Annex B. LaTeX.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\LaTeX$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Markdown admet directament $\\LaTeX$, si posem el codi entre simbols `$`. \n",
    "\n",
    "Si volem fer un bloc $\\LaTeX$ el posarem entre dobles simbols `$$` \n",
    "\n",
    "Així el text següent:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`$\\int_{a}^b f(x)dx = F(b) - F (a)$`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a una cel·la de format Markdown el veuriem així"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\int_{a}^b f(x)dx = F(b) - F (a)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O, si fem servir un bloc:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`$$\\int_{a}^b f(x)dx = F(b) - F (a)$$`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "així:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\int_{a}^b f(x)dx = F(b) - F (a)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si no coneixeu la codificació $\\LaTeX$, us recomano la guía Markdown i $\\LaTeX$ per a jupyter: https://towardsdatascience.com/write-markdown-latex-in-the-jupyter-notebook-10985edb91fd.\n",
    "\n",
    "També és molt útil un editor $\\LaTeX$ en línia, com el que trobem a https://latexeditor.lagrida.com/\n",
    "\n",
    "Amb aquest editor ha estat molt fàcil aquest altre exemple:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x(t) = x_{0} + v_{0}\\cdot t+\\frac{1}{2}\\cdot a\\cdot t^{2} $\n",
    "\n",
    "$v(t) = v_{0} + a\\cdot t$\n",
    "\n",
    "$a(t) = ct$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encara que de vegades trobem a faltar símbols a aquest editor, com en el cas de la derivada temporal $\\dot{m}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\overrightarrow{F} = \\frac{\\Delta\\overrightarrow{p}}{\\Delta t}\\equiv \\frac{\\Delta(m\\cdot \\overrightarrow{v})}{\\Delta t}=\\frac{\\Delta m}{\\Delta t}\\cdot \\overrightarrow{v}+m\\cdot \\frac{\\Delta \\overrightarrow{v}}{\\Delta t}=\\dot{m}\\cdot \\overrightarrow{v}+m\\cdot \\overrightarrow{a}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En aquest cas podeu sempre consultar a la Internet qualsevol de les moltes referències existents, com ara a la Wikipedia https://en.wikipedia.org/wiki/Wikipedia:LaTeX_symbols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "També podem visualitzar exprexions $\\LaTeX$ amb `%%latex` a una cel·la Python, encara que no podrem amagar el codi $\\LaTeX$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "x(t) = x_{0} + v_{0}\\cdot t+\\frac{1}{2}\\cdot a\\cdot t^{2} \\\\\n",
       "v(t) = v_{0} + a\\cdot t\\\\\n",
       "a(t) = ct\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "\\begin{align}\n",
    "x(t) = x_{0} + v_{0}\\cdot t+\\frac{1}{2}\\cdot a\\cdot t^{2} \\\\\n",
    "v(t) = v_{0} + a\\cdot t\\\\\n",
    "a(t) = ct\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Molt interessant la possibilitat d'utilitzar el sistema de tancar el codi $\\LaTeX$ entre símbols `$` per afegir fòrmules a les gràfiques:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/matplotlib/axes/_base.py:3604: MatplotlibDeprecationWarning: \n",
      "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n",
      "  alternative='`bottom`', obj_type='argument')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load http://matplotlib.org/mpl_examples/showcase/integral_demo.py\n",
    "\"\"\"\n",
    "Plot demonstrating the integral as the area under a curve.\n",
    "\n",
    "Although this is a simple example, it demonstrates some important tweaks:\n",
    "\n",
    "    * A simple line plot with custom color and line width.\n",
    "    * A shaded region created using a Polygon patch.\n",
    "    * A text label with mathtext rendering.\n",
    "    * figtext calls to label the x- and y-axes.\n",
    "    * Use of axis spines to hide the top and right spines.\n",
    "    * Custom tick placement and labels.\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "\n",
    "\n",
    "def func(x):\n",
    "    return (x - 3) * (x - 5) * (x - 7) + 85\n",
    "\n",
    "\n",
    "a, b = 2, 9  # integral limits\n",
    "x = np.linspace(0, 10)\n",
    "y = func(x)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.plot(x, y, 'r', linewidth=2)\n",
    "plt.ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = func(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='0.9', edgecolor='0.5')\n",
    "ax.add_patch(poly)\n",
    "\n",
    "plt.text(0.5 * (a + b), 30, r\"$\\int_a^b f(x)\\mathrm{d}x$\",\n",
    "         horizontalalignment='center', fontsize=20)\n",
    "\n",
    "plt.figtext(0.9, 0.05, '$x$')\n",
    "plt.figtext(0.1, 0.9, '$y$')\n",
    "\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "\n",
    "ax.set_xticks((a, b))\n",
    "ax.set_xticklabels(('$a$', '$b$'))\n",
    "ax.set_yticks([])\n",
    "\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}