Aula_08_Pos_Ciencia_De_Dados.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Aula 08 - Pos_Ciencia_De_Dados.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "wduW81wRUSU2",
        "D47hKRi_MJZy"
      ]
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "emullE1LjVR0"
      },
      "source": [
        "# **Turma de Pós-Graduação de Ciência de Dados**\n",
        "\n",
        "**Disciplina: Linguagem de Programação Python**\n",
        "\n",
        "**prof: Sérgio Assunção Monteiro, DSc**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q3hPPlfSjcGu"
      },
      "source": [
        "**Aula 08**"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Programação simbólica com o pacote sympy**"
      ],
      "metadata": {
        "id": "wduW81wRUSU2"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RcT56f1bjQ1G"
      },
      "source": [
        "import sympy as sp\n",
        "sp.init_printing()"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eZPJWARNl0B4"
      },
      "source": [
        "x = sp.Symbol('x')\n",
        "y,z=sp.symbols('y,z')"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p4Ewv7yqmVf_",
        "outputId": "ee9c6116-d361-4499-bccd-132e8a2628e0"
      },
      "source": [
        "g = x**2 + y**2 + z**2\n",
        "sp.pprint(g)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " 2    2    2\n",
            "x  + y  + z \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "cXENwdP_AgUv",
        "outputId": "6f5d6008-008c-43ed-fbc9-b8998eb5f29b"
      },
      "source": [
        "g\n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{2} + y^{2} + z^{2}$",
            "text/plain": [
              " 2    2    2\n",
              "x  + y  + z "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "TbrF1fBtmv7P",
        "outputId": "d7c7a2d3-4c12-4ac1-9950-c1bb4895cbb3"
      },
      "source": [
        "h = x**2 + 2*x - 5\n",
        "h\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{2} + 2 x - 5$",
            "text/plain": [
              " 2          \n",
              "x  + 2⋅x - 5"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ByoK-GtinCTt",
        "outputId": "de535b20-6c87-42ac-ba39-24ab893d7b4f"
      },
      "source": [
        "print(h.subs(x, 1))\n",
        "print(h.subs(x, z))\n",
        "print(h.subs(x, y**2))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-2\n",
            "z**2 + 2*z - 5\n",
            "y**4 + 2*y**2 - 5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "id": "BXQ5K7uXnQVu",
        "outputId": "dbc6c59f-9fcf-46eb-921f-db2328e644ef"
      },
      "source": [
        "f = (10*x**2 - 100*x + 250)/(x - 5)\n",
        "f"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{10 x^{2} - 100 x + 250}{x - 5}$",
            "text/plain": [
              "    2              \n",
              "10⋅x  - 100⋅x + 250\n",
              "───────────────────\n",
              "       x - 5       "
