examples/latexify_examples.ipynb

{
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      "cell_type": "markdown",
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        "id": "W5mNJI3Bnl6n"
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      "source": [
        "# `latexify` examples\n",
        "\n",
        "This notebook provides several examples to use `latexify`.\n",
        "\n",
        "See also the\n",
        "[official documentation](https://github.com/google/latexify_py/blob/documentation/docs/index.md)\n",
        "for more details.\n",
        "\n",
        "If you have any questions, please ask it in the\n",
        "[issue tracker](https://github.com/google/latexify_py/issues)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fWCVgcRHoLd8"
      },
      "source": [
        "## Install `latexify`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Collecting latexify-py\n",
            "  Downloading latexify_py-0.4.2-py3-none-any.whl (38 kB)\n",
            "Collecting dill>=0.3.2 (from latexify-py)\n",
            "  Downloading dill-0.3.7-py3-none-any.whl (115 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m115.3/115.3 kB\u001b[0m \u001b[31m5.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: dill, latexify-py\n",
            "Successfully installed dill-0.3.7 latexify-py-0.4.2\n"
          ]
        }
      ],
      "source": [
        "# Restart the runtime before running the examples below.\n",
        "%pip install latexify-py\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Mzq4_dNoSmc"
      },
      "source": [
        "## Import `latexify` into your code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "hViDMhyMFNCO",
        "outputId": "b46edb25-5952-4cff-da1e-d65e7e3caad0"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'0.4.2'"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import math  # Optional\n",
        "import numpy as np  # Optional\n",
        "import latexify\n",
        "\n",
        "latexify.__version__\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4QJ6I2s7odX1"
      },
      "source": [
        "## Examples"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "NvbEYSwXFaeE",
        "outputId": "5d0ca2a4-a285-4053-9cc4-3776746443be"
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      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-1.0\n",
            "\\mathrm{solve}(a, b, c) = \\frac{-b + \\sqrt{ b^{2} - 4 a c }}{2 a}\n"
          ]
        }
      ],
      "source": [
        "@latexify.function\n",
        "def solve(a, b, c):\n",
        "  return (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)\n",
        "\n",
        "print(solve(1, 4, 3))  # Invoking the function works as expected.\n",
        "print(solve)  # Printing the function shows the underlying LaTeX source.\n",
        "solve  # Displays the expression.\n",
        "\n",
        "# Writes the underlying LaTeX source into a file.\n",
        "with open(\"compiled.tex\", \"w\") as fp:\n",
        "  print(solve, file=fp)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
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      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle \\frac{-b + \\sqrt{ b^{2} - 4 a c }}{2 a} $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf78a9b0>"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# latexify.expression works similarly, but does not output the signature.\n",
        "@latexify.expression\n",
        "def solve(a, b, c):\n",
        "  return (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)\n",
        "\n",
        "solve\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
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        },
        "id": "G73dnoqqjg4A",
        "outputId": "b9f53cf8-4a34-452c-8d9b-946ddd0998df"
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        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'\\\\mathrm{solve}(a, b, c) = \\\\frac{-b + \\\\sqrt{ b^{2} - 4 a c }}{2 a}'"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# latexify.get_latex obtains the underlying LaTeX expression directly.\n",
        "def solve(a, b, c):\n",
        "  return (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)\n",
        "\n",
        "latexify.get_latex(solve)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
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        "outputId": "669e070d-2718-49cb-a2fe-0defe0286b27"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle \\mathrm{sinc}(x) = \\left\\{ \\begin{array}{ll} 1, & \\mathrm{if} \\ x = 0 \\\\ \\frac{\\sin x}{x}, & \\mathrm{otherwise} \\end{array} \\right. $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf78a5f0>"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "@latexify.function\n",
        "def sinc(x):\n",
        "  if x == 0:\n",
        "    return 1\n",
        "  else:\n",
        "    return math.sin(x) / x\n",
        "\n",
        "sinc\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
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        "outputId": "e448ff37-4753-4090-b2b1-1ef21b279b34"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle \\mathrm{fib}(x) = \\left\\{ \\begin{array}{ll} 0, & \\mathrm{if} \\ x = 0 \\\\ 1, & \\mathrm{if} \\ x = 1 \\\\ \\mathrm{fib} \\mathopen{}\\left( x - 1 \\mathclose{}\\right) + \\mathrm{fib} \\mathopen{}\\left( x - 2 \\mathclose{}\\right), & \\mathrm{otherwise} \\end{array} \\right. $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf789b10>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Elif or nested else-if are unrolled.\n",
        "@latexify.function\n",
        "def fib(x):\n",
        "  if x == 0:\n",
        "    return 0\n",
        "  elif x == 1:\n",
        "    return 1\n",
        "  else:\n",
        "    return fib(x-1) + fib(x-2)\n",
        "\n",
        "fib\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
