Aula3_Curso_Pytho2_0_aluna_o.ipynb

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  "metadata": {
    "colab": {
      "name": "Aula3-Curso-Pytho2.0-aluna-o.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPzA7OKLzaFCoOOR4znmUtx",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/williamcostaesilva/aula1_revis-o_python_basico/blob/main/Aula3_Curso_Pytho2_0_aluna_o.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4CFuBPWO-ovZ"
      },
      "source": [
        "![images-2.png](data:image/png;base64,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)\n",
        "\n",
        "# Universidade Federal do Amazonas\n",
        "# Departamento de Engenharia de Produção\n",
        "\n",
        "## - Projeto Super 2021 - Curso Python 2.0\n",
        "\n",
        "### Aula 3 - Biblioteca Numpy\n",
        "\n",
        "**  Prof. William Costa **\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "al5kVpxK_OEs"
      },
      "source": [
        "![numpy.png](data:image/png;base64,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)\n",
        "\n",
        "\n",
        "## Aula 3 - Biblioteca Numpy\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k19sjpJBDOuB"
      },
      "source": [
        "# - Finalizando o contéudo da aula passada (derivada, integral, solver)\n",
        "### Biblioteca sympy - matemática simbólica\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5FoWH-QBKQOT"
      },
      "source": [
        "# Importando a biblioteca sympy\n",
        "import sympy as sp\n",
        "sp.init_printing()"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "TVEwozN0NmMK",
        "outputId": "00b75898-a2c3-47d1-cce8-b17a7e0d1120"
      },
      "source": [
        "# Criando um funçao sin(x)**2\n",
        "x = sp.symbols('x')\n",
        "fx = sp.sin(x)**2\n",
        "fx"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\sin^{2}{\\left(x \\right)}$",
            "text/plain": [
              "   2   \n",
              "sin (x)"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ru-TSLoyOBmY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "outputId": "6b6f51eb-d34b-46e7-97ac-040c316e3a05"
      },
      "source": [
        "# DERIVADA \n",
        "# sp.diff() - calcula a derivada de uma função\n",
        "C = sp.symbols('C')\n",
        "dfdx = sp.diff(fx,x)\n",
        "dfdx += C\n",
        "dfdx"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle C + 2 \\sin{\\left(x \\right)} \\cos{\\left(x \\right)}$",
            "text/plain": [
              "C + 2⋅sin(x)⋅cos(x)"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k3HxPtKvYNxJ"
      },
      "source": [
        "# Derivando a expressão em funçao de x\n",
        "x,y = sp.symbols(['x','y'])\n",
        "sp.init_printing()\n"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "1pWBh5b6Y5vp",
        "outputId": "38001f23-cba0-45b9-8096-2bf7eb2f01ae"
      },
      "source": [
        "# Derivando uma expressão duas ou mais vezes - derivada de 2a ordem , 3a, ...\n",
        "#expres\n",
        "expres = sp.exp(2*x) + sin(x)\n",
        "expres"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle e^{2 x} + \\sin{\\left(x \\right)}$",
            "text/plain": [
              " 2⋅x         \n",
              "ℯ    + sin(x)"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "-5KSNMAWZI-J",
        "outputId": "a3dae79c-98dd-438d-cbc3-6448d010bad0"
      },
      "source": [
        "# Calcular a derivada \n",
        "dfdx = sp.diff(expres,x)\n",
        "dfdx"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 e^{2 x} + \\cos{\\left(x \\right)}$",
            "text/plain": [
              "   2⋅x         \n",
              "2⋅ℯ    + cos(x)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "OfprfEYJZ3qf",