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "pySIbah-nX-u",
        "outputId": "a8bd8abc-99a6-45b8-a999-dbb2d1b23b03"
      },
      "source": [
        "f.simplify()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 10 x - 50$",
            "text/plain": [
              "10⋅x - 50"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "eE6w5cfuPnS6",
        "outputId": "e5ec6cfd-aa48-477f-940c-a0e65297d4e0"
      },
      "source": [
        "f = (x+1)**3+(x+5)**2\n",
        "f"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left(x + 1\\right)^{3} + \\left(x + 5\\right)^{2}$",
            "text/plain": [
              "       3          2\n",
              "(x + 1)  + (x + 5) "
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "1ZmDKYUIBMNe",
        "outputId": "20272125-ee37-4bad-e024-a78fba58bebf"
      },
      "source": [
        "sp.expand(f)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{3} + 4 x^{2} + 13 x + 26$",
            "text/plain": [
              " 3      2            \n",
              "x  + 4⋅x  + 13⋅x + 26"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "yeIQtYOFQQeB",
        "outputId": "504efcf7-877a-4b2a-95f2-8f12f6dfbc0c"
      },
      "source": [
        "f = 3*x**4-36*x**3+99*x**2-6*x - 144\n",
        "f"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 3 x^{4} - 36 x^{3} + 99 x^{2} - 6 x - 144$",
            "text/plain": [
              "   4       3       2            \n",
              "3⋅x  - 36⋅x  + 99⋅x  - 6⋅x - 144"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "4lgIHgTOBP08",
        "outputId": "cf0f7d87-c4c7-4d95-d889-e911d29ee7f4"
      },
      "source": [
        "sp.factor(f)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAARAAAAAVCAYAAACOsLESAAAABHNCSVQICAgIfAhkiAAABgNJREFUeJztm3uIFVUcxz+uZm4GW1lphQXlGoWUGQWCxbUnFZKRBEnQLfsjaK2lJ0nREsSqaA+MXoSsUZS1tpFFtdEDVFhLXEtoS3PbHrrrg9KC1nLz9sfvDDt79pw5c+c+ZmZ3PnDZe885vzPn9z2/OTPzm7OQkZGRETNrgH3AxLgHUmYuBgrAXSHaZhpkGox2/1kGfAb8CvQDvwOdwBPAJIvNJcBR4P5yjLQK3AC0A78hPnYD7wCzLe3bgF7g+IA+06RBlDkeSRpMQk6ENuBHRINDwEZgEVBjsXNpkBb/PRYAq4ANwJ/IAvF6QPswMcC/QAewGliqDvC16nw3MNVg0w4cBGqLGn48LEN8OQC8ivjYivh9FLjNYHOpslkS0G+aNIgyxyNJg7sRX/YAbwDNiBYHVXkrMMZg59IgLf57bEP8+Qvowr2AhIkBJljKn1LGL2jl05ET7xX3eGNnCvAf0AecqtXNRfzrtth2AT9jvjqlSQMofo49RooGVwDzGO7HFOAXRIObLbY2DeLwP4+MNRfRfi5QjyyWOdwLCBj814U4bDF8W/2t18rvVANYa7FrxzwhY4AWVbc0aMRl5CzE383Ic6qfL5CV+BSL7VvAmcDVhro0aQDFz7FHVA2S5v/nwHrkhPfTB7ykvucstjYN0hYDIDG/Ux07LEExEMhj6kArtfItwAD2pNGFyFX/O2Csr3yl6u/lYgdSAicB/yDPcSdrdZer8bRZbK9S9SsMdWnSIAjbHHtE1SAt/gM8hIzpGUu9TYM4YiBPaXcgfnKEuwMJioEhPAg0IUJuUEbfMPQKPRERbbujrxZln1e/l6jfa7EnrCpFI3Ll2YfcbjYjV97DyFVCf7TxqEPG/JVWnkYNPMLMsZ9SNGghef7rjEN8KADXWtqYNIgrBvJUfwGxxcAw+lRD7/MRMFlrM13VtTv6mopkun8CGpTNx8B41yAqxHzkzYPfv53AQoddP6KLn7RqAOHmWCeqBkn0X2cFMq4PHe10DeKKgTzVX0DAHANWJgM3AT8gWetZvrrZDK6gLpoZDNRNwHEhj9/D0CB3fVwCPIxcLZ4GzlbjmAV8ouyXB9juVrZ+Kq1BD+X130TQHOuUokFSYsDEvcq2C3nUDULXIInnQUvIfj1yhNduiP/jHI33InmBrcAO4DVghqrrV39