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        "outputId": "a47dcd59-2ff9-4aa1-935d-7c789b39057e"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle \\mathrm{greek}(\\alpha, \\beta, \\gamma, \\Omega) = \\alpha \\beta + \\Gamma \\mathopen{}\\left( \\gamma \\mathclose{}\\right) + \\Omega $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958da900c40>"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Some math symbols are converted automatically.\n",
        "@latexify.function(use_math_symbols=True)\n",
        "def greek(alpha, beta, gamma, Omega):\n",
        "  return alpha * beta + math.gamma(gamma) + Omega\n",
        "\n",
        "greek\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
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        "id": "ySyNPS0y4tzu",
        "outputId": "2d95b5ce-a9b8-42b1-eb55-dc8bd0097d69"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle f(x) = g \\mathopen{}\\left( x \\mathclose{}\\right) $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf789b40>"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Function names, arguments, variables can be replaced.\n",
        "identifiers = {\n",
        "    \"my_function\": \"f\",\n",
        "    \"my_inner_function\": \"g\",\n",
        "    \"my_argument\": \"x\",\n",
        "}\n",
        "\n",
        "@latexify.function(identifiers=identifiers)\n",
        "def my_function(my_argument):\n",
        "    return my_inner_function(my_argument)\n",
        "\n",
        "my_function\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
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        },
        "id": "TyacQaDM4Ei7",
        "outputId": "8e971bbd-2c74-45d2-d0fa-7f46569b10a6"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle f(a, b, c) = \\frac{-b + \\sqrt{ b^{2} - 4 a c }}{2 a} $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf789a20>"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Assignments can be reduced into one expression.\n",
        "@latexify.function(reduce_assignments=True)\n",
        "def f(a, b, c):\n",
        "    discriminant = b**2 - 4 * a * c\n",
        "    numerator = -b + math.sqrt(discriminant)\n",
        "    denominator = 2 * a\n",
        "    return numerator / denominator\n",
        "\n",
        "f\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
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        },
        "id": "oD8MFS2WE-2U",
        "outputId": "f9fad1bd-b7eb-41cc-8743-ec0d80cca8bc"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$$ \\displaystyle \\mathrm{transform}(x, y, a, b, \\theta, s, t) = \\begin{bmatrix} 1 & 0 & s \\\\ 0 & 1 & t \\\\ 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} \\cos \\theta & -\\sin \\theta & 0 \\\\ \\sin \\theta & \\cos \\theta & 0 \\\\ 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} a & 0 & 0 \\\\ 0 & b & 0 \\\\ 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ 1 \\end{bmatrix} $$"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedFunction at 0x7958bf789960>"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Matrix support.\n",
        "@latexify.function(reduce_assignments=True, use_math_symbols=True)\n",
        "def transform(x, y, a, b, theta, s, t):\n",
        "  cos_t = math.cos(theta)\n",
        "  sin_t = math.sin(theta)\n",
        "  scale = np.array([[a, 0, 0], [0, b, 0], [0, 0, 1]])\n",
        "  rotate = np.array([[cos_t, -sin_t, 0], [sin_t, cos_t, 0], [0, 0, 1]])\n",
        "  move = np.array([[1, 0, s], [0, 1, t], [0, 0, 1]])\n",
        "  return move @ rotate @ scale @ np.array([[x], [y], [1]])\n",
        "\n",
        "transform\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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        "outputId": "48660400-a812-41e2-91ea-23e49ea20c7f"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$ \\begin{array}{l} \\mathbf{function} \\ \\mathrm{fib}(x) \\\\ \\hspace{1em} \\mathbf{if} \\ x = 0 \\\\ \\hspace{2em} \\mathbf{return} \\ 0 \\\\ \\hspace{1em} \\mathbf{else} \\\\ \\hspace{2em} \\mathbf{if} \\ x = 1 \\\\ \\hspace{3em} \\mathbf{return} \\ 1 \\\\ \\hspace{2em} \\mathbf{else} \\\\ \\hspace{3em} \\mathbf{return} \\ \\mathrm{fib} \\mathopen{}\\left( x - 1 \\mathclose{}\\right) + \\mathrm{fib} \\mathopen{}\\left( x - 2 \\mathclose{}\\right) \\\\ \\hspace{2em} \\mathbf{end \\ if} \\\\ \\hspace{1em} \\mathbf{end \\ if} \\\\ \\mathbf{end \\ function} \\end{array} $"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedAlgorithm at 0x7958bf78aef0>"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# latexify.algorithmic generates an algorithmic environment instead of an equation.\n",
        "@latexify.algorithmic\n",
        "def fib(x):\n",
        "  if x == 0:\n",
        "    return 0\n",
        "  elif x == 1:\n",
        "    return 1\n",
        "  else:\n",
        "    return fib(x-1) + fib(x-2)\n",
        "\n",
        "fib\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
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          "height": 261
        },
        "id": "kbw_1txkGfnX",
        "outputId": "fdc58207-1c06-4d88-e249-b0b011bd98c0"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$ \\begin{array}{l} \\mathbf{function} \\ \\mathrm{collatz}(x) \\\\ \\hspace{1em} n \\gets 0 \\\\ \\hspace{1em} \\mathbf{while} \\ x > 1 \\\\ \\hspace{2em} n \\gets n + 1 \\\\ \\hspace{2em} \\mathbf{if} \\ x \\mathbin{\\%} 2 = 0 \\\\ \\hspace{3em} x \\gets \\left\\lfloor\\frac{x}{2}\\right\\rfloor \\\\ \\hspace{2em} \\mathbf{else} \\\\ \\hspace{3em} x \\gets 3 x + 1 \\\\ \\hspace{2em} \\mathbf{end \\ if} \\\\ \\hspace{1em} \\mathbf{end \\ while} \\\\ \\hspace{1em} \\mathbf{return} \\ n \\\\ \\mathbf{end \\ function} \\end{array} $"
            ],
            "text/plain": [
              "<latexify.ipython_wrappers.LatexifiedAlgorithm at 0x7958bf78bac0>"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Another example: latexify.algorithmic supports usual control flows.\n",
        "@latexify.algorithmic\n",
        "def collatz(x):\n",
        "  n = 0\n",
        "  while x > 1:\n",
        "    n = n + 1\n",
        "    if x % 2 == 0:\n",
        "      x = x // 2\n",
        "    else:\n",
        "      x = 3 * x + 1\n",
        "  return n\n",
        "\n",
        "collatz\n"
      ]
    }
  ],
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