        "outputId": "288bc219-cfdd-4b53-b42c-00c24f856a28"
      },
      "source": [
        "# Calcular a  1a derivada de fx\n",
        "df2dx = sp.diff(expres,x,x)\n",
        "df2dx"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 4 e^{2 x} - \\sin{\\left(x \\right)}$",
            "text/plain": [
              "   2⋅x         \n",
              "4⋅ℯ    - sin(x)"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ONrkhCJGcMBF"
      },
      "source": [
        "# Exemplo - fx = x**3 + 5* x**2 + x\n",
        "# Atividade - escrever a expressão acima usando a matemática simbólica\n",
        "# calcular a primeira derivada da funçao  fx\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "REA8PeIhYbCa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "5208d09e-76c4-47bb-b689-912a4dbf181c"
      },
      "source": [
        "##### COMO ESCREVER/EXPRESSAR NA FORMA df/dx\n",
        "y = x**2 + x -1\n",
        "y\n",
        "sp.Derivative(y,x)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{d}{d x} \\left(x^{2} + x - 1\\right)$",
            "text/plain": [
              "d ⎛ 2        ⎞\n",
              "──⎝x  + x - 1⎠\n",
              "dx            "
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zFRr-_yfaN4c"
      },
      "source": [
        "# Escrever de forma simbólica a derivada : \n",
        "# f = sp.exp(2*x) + sp.sin(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R87ekozicoLF"
      },
      "source": [
        "## INTEGRAL - "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T2KoWAQfaVB-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "outputId": "47415a80-64ac-4912-b588-0670c3284aa1"
      },
      "source": [
        "#  definida e indefinida\n",
        "# sp.integrate()\n",
        "import sympy as sp\n",
        "sp.init_printing()\n",
        "\n",
        "# criando as variaveis simbólicas x , y e z\n",
        "x, y, z= sp.symbols(['x','y','z'])\n",
        "f = sp.cos(2*x) * sp.sin(3*x)\n",
        "f\n",
        "sp.integrate(f,x)"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle - \\frac{2 \\sin{\\left(2 x \\right)} \\sin{\\left(3 x \\right)}}{5} - \\frac{3 \\cos{\\left(2 x \\right)} \\cos{\\left(3 x \\right)}}{5}$",
            "text/plain": [
              "  2⋅sin(2⋅x)⋅sin(3⋅x)   3⋅cos(2⋅x)⋅cos(3⋅x)\n",
              "- ─────────────────── - ───────────────────\n",
              "           5                     5         "
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8RC_e4iNct14",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "outputId": "75580cc7-20e5-4179-f628-37f6bf452d25"
      },
      "source": [
        "#  definida e indefinida\n",
        "# sp.integrate()\n",
        "import sympy as sp\n",
        "sp.init_printing()\n",
        "\n",
        "# criando as variaveis simbólicas x , y e z\n",
        "x, y, z= sp.symbols(['x','y','z'])\n",
        "f = sp.cos(2*x) * sp.sin(3*x)\n",
        "\n",
        "sp.integrate(f,x) + C"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle C - \\frac{2 \\sin{\\left(2 x \\right)} \\sin{\\left(3 x \\right)}}{5} - \\frac{3 \\cos{\\left(2 x \\right)} \\cos{\\left(3 x \\right)}}{5}$",
            "text/plain": [
              "    2⋅sin(2⋅x)⋅sin(3⋅x)   3⋅cos(2⋅x)⋅cos(3⋅x)\n",
              "C - ─────────────────── - ───────────────────\n",
              "             5                     5         "
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uk_5C7iGr83J"
      },
      "source": [
        "# Integrando a função\n",
        "# .integrate(funcao,arg)\n",
        "# Integral indefinida\n",
        "# definindo uma função\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UwLDs0ClsfK1"
      },
      "source": [
        "# Exemplo - f(x) = x**3 \n",