tWX0/+33fFwF/h7AB2IU96WdiT0BdDnmN28bQd/VbkRNoB/AAkkgzvY2pZdBnj0prUE7/bQTNsU4pGiQhBkw0AM8h+YkrkbvTIHQNqnEePAucoJXNBG5ENq/1aHXbQvYbBVMMhKITWaW8BOTp6vdGh91CJO/Qq9q/GOXgZcC7RV1sqX8X+yu8GsSHXVp52jRwoc+xn1I0SKr/jch4tmPPf/kxaRBXDOSp/iOMLQZCsVcd5ET1ewySjNxvtYDrkY1L3yLJue+BI8C5UQZQIquQ8T9pqfcSifMMdeepunVaedo0cKHPsZ+oGiTV/0cQfzoxL5gmTBrEFQN5qr+A2GIAkGRQnaG8hsFNRpu0ulZVPs1gNwe5ResGTlNlC1T79xwDrQS3qGP3AWdoddchK2s/5u3cdyjbBkNdmjSIMsceUTRImv8ej6sxbMGd8/Bj0yCOGMhT/QUkKAZoRE6gTxl8xbkauV0pILde52s2t6q6e7Tymci23l7gHK3O2zZ9mWOw5aYG8a2A7P1fg+RE3kcWjwJwn8X2TSRxZNrmnSYNosyxR7EaJNF/gNvVsQeQV9hNhk/eYmvTII4YyFPaAjIfSba2IG+DCkgceGWmvR5BMcAM4HkkAXNANTyEONqEeaUej9z2bvaVTUOu8n8AFxhsvM0oHWa/KsoxyEnUgSwiA8jt5wfANRabOuSks10t0qRBlDmG4jVIqv8gfrreYnxpsAvSII4YyFPaAtJEsAY9WntXDETmUXXAi8rdcUJYjPg3J6BNpkGmwWj3PzITkH+wWV/ujhNALfJasNXRLtMg02BU+j92eNuiGUD2EByLJKWOlKHPpFCP/P/McuRZ1kamQabBaPc/IyMjIyMjI6NK/A9OXf5yzTegWQAAAABJRU5ErkJggg==\n",
            "text/latex": "$\\displaystyle 3 \\left(x - 8\\right) \\left(x - 3\\right) \\left(x - 2\\right) \\left(x + 1\\right)$",
            "text/plain": [
              "3⋅(x - 8)⋅(x - 3)⋅(x - 2)⋅(x + 1)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "qfLS4YCwQkL5",
        "outputId": "84f9b6d8-5c02-4127-e995-cc8d8f702caa"
      },
      "source": [
        "y = (sp.sin(x))**2*sp.exp(2*x)\n",
        "y"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle e^{2 x} \\sin^{2}{\\left(x \\right)}$",
            "text/plain": [
              " 2⋅x    2   \n",
              "ℯ   ⋅sin (x)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "tDHwy5KHBYQM",
        "outputId": "669143c9-ca94-42fd-99be-bd9d088c79a2"
      },
      "source": [
        "z = sp.diff(y,x)\n",
        "z"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 e^{2 x} \\sin^{2}{\\left(x \\right)} + 2 e^{2 x} \\sin{\\left(x \\right)} \\cos{\\left(x \\right)}$",
            "text/plain": [
              "   2⋅x    2         2⋅x              \n",
              "2⋅ℯ   ⋅sin (x) + 2⋅ℯ   ⋅sin(x)⋅cos(x)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "YSUv-_bsQ6Q3",
        "outputId": "9b003d8a-6cdb-471f-bbb6-92d217c04870"
      },
      "source": [
        "z.subs(x, 5)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 e^{10} \\sin{\\left(5 \\right)} \\cos{\\left(5 \\right)} + 2 e^{10} \\sin^{2}{\\left(5 \\right)}$",
            "text/plain": [
              "   10                    10    2   \n",
              "2⋅ℯ  ⋅sin(5)⋅cos(5) + 2⋅ℯ  ⋅sin (5)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "AxyTsH-MRQd5",
        "outputId": "d0e0ec19-bb13-45fc-ac2b-a1c29007197a"
      },
      "source": [
        "f = x**2 * sp.sin(x**2)\n",
        "f"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{2} \\sin{\\left(x^{2} \\right)}$",
            "text/plain": [
              " 2    ⎛ 2⎞\n",
              "x ⋅sin⎝x ⎠"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "id": "24bRksm6Bf-k",
        "outputId": "5e1a69a0-adfe-4b73-cc76-d2afed4f0a77"
