1
  f_2 --> __multiply_2
  v --> __add_4
  v_o --> __add_4
  __add_4 --> __multiply_3
  v --> __add_6
  v_s --> __negation_7
  __negation_7 --> __add_6
  __add_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:#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
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#42a5f5,stroke-width:1px
  linkStyle 10 stroke:#ef5350,stroke-width:3px
  linkStyle 11 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "x = A \\cos(\\omega t + \\phi)",
      "chartScript": {
        "script": "-A*cos(omega*t + phi) + x",
        "variables": [
          "A",
          "omega",
          "phi",
          "t",
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "A \\cos{\\left(\\omega t + \\phi \\right)}",
      "chartScript": {
        "script": "A*cos(omega*t + phi)",
        "variables": [
          "A",
          "omega",
          "phi",
          "t"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "A",
      "subexpr": "A",
      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "__cos_3",
      "type": "function",
      "latex": "\\cos",
      "op": "cos",
      "subexpr": "\\cos{\\left(\\omega t + \\phi \\right)}",
      "chartScript": {
        "script": "cos(omega*t + phi)",
        "variables": [
          "omega",
          "phi",
          "t"
        ]
      }
    },
    {
      "id": "__add_4",
      "type": "operator",
      "op": "add",
      "subexpr": "\\omega t + \\phi",
      "chartScript": {
        "script": "omega*t + phi",
        "variables": [
          "omega",
          "phi",
          "t"
        ]
      }
    },
    {
      "id": "__multiply_5",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\omega t",
      "chartScript": {
        "script": "omega*t",
        "variables": [
          "omega",
          "t"
        ]
      }
    },
    {
      "id": "omega",
      "type": "scalar",
      "latex": "\\omega",
      "subexpr": "\\omega",
      "chartScript": {
        "script": "omega",
        "variables": [
          "omega"
        ]
      }
    },
    {
      "id": "t",
      "type": "scalar",
      "latex": "t",
      "subexpr": "t",
      "chartScript": {
        "script": "t",
        "variables": [
          "t"
        ]
      }
    },
    {
      "id": "phi",
      "type": "scalar",
      "latex": "\\phi",
      "subexpr": "\\phi",
      "chartScript": {
        "script": "phi",
        "variables": [
          "phi"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__equals_1"
    },
    {
      "from": "A",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "omega",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "t",
      "to": "__multiply_5",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_5",
      "to": "__add_4"
    },
    {
      "from": "phi",
      "to": "__add_4"
    },
    {
      "from": "__add_4",
      "to": "__cos_3"
    },
    {
      "from": "__cos_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
  x["$x$"]:::scalar
  __multiply_2(("$\times$")):::operator
  A["$A$"]:::scalar
  __cos_3{{"$\cos(\cdot)$"}}:::function
  __add_4(("$+$")):::operator
  __multiply_5(("$\times$")):::operator
  omega["$\omega$"]:::scalar
  t["$t$"]:::scalar
  phi["$\phi$"]:::scalar
  x --> __equals_1
  A --> __multiply_2
  omega --> __multiply_5
  t --> __multiply_5
  __multiply_5 --> __add_4
  phi --> __add_4
  __add_4 --> __cos_3
  __cos_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:#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