        "# Escrever a expressão com a simbologia matemática\n",
        "# depois calcular integral indefinida da função f(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "Otv_kVlLtVgf",
        "outputId": "7980daf5-ed4e-461b-ab1e-cdff184b7b8d"
      },
      "source": [
        "# Integral Definida\n",
        "# sp.integrate(funcao,(variavel,L-inf,L-sup))\n",
        "# Exemplo anterior funcao f , limite inferior = 0 e limite superior=pi\n",
        "f = x**2 + 1\n",
        "f\n",
        "sp.integrate(f,(x,0,5))"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{140}{3}$",
            "text/plain": [
              "140/3"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "IMRbFcqvvTya",
        "outputId": "8c72fa44-5e44-4ff6-c3b7-33e4d6ec4056"
      },
      "source": [
        "# Integral dupla (multipla vezes)\n",
        "# definindo a função\n",
        "w = 4 - y**2\n",
        "w\n",
        "sp.integrate(w,(y,0,2),(x,0,3))"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 16$",
            "text/plain": [
              "16"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UBMBCLjSvpM4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        },
        "outputId": "1c8a2931-a1fa-4adb-c066-b4db2276ced4"
      },
      "source": [
        "# Escrevendo a integral literalmente\n",
        "# Integral(expresao)\n",
        "import sympy as sp\n",
        "sp.init_printing()\n",
        "x = sp.symbols('x')\n",
        "f = 1/x\n",
        "f\n",
        "Integral(f,(x,1,5))"
      ],
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAAArCAYAAAD8I09bAAAABHNCSVQICAgIfAhkiAAABEZJREFUaIHtml+IFVUYwH/rmlxllYhakdjCtUwL3FxJI8wmESNBU9OXfYggCIJE8kVaNPbBVMpeFBIJYqkeFFkRNzN6KEgF/2CK2G4Raq67rf1x1W1R0a3rw/ddZu7cmTt/7hyv484PLnPnnO/ffPfMme+cuZCRKtqAvOtzqZoBVZvRBmz+CliO8/8M+EgNJhI8zAgftU5GGbDZCPwBnAd26vmIpSZhe68C44FfgHpgHTANeAa4nLCv+44aoDaiTh3wF7Am+XDSQZgpIgdsAgaAa8BHhE/0EPAz8GSs6EYIX1JaerWG1M0B/cAHZkJLP/XA/0hSVwEr9ftFH/ktwEvAZGAO8DUwCDxuPNKUshB71D6ETA37gXZgnIf8TqSCuAX0AR3A03cj0LTSgiT3RrUDSStBD7nxehw0Hcj9SlCC6/Q4ZDqQe5QG5A7eE9dA2BH8b1wHPqwAtgEHkbsjD3wVUncisr+xLeGYvJilx5/iGgjaizA1gtcBTWq3F1ntheU1ZGDEHlURaNbjibgGqjWC3wOmAhOAdyLqLkOW3T8mHJMXFY/gas3BPwC/IVNDFCYA84FO7G3Q79TO6y7ZGqSczAOby9gcDawGTgM3gQvAWtVvRsrOPx3ylforYp8qfB5WIQYW4efgQtm4xNHWhCS7i+Il/Ccqu6OMvTHYCTsJfIxc6w3gM23f59KpxF8J36vS1ihKEbEIn+DdyN2Uc7W3q4039bxVz3dR/i4tJHE9xTuL87AXWG0eenH9lXBcFT+MohQRi3AJziHPgt0efQ3IqDsPvKv2vkVGqB+zVa7Tp79L+xcn5M+TblV+P6piBCzCJXixyrX49G/CHnWH8V7KOylsYj3v039Q+x+txF+1qog4LEf2OPb79P/t+P4WcD3A3kKkGjnq09+I7GX3JeTPk6sUzzUmsAgewbXAP8ABn/4WZNevX21tD/CZUzm/8qtZ+79JyJ8vw3iXJEliEZzgl1XmbY++RcjIPg08gryuug08VcbeA8i19fr0d6i/DQn582Qs9hzzSlTlCFgEJ3grUhpNdLXPRW7Nc8AkbVuh9vYG+C08X9wPsbXY170sQX8l1DscvRBVOYClSKnTjjx988BZR9sWh2wN0AMcctl4FpnC+oEprr5C9fNimRjeUJlbwBfIq7BjSHXQo33OFwWV+iuhETvBM6IohqDNYdvr87tD9jltc744fQL578UVn9gWqM6RgDhWI6PxNrJa60Dm3wvInJ+0vyKasC94chTFhNl4D8RghLnYCX64jNw8ZDnZh5mKoxs4lbDNu4azDp6NlCWf6nmDHoeRV/Z+1AFnkNvNxKul6cj8l3oKc+51YCZS0OeRCTwsQ5itmVNPJ6UPnCg1cJbgAB5E6tFryLy3pLx4CVmCDZMl2IWJv69mOMgSbJgk/uFeh6x0QH6wx5CyagBZcmZUiIX3cre9eiFlZGRkZGTAHVZeQ+Lwu9skAAAAAElFTkSuQmCC\n",
            "text/latex": "$\\displaystyle \\int\\limits_{1}^{5} \\frac{1}{x}\\, dx$",
            "text/plain": [
              "5     \n",
              "⌠     \n",
              "⎮ 1   \n",
              "⎮ ─ dx\n",
              "⎮ x   \n",
              "⌡     \n",
              "1     "
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qsr-WLjK9OgJ"
      },
      "source": [
        "# Exemplo -Escreva a integral da função =x**2 + 4*x + 5\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "co_GCEC8cyhp"
      },
      "source": [
        "# - SOLVERS \n",
        "** solveset(eq, arg) ou solve **"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "PGjAQnJbdBpq",