      },
      "source": [
        "g = sp.integrate(f,(x,0,5))\n",
        "g"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle - \\frac{25 \\cos{\\left(25 \\right)} \\Gamma\\left(\\frac{5}{4}\\right)}{8 \\Gamma\\left(\\frac{9}{4}\\right)} + \\frac{5 \\sqrt{2} \\sqrt{\\pi} C\\left(\\frac{5 \\sqrt{2}}{\\sqrt{\\pi}}\\right) \\Gamma\\left(\\frac{5}{4}\\right)}{16 \\Gamma\\left(\\frac{9}{4}\\right)}$",
            "text/plain": [
              "                               ⎛5⋅√2⎞       \n",
              "                      5⋅√2⋅√π⋅C⎜────⎟⋅Γ(5/4)\n",
              "  25⋅cos(25)⋅Γ(5/4)            ⎝ √π ⎠       \n",
              "- ───────────────── + ──────────────────────\n",
              "       8⋅Γ(9/4)             16⋅Γ(9/4)       "
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "kgn4Rtn8R3Ug",
        "outputId": "bc730825-e74d-4c3b-cc3f-2a81df82c4b0"
      },
      "source": [
        "g.evalf()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAANcAAAASCAYAAADIWEuyAAAABHNCSVQICAgIfAhkiAAABdNJREFUaIHt2lusXUUZB/AfWKWipCpiiRGtNqKFEiLeUBFOS2wUU4O3+CJXCw8qIlGjIsSjiRGREBAjl4AaNfGxQUFEbECwSoDQBhMQFHtqCVQplyrWgsXDwzc7e53VvdbeM/sSHvY/WZl9Zr5v/v+z1ly/GaaYYornPQ7EOqzHX/Ff7MTv8Snsm1nfx3AZbsO/MI+ftdifmmzanmdHoDnXp0QXfAcbsC1xPI5N+HrS0Ibjk77teBoP40ac0MfvkxVN68bEMU6e1+CHyeZpzOESvHwATYPqmtP8HbdXDRcNSDoIPo7L8Qhuxt+xFB/B1fhAspkfsL7zcCSewkN4cx/7zfhGQ9l7sRo3jEBzrk+JLjgHd+Mm/BMvwdGYxZnp97YefhfiS+Kd/QI7cBDeihn8qkHLIfi+eN8vbbAZlmOcPMvxB7wK1+LPeAfOxvvxHjw2Il07Raet46k+fsVYjbX2HrkPFg1wHh/NqG8V3oh9xIvsN3O14Y/J/0O1/BLNo/w/m3TB4gafbyWfH/QoOyOV/Rgv6lH+woY698Fv8SC+q33kLuUYN8+Nyf6sWv7FKf+KEemaS8/zBucKwZcV+s8o71xHJN+H8IIMvxLNOT6luo5MfjfV8vcTM9xWvRtjG87G/3GsmBmbGtcwHOPkWZ7q2mLvQe8AMaP8R8z+w+gio3ONclnYhv+ldM+E+Ko4M6XX6L23aUKJ5hyfUl1rU3pPLf99Ysl0iWgoH8RK7MYdYpbshRW4AJfiVjEzN6GUY9w8q1L6m2Rfxb+xEWvEUnrDELo62E/sz14rOu09yXfBd5xE51qEk9PvX0+Ar4oXi5fwrNgPDYoSzTk+Obq+KPYAS/A2HCM+5gU1u7endLcIfKysld8qgkSP1jT/VCxnz+2jo5RjEjxvSukDDfX9RXSuQy3sXLm6Ojg4+VWxBafhdxn1DI2LxDR7/RB1zChbFp6S/K7L9CvRnOOTo2u7hRGpG0QApY7LU/ke0fmOEZ3yCN39yC01n2+KDv6uSt6s5mVRCcckeK5qqYvuPvWrQ+oiorWrxTfYX3T8K8SMuUss23tiTv+wcfXp19g/l+zuwyv62LZhZkC+OjYmv7X9DCso0ZzrU6JrKT6M+0Wo+aha+ZWpzt1YVivbX0QW53Ub0jtF472wZjuruXHlckyKp6RzlehqQ2dwXd/JqG/+HhQfb9Dn4Rayz4p17L1iTfx4pthhcTjeLQIGbaHhKko05/qU6IJ/iA+3Rpxz/aRW/mRKN9l7w71LjPhEeHpR8n8A52doyOEwQZ6dKV3SUF8nv1Nvqa42dKKRx46ovkZ8XvTiP4lzh2ExI3/mujT5zA5oX6K5xCdXVy9sSnW8spJ3uu6ysRc6Ieav4GUGX51Uz3NyOEyQZ136+8oG+85S8vghdbVhie5si/EENL4sNtubRdRnxxg4+mExThLr6WsGsC/RXOKTq6sJr05pNTq1QXzcw8SKpB416wQFtojbC038R+Et4sbJ/RZG5nI4TJDn5pSu6WF/gDhA3oXbh9TVhqNT+rcB7bNxvngpdxl8v7Jc3L5oO3yckTdznZTsfzmAbYnmEp8cXYfqvcTZV3f/sLFH+bWp7Jxa/hrR4J5oqLeKWe17jlFwjINnmEPkQXWt0PusbJmISM6rRB1HOXOdoht9uU1s8uuYEyfuVWzA6/B6C9fXJ6aHCH0SG9iO/w4Rpu6FzhnSVWPQXPp/5ug6Ad8Wo+cWcW1nKY7DG0QE8Ywefp8Ro+7F4mxok3ivJya963T3J6WYBEcJz6fF9afvieXffSJosUrsrb42Ak2fwBfEUcBWcYa2POlbLPbQF42AZy/M6r9+vaWH31wqW5ZZ31yDjhWpfJv+Nx9KNJf45OpaKe65bRaDyB7RkO5M/G2z5UHihshWPJP81+tu/vthVv9o2bAc4+I5BD8S9z6fSX45F3f76ToOPxf3Fp8UlwYeFbdlThbXqKaYYooppphiiimmmKKK5wCbwtf+W+9rtAAAAABJRU5ErkJggg==\n",
