{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Sección 3.2\n", "Mostrarémos que esta ecuación corresponde a una parábola usando sympy" ], "metadata": { "id": "DTAvc7GeNUiN" } }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 56 }, "id": "2221b8e9", "outputId": "43f54b6b-3871-41bc-fab7-e3906b81a1ed" }, "source": [ "import sympy as sym\n", "\n", "# Definimos las variables\n", "x, y = sym.symbols('x y')\n", "\n", "# Definimos la expresión\n", "expresion = 3*x**2 - 12*x + 4*y + 8\n", "\n", "# Display the original and factored expressions\n", "print(\"Expresión original:\")\n", "expresion" ], "execution_count": 4, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Expresión original:\n" ] }, { "output_type": "execute_result", "data": { "text/plain": [ "3*x**2 - 12*x + 4*y + 8" ], "text/latex": "$\\displaystyle 3 x^{2} - 12 x + 4 y + 8$" }, "metadata": {}, "execution_count": 4 } ] }, { "cell_type": "markdown", "source": [ "Si bién, no hay forma directa de factorizar la ecuación para darle forma de ecuación canónica de parábola, podemos jugar un poco con la función factor para lograrla" ], "metadata": { "id": "ZguBS9F8TYyg" } }, { "cell_type": "code", "source": [ "# Factorizamos los terminos de \"x\" y de \"y\" de forma separada\n", "\n", "x_terminos = 3*x**2 - 12*x\n", "y_terminos = 4*y + 8\n", "\n", "factored_x_terms = sym.factor(x_terminos)\n", "factored_y_terms = sym.factor(y_terminos)\n", "\n", "# Combinamos las partes factorizadas\n", "factored_expression_parts = factored_x_terms + factored_y_terms\n", "\n", "print(\"Expresión Original:\")\n", "display(expresion)\n", "\n", "print(\"Términos de 'x' factorizados:\")\n", "display(factored_x_terms)\n", "\n", "print(\"Términos de 'y' factorizados:\")\n", "display(factored_y_terms)\n", "\n", "print(\"Términos factorizados de 'x' e 'y' combinados:\")\n", "display(factored_expression_parts)\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 172 }, "id": "YfhZhKfyiILX", "outputId": "6ce458fa-f992-4305-f12e-bd271bebf307" }, "execution_count": 5, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Expresión Original:\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "3*x**2 - 12*x + 4*y + 8" ], "text/latex": "$\\displaystyle 3 x^{2} - 12 x + 4 y + 8$" }, "metadata": {} }, { "output_type": "stream", "name": "stdout", "text": [ "Términos de 'x' factorizados:\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "3*x*(x - 4)" ], "text/latex": "$\\displaystyle 3 x \\left(x - 4\\right)$" }, "metadata": {} }, { "output_type": "stream", "name": "stdout", "text": [ "Términos de 'y' factorizados:\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "4*(y + 2)" ], "text/latex": "$\\displaystyle 4 \\left(y + 2\\right)$" }, "metadata": {} }, { "output_type": "stream", "name": "stdout", "text": [ "Términos factorizados de 'x' e 'y' combinados:\n" ] }, { "output_type": "display_data", "data": { "text/plain": [ "3*x*(x - 4) + 4*(y + 2)" ], "text/latex": "$\\displaystyle 3 x \\left(x - 4\\right) + 4 \\left(y + 2\\right)$" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "Utilizarémos el módulo **plot_implicit** de sympy para graficar esta ecuación, de manera sencilla" ], "metadata": { "id": "tWy7hm23Wcca" } }, { "cell_type": "code", "metadata": { "id": "58a8c2cf", "colab": { "base_uri": "https://localhost:8080/", "height": 503 }, "outputId": "2e812d02-cac1-464e-b89b-900ef92c6b51" }, "source": [ "from sympy.plotting import plot_implicit\n", "\n", "# Renderizamos la expresión original igualándola a 0\n", "plot_implicit(sym.Eq(expresion, 0), (x, -5, 5), (y, -10, 10), title= r'Expresión original: $3x^2 - 12x + 4y + 8 = 0$')" ], "execution_count": 9, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 9 } ] }, { "cell_type": "markdown", "source": [ "Ahora, alternativamente, generamos la gráfica usando Matplotlib. Es evidente que esta lirbería, pese a ser más compleja, nos da un mejor control de la gráfica a generar" ], "metadata": { "id": "kY9jxgBSXsVe" } }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 565 }, "id": "3c4b6031", "outputId": "fc7af280-929e-4c78-c5b8-a68c51fcfb65" }, "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Definimos el rango de \"x\" dándole valores numéricos con Numpy\n", "x_values = np.linspace(-2, 6, 400) # Choose a suitable range for x\n", "\n", "# Calculamos los valores de \"y\" en la ecuación 3x^2 - 12x + 4y + 8 = 0\n", "# Resolvemos, en función de \"y\": 4y = -3x^2 + 12x - 8\n", "# y = (-3x^2 + 12x - 8) / 4\n", "y_values = (-3 * x_values**2 + 12 * x_values - 8) / 4\n", "\n", "# Generamos la gráfica\n", "plt.figure(figsize=(8, 6))\n", "#renderizamos la expresion en formato raw string (r'') para poder mostrar la expresión en formato LaTeX en la etiqueta\n", "plt.plot(x_values, y_values, label=r'$3x^2 - 12x + 4y + 8 = 0$')\n", "\n", "# Agregamos etiquetas y título\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.title('Gráfico de la parábola')\n", "plt.grid(True)\n", "plt.axhline(0, color='black',linewidth=0.5) # Add x-axis\n", "plt.axvline(0, color='black',linewidth=0.5) # Add y-axis\n", "plt.legend()\n", "plt.show()" ], "execution_count": 10, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" 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