        "outputId": "8d0d85f8-8bf1-497c-8499-7f35602ce470"
      },
      "source": [
        "# Declarando um expressão\n",
        "import sympy as sp\n",
        "sp.init_printing()\n",
        "\n",
        "# Declarando uma expressão\n",
        "x = sp.symbols('x')\n",
        "fx = x**2 + 6 *x +9\n",
        "fx"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{2} + 6 x + 9$",
            "text/plain": [
              " 2          \n",
              "x  + 6⋅x + 9"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "09Q7be8ydycH",
        "outputId": "4ead8f7a-41f4-4ef4-e736-2c29aa5bde81"
      },
      "source": [
        "# Encontrando a raiz da expressão - SOLVER\n",
        "# sp.solveset()\n",
        "sp.solveset(fx,x)"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAWCAYAAABkKwTVAAAABHNCSVQICAgIfAhkiAAAAklJREFUWIXt10+ITVEcB/CPGTJKBk1GJBJT/iyQrBSJEkmys5cFsbGwERsZakpIVjbGho2FsqFmIZREzAIbM2U0FkOzGM8YjMU5z7zevHfvu/fNmCm+dTp1z/f3+33Puef8fufwD+MQnmIQP7FhauX8wVmMoB930VaJNDPBwVp0Ygh30BedTTQuYLMgsAUF9Aqir2Kggk0XmoTF3o8l2JIl6FGM4nhO0bXiu7A7bqAdV/Asxu7DshT75/iFuVmCno4BdmUUmxVNVb6fi/Gvpdjfirxxi9CQYNQY+5E0dXXiW5Xvt2O/OsW+qK+xfCBpclONfbF/lddBUkKZH/tCXucZcVI4N81CgtkqTKw9xa7455trDTTD2EFdnFlmPvQLZ6fY7qO1BrtTkX8ijbgbHcay1fUUfk+ZoLTWWYPYVhzAW3zEphT+0qhjRDin57CiEvFSiZDXWJfi+CHeZGgXU/yVYjmG0V0D9wi+lmjfXo04TyiMBXxQIQv9RbwQxLYkcPZGziPhZ8yqxXFnNFpfp8B68ClqWJDA6YicneUDSaWgN/YLc0tLR5vKWa5BODuL8BhfEnwUJ95TPpBUCorFcTJr4R6cF7bUe+Ee2YptWClk0MMpPor6fpQPJE1uNKvSHHiAVUJN2yjU1iG8w01cxucafY3TmzS54dgn7fd60Y1jdfoo6qt2jauIg8Jq3BMupdPtqjZbeOYMxpZJ3xyh1pUW4en0WC3VdaYSKWlbFoQ73g6sEe59k/FYzYMuIYEM4AleTqma/5hg/Aa86ZDuQOTT6QAAAABJRU5ErkJggg==\n",
            "text/latex": "$\\displaystyle \\left\\{-3\\right\\}$",
            "text/plain": [
              "{-3}"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jCLlUgzpeCHQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "6493736d-13d5-436b-dd4f-e942afd86906"
      },
      "source": [
        "# método sp.solve()\n",
        "sp.solve(fx,x)"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ -3\\right]$",
            "text/plain": [
              "[-3]"
            ]
          },
          "metadata": {},
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xlOYM_gIeZhp"
      },
      "source": [
        "# Exemplo: f(x) = x**3 + 5 *x**2 + x\n",
        "# Escrever a funçao acima usando a matemática simbólica,depois\n",
        "# Aplique o método .solve( ) ou solveset() e encontrar a raiz ou raízes da expressão\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "Y3n2R_EegMIH",
        "outputId": "0bb864e3-04fa-4ccd-e080-ae6db6cbfb8b"
      },
      "source": [
        "# Aplicando o SOLVER sistemas lineares 3 x 3\n",
        "x1,x2,x3 = sp.symbols(['x1','x2','x3'])\n",
        "coef = sp.Matrix([[3,2,4],[1,1,2],[4,3,-2]])\n",
        "X = sp.Matrix([[x1,x2,x3]]).T\n",
        "R = sp.Matrix([[1,2,3]]).T\n",
        "\n",
        "# coef * X = R\n",
        "#coef*X-R=0\n",
        "sistema = coef*X-R\n",
        "resposta = sp.solve(sistema,(x1,x2,x3))\n",
        "resposta"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left\\{ x_{1} : -3, \\  x_{2} : 5, \\  x_{3} : 0\\right\\}$",
            "text/plain": [
              "{x₁: -3, x₂: 5, x₃: 0}"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "OUWz3xDJmgP0",
        "outputId": "a6a79edb-9b5a-4e43-9efe-0d34493cd354"
      },
      "source": [
        "X"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}x_{1}\\\\x_{2}\\\\x_{3}\\end{matrix}\\right]$",
            "text/plain": [
              "⎡x₁⎤\n",
              "⎢  ⎥\n",
              "⎢x₂⎥\n",
              "⎢  ⎥\n",
              "⎣x₃⎦"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z5tJW1DrmiCg"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}