            "text/latex": "$\\displaystyle -2.17227364646045$",
            "text/plain": [
              "-2.17227364646045"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "rL9nusM-SIwD",
        "outputId": "5d3eb440-e3b6-43d9-eafd-834b09005e4c"
      },
      "source": [
        "y = sp.Eq(x**3+15*x**2,3*x-10)\n",
        "y"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x^{3} + 15 x^{2} = 3 x - 10$",
            "text/plain": [
              " 3       2           \n",
              "x  + 15⋅x  = 3⋅x - 10"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "id": "2uDft13BBoGm",
        "outputId": "cb43b31b-b84d-4edc-c67b-42a0a3b39699"
      },
      "source": [
        "z=sp.solve(y,x)\n",
        "z[0]"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAA7CAYAAABFaS09AAAABHNCSVQICAgIfAhkiAAAE6BJREFUeJztnXu0HVV9xz95JySQBIQgFQgoEJ4JIBBoQ04QoTEBUgpqKY9LeWgXoIUiFhC8oogCipSnKPRGKVKwogXBLl4pAWEpEgQKgiLHghCUN0gUgukfv5l1586dx97zOHPPvd/PWrPuPbP37P3bv71nzu/s+e3fBiGEEEIIIYQQQgghhBCiGxjVtABCCCGEKMUYYHXTQggxzJCNLIQQQgj+EripaSGEEIMZ3bQAQgghhCjFYmRoCyGEEEIIUTk/BzZuWgghxGA0oy2EEEIMDaYB9wMPAo8Axzhcs0nw9+m6hBJCCCGEEKLbGQOsFfw/GXgKWC/nmn8EvlinUEKI4mhGWwghhBgavAO8Gfw/AYt6kBf5QP7ZQgghhBBCODAN87l+EzguJ+8k4P/QpJkQQgghRjgTmhZANM54j7wzgHuCv2ksBr5dSiIhRK3oV7AQQtTPfsBfNS3EMGVNxUedzAH+2jHv89jM9ryMPIuAH5YVqgNU3UdD9RBCCCFEh9kauKppIYYpOwMfb1oIT74CzE5JmwGsHfw/FYs8sn1GWb/GXE2GMt3YR0IIIYToAkYDdwMbNi3IMOVMui9+9FTMJWRMQtquWGi/nwMPAR/LKGcH4H8ql656urGPhBBCBLRJfoUXvk4dA3weC5P1x+DvF4CxnRZUjEiOBK5tWohhzDebFqAgXweOKlnGacCnKpClbrq1j4QQQgDrY7OF4bEj8GfgiCD9NOAlzEd2JrA/8DJwRqcFFSOOUcATwD5NCzJMmYH9aO5GdgWeASaWKOMeYJtqxKmNbu4jIYQQCZwOvIKFvQKLL7s0lmcpijsr6mcB9hZFb0/qoQfYo2khSvAi8OGC164H/LJCWeqih+7uIyFKo6gjYjgxCnsdezWwKjh3N2bwzAo+bwPsBdzccenESOMg4GFgddOCDFN2A+5rWogSrMDGSBEWAj+qUJa66PY+EkIIEWEfzD87uqJ/FHA25k7ydpCuV5miEzwCXNG0EMOUccDFNZZ/EvasOKTGOs7FQvjF2RIzwjfKuPZaYN86hKqQuvtIiBFJm/T4kiubE0uMEK4HfhI791Hg6eDv9sBhmM922YVIQmQxHttO+7Sa6zkIuAhYDryGPWuvdrx2BibjRZgrwtHADcCvsDdCr2JvhI5i6L39XIDd02l8Gbgdu/dXYff8CuCzWFvzuAbT5ZYJaVXp7bigjuiGNAcE168Bjkm5bizWrrwNkIrI1kN+rOh3cuoNyeujdkYdafaCT78W7Zsy91RIN9xbPZTv60MjeY9OSC/a9naGTHm2ZB26j5YJns+XOnwHXwW+lnD+jRrqEiJkA+xLKr5l8XnA+fRHfngY2BQ4FbiyY9KJkcam2EP81Zrr+Qz2BucNbHHdrOzsAzgAk/F7wMHAZcBzwJ3Ytt4zgAOxqBELgzxDZVOOfbEvuzROBB4AbgV+B0wG5gK9wLHB/09nXP8vwFkk+0FXpbdwbGyGzWxPwNyMlgRy7wd8I+G6PYCfAX/KkJ+Csj0IfC6lvHmY290tOfWG5PUR+NsLPv1atG/K3FMh3XBvle3rjbE3Fm8AU1LylL0/itiSdeg+WiaUf76Uoh0cQnSaU4DXGXzDvwgcHzt3KrbRgxB1sSv28D6s5noWAFtgLlIt/GbfbgFewEJg7oUZdvEZng2xL6c1wN+WF9eb0SRPCH0957q0aB5nY225tIRMVelt/yA9aafI24E/kNyOc0mf7Y5SdZ/eG1yzf+x80T5q428v+PRr0faXuadCOnVv9QTXtwpen0ZaX4eMAm4DnsQms9JmtIu2vU1xW7IO3UfLhHqfL7m0kaEtOk8YRi1p9qcPm5VYhIX3+xvg99jubELUxTw6b5y2cDcK1sFmRP/NIe9pQbkX5WWsmOnYgr8jYuc3x35YF2E21pZbM/IsCPKcl5BWpd72DtKXJKSdGKQtSkh7hGz/bRd8+3T7IP8zDNxop0wftanOXnDp1yiu7W/hb2h38t7qoXpDO62vo3wSW/e0JzaLm2ZoZ5HV9jbFxkYduvcpM3Ec1uE6MgHz29kE+0X+EHAX7n5dQvjSwmYgDk1IOwHbsOZSzL3kOcwgP6tTwokRSRj1Ju2VatMsxvzIb3DI+3bwt9PRU7bFXCoWMzBE52L6N6TyZb/g70MZeXYK/j6QkFal3sKxsSoh7Ubgq5i80bZuhn3pP+tQfxnZ4hwb/L2Sgd/lZfuoKnvBpV+j1Dmmu+HeyiKtr0O2Br4EXIj11V4F68lre5GxUYfufcr0HYeFaJPsvP5rYH6dFQshxBBic+zZd0IH62zhPvt2PebrmLdhylhsXcMamolysQXmqzkucu5yj+tPxmbcLsAWt63BtjdfP+Oafw/ybZWQVqXeDg/S35+S/gsG+3keT/lJAt8+nYRt8rWa5K3Ui/ZRm+L2QpF+DfFpfwv/Ge1O3ls9VDujndfXY4H7gcfp36uiF/8Z7by2tyk2NurQfVaZZcZhYT6L/bqZAawFbIfdcH8G3mRg2DUhhBiujMVmTD7TwTpbuBkFE7H1DNc7lHl+UGbRGeQqeBz4QPD/ZPzcvlYy8Iv6FgZG+UjiMUw/o2Lnq9bbCUGe6Snpoe/rjpFzP8L8/8vg26dHBPmzNvkq0kdl7IUi/Rri0/4WfoZ2p++tHqo1tPP6+ixsRnn3yLle/A3tvLYXGRt16D6vzELjsE3yr4i0w3XwhY1ymXqvSwYhhEijTfXPnRXYGoFO1dlyzLdfkC8vRvQngnyPAevm5IX6nt1fwWaMwFb/L3S8LsoMbH3G45jbxU4p+SZjhsTyhLSq9XYh8FRG+vygnDMjsv2GwT8AfPDtU7Ct3tfQ/1o8iSr6KMTHXnDt1xDf9rfwG6t13Vvgf3/1OZYbJauvd8Nmus+Nne/Fz9Au0vaQrLFRh+5dy8wch3Ef7SexLYNdcfUTuxz4Z8xxPo+6ZBBCiDTqeO7ciS1462SdLhwIvEX2bM7xmCH4KDZT+ZJDuXW15yYsgsWJmOFzqkcdIc9jX84PYAunv4XNksWZjUUoSPLPrlpvO2FjJI17sNf4i7GZxL2BO7Av/iIU6dNtsXCCz5C9m24VfRTiYy+49isUa78vdd1bYKHupsXOzcF+2Cxl8OLBBx3LDcnq67GYbp8AzvAsN0rZPsgaG3Xo3qVM8BuHtTEVezj4PISrwOfXnw4dOob30WnmYu4jk/IyVkQLa2fW7NsYLExVVnzcfwrKeRhbQNw0Y4FXMJ/pKsJmrcDa966EtOODtJ7Y+ar1NhrbDCXPP/Qa7HX5htguo0W3bC/apxcG1/Xm5Kuyj4raC1n9WrT9LfLvqZAm7q2eoLxWBWVl9fU03J+zSbGvoZq2p42NOnTvUmYSWeOwVvYNKn600xULIUSD3EfnQvy1yDcKwtB1x6akfzpIX0EDXxQZ/AfwbdLl9uF5rI1JvtFXBWk7xM5Xrbe9sZ3q0sKnhRwSlHs05mayjkPZZWULmYjN+KUtjItTVR8VtRfS+rXMmG7hbmg3cW/1UI2hndfXk7ANXpKOBwIZlgefP5JwfVVtTxsbdeg+r8w0sp4vpdka8yGLMxPbXWsN9W9HLIQQQ4k9yV5EViUt8o2Cf8V8kJMW7JwRXH8//r6TdXMYNrP7Hoe8W2IzX3FG07+hxD0p1z6IhduLu1VWrbdrgCMd8k3H3or8EtvExpcyfXpYcO2NHvld+6iIvVCkX8uO6RbuhnYT91YP1Rjavn0dpZf+H4NJ+La9yNioQ/dpZXqPwyrjaH8E8525C1uw8TrwXizg/kTM5+f8CusTw5ep2Li5pmlBhCjJXdgryy1I3s67LEvo3/Bkw+Dv7vQvhHoBC0EFtohuCbbr2/Oxco6gP6LAcmzBUJw2xRZYVcHN2GzUMw55PwScA9yNzQK/iH1ZzsfCLq4keWfFCcA2mLEdja1btd7+AttwZmlC3jgvAz/GfrD5umSU7dNwJu8Kx/p8+qiIveDbr0Xb73NPhXTzvQX+fe1Kkbb7jo06dJ9VZtHnSyXMB76Dxf58BfsV/ntsh5zDKbdSWowsDqZ5f14dw+9oivUxl4Q6noG9ZLe5Hcm7S3DupALlrAGWVS69HzMd820HXIwZzC9gRvOrwE+xdqbNau2MtTMeA7pqvX0LMxxcOTkoZ0uPa4rKFrJ1kP40+e4tUWY65puPv73g26+9FGt/3nXthGuaurd6gutbBa+H4n0d0htcnzSjHab5tN13bNSh+6wyiz5fhBhSXAGs3bQQQlTILOCDDcvwRezLY7OG5eg2qtTbPMz304dZWCQDMXTRvdUcdehe/SmGNaOwndmEGG40/VbvMfxDfolq9VZ0DIyuqH5RD7q3mqMO3as/RdcyF7gM22Vp/5Q8u2E+rUIIIYQQQghPpmMxO5M4C1s4JoQQQgghuog5DI0NGEYCaf6oh2KLBuanpH+nHnEyaXqRnsshhBBCCDFk2YDBIXlGAk0Zdrtg0UOSGAt8N+H8RigEpBBCCCFE13EBQ2uns05wEMmB3zvF5cBakc+LsCDwV5G8W97RwF4dkCtK0zoSQgghhOhqNgaua1qIBmh6UeFB+L1FWAqMq0mWNJrWkRBCCCGGKSMlZNDB2K5AI4mpWLD3JrkdOMQx73hs+9636xNnEENBR0IIIYQQXc2t2EYBI4m/o9zCz0uAGyqQow28O/J5R+C4hHz7YLtcdZKyOhJCCCGEGPG8jC20K8OewH8Bv8UWC/Zk5L0c+BpwKhZh4zVsC9Ebse07O8EnS14/HZgSO1ekXXdgvtlg/tcPAb9KyHcB6UavS31tkhd1/jClTEjWUW9CGStjeY4L2vFacNxLfxt9ZPYZU9Cvf9fyq6CNn15PDdIvTjifJW9vQh1xvYc0oQchhBDCm5HgOjIemIZ9EZdhCvAIZpytysg3CtuM5ftAC7gU2AMzMlcDtwHrlpQljynA67FzLsZhlJeBNyKfi7brdfoN6DuADwAzga1j+TYAfpcii0t9u2Az5+GxE2aspfnmJ+ko5PFYWdvH0p8BPh3U8f6gXd8HdvCU2XVMwUD9u5afRh9m2Lrgo9e5wLHYOIvjIm+e3qFaPQghhBCiJO/GfH+r5A3SZx93BV7EQtjFmQK8A+xXsTzvBbaNfD6IwTP4BwALgfcBWwJnY/7QOzCY92DG1KzIuaLtuhr4VOzcXbFzs4AzE65Nw0WPp2P+15OCzy46AjNAH/GQJeQl4GMZ6XkyZ40pyNa/S/lR+nA3tOPE9RoyFXgSWAAsY/CMdpy4vL246b1KPQghhBC1MhJmtN/EZsEmdKi+Jdhr9dUJaWtjOn+5wvrGYUb0CZFzGwHPxvL9ALgFc9t4AjOYXgd2TyhzNqa3JyLnirZrIvCH2LmbgMWRz4vIdvHwqQ+sv4/CjPxVuOsoZPMg7Sng2uBzGmOAj2IG3o9LyJxHlv6rKN+FuF6jXIHFRr/TsawkeV30PhT0IIQQQogIf6TaGNpZs4//CxyYknYdsAIzzqrm3qDcScAxOXlD4/Atkl/Pnw7cFztXtF3/zeCY2dtghtL04PPVmBHnSp4e98Fm5GfHzrvoaCHwYWymf29sdnYlsF4s3/bYOFiNzfBmueG4yJw3o52lf5fyo/RRbEY7Ta/HAD+jPzTjMvJntOPyuuq9Sj0IIYQQogIeZfACqS+QvztiK6W8NKPofdhMX9IGKF/FZuvSZkfLyAPwZey1/QHAJil5XI3D67AFZyFl2vUggw0zMDeDQ4B1MB9bV/LqA7ge+EnCeRcdxZmC+Y6fFDs/HtPLzsA5wAukL8JzkTnL0M7Sv0v5pwXlh8fb2I+s6DmXqDxJet0KW4S4VeTcMrINbRd9JOm9rB6EEEIIUQMXAH8fO/cuzDc461iLZNKMopMxt4ik+p9joM9znDLygC1au4SB7hFxXI3DJ4CPRz4Xbdc44Dckz1ZfCFyDxThfkiGzT31giyrfInnG2kVHSdwJXJaT5zbgyoTzLjJDtqGdpn/X8tfF+j08/hPboTN6Lu5zHSdNrz3Yj8DVkWMNti5iNYNdtlz1AYP1XlYPQgghhKiBBZhhURVpRtFybBvxKBdir8DjUTbq4D4s6oMrScbhZGwx2dzIuaLt2gX4RkraB7EFhFcyOIxgEq56PAXzPU8r01dHEzEDLm+x5h2YC0wUn77PMrST9O9bfpQ+/F1H0vQ6DfuxFj1+iv2I2o6BP7J85E3Se9V6EEIIIURFfI9yfptTgDnB8SZmAMyh3wVhfeyV/IzINZdgofT2AjaMHC6GZRHOw++1eZJxuDtmaIez52XadS6wRUrd44MybnaQ07W+UdhsfJpxD/k6Oh+YD2wG7IbNoL4GbBrJ8yXM1WIm5o5zDjaDu9BT5rwxBcn6dy0/jT78DG0XvUZZxmDXkTx58/Rehx6EEEIIURF7Ym4KRWmR7DfdF6T/A4OjTqT5WveWkCOLcRlpLsYhmMvILyKfi7ZrKvD5HHm/C3wiJ49rfWBvLtZgIeDSyNIRWLSLZzE3id9ibhbbxPL0YS4xf8L8iG8D9i0gcyslT18kT5L+XctPo88xX4iLXqMsY7ChnSdvnt7r0IMQQgghKuRwLPxXHfwAe70+VOkj3zhMomi7jiTf73ceFrNbpDPUx1WnkB6EEEKILmBiTeWeAmxcU9lNUrRdeUa2cGO4jitfpAchhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghRjD/D9Kofrj/ROuvAAAAAElFTkSuQmCC\n",
            "text/latex": "$\\displaystyle -5 - \\frac{78}{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{27 \\sqrt{5321}}{2} + \\frac{7425}{2}}} - \\frac{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{27 \\sqrt{5321}}{2} + \\frac{7425}{2}}}{3}$",
            "text/plain": [
              "                                                           _________________\n",
              "                                          ⎛  1   √3⋅ⅈ⎞    ╱ 27⋅√5321   7425 \n",
              "                                          ⎜- ─ - ────⎟⋅3 ╱  ──────── + ──── \n",
              "                     78                   ⎝  2    2  ⎠ ╲╱      2        2   \n",
              "-5 - ────────────────────────────────── - ──────────────────────────────────\n",
              "                      _________________                   3                 \n",
              "     ⎛  1   √3⋅ⅈ⎞    ╱ 27⋅√5321   7425                                      \n",
              "     ⎜- ─ - ────⎟⋅3 ╱  ──────── + ────                                      \n",
              "     ⎝  2    2  ⎠ ╲╱      2        2                                        "
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RYM8N_gQSsie"
      },
      "source": [
        "x,y,z=sp.symbols('x,y,z')\n",
        "eq1 = sp.Eq(x+y+z,0)\n",
        "eq2 = sp.Eq(2*x-y-z,10)\n",
        "eq3 = sp.Eq(y+2*z,5)"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "5PQJ-x40BzBW",
        "outputId": "08dca9c9-20da-40bf-c4df-c215fade8fa3"
      },
      "source": [
        "eq1"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle x + y + z = 0$",
            "text/plain": [
              "x + y + z = 0"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "WnZv_wtxB17b",
        "outputId": "4d7b822f-9e66-4ab9-8b2f-0c3b9054a7de"
      },
      "source": [
        "eq2"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 x - y - z = 10$",
            "text/plain": [
              "2⋅x - y - z = 10"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "duN7T3CuB2QL",
        "outputId": "9967af40-2d25-4db5-d4f5-ad3fc2f016ee"
      },
      "source": [
        "eq3"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle y + 2 z = 5$",
            "text/plain": [
              "y + 2⋅z = 5"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "FELBn1pMBw2M",
        "outputId": "f79b1eed-83cf-4586-e265-c4d44b1b9353"
      },
      "source": [
        "sp.solve([eq1,eq2,eq3],[x,y,z])"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left\\{ x : \\frac{10}{3}, \\  y : - \\frac{35}{3}, \\  z : \\frac{25}{3}\\right\\}$",
            "text/plain": [
              "{x: 10/3, y: -35/3, z: 25/3}"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6qYR9lh1UWvJ",
        "outputId": "2039e8d1-a86f-4ac1-cc54-1c3e3db2e64c"
      },
      "source": [
        "A = sp.Matrix([[1,2,5],[3,4,6],[-1,0,3]])\n",
        "sp.pprint(A)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "⎡1   2  5⎤\n",
            "⎢        ⎥\n",
            "⎢3   4  6⎥\n",
            "⎢        ⎥\n",
            "⎣-1  0  3⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GoGaxP11U2l2",
        "outputId": "54ae53e8-1881-417e-f772-67a831872cf0"
      },
      "source": [
        "b = sp.Matrix([1,0,-2])\n",
        "sp.pprint(b)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "⎡1 ⎤\n",
            "⎢  ⎥\n",
            "⎢0 ⎥\n",
            "⎢  ⎥\n",
            "⎣-2⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DSBlzJ90U748",
        "outputId": "5b49d4ae-e3d1-45e9-df3c-0e8b3b0b6319"
      },
      "source": [
        "sp.pprint(A.inv()*b)\n",
        "sp.pprint(A.LUsolve(b))"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "⎡ 14  ⎤\n",
            "⎢     ⎥\n",
            "⎢-33/2⎥\n",
            "⎢     ⎥\n",
            "⎣  4  ⎦\n",
            "⎡ 14  ⎤\n",
            "⎢     ⎥\n",
            "⎢-33/2⎥\n",
            "⎢     ⎥\n",
            "⎣  4  ⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C0yku3A6VOb7",
        "outputId": "c376b1ac-85b0-4e76-8411-5b7253b85e9a"
      },
      "source": [
        "sp.pprint(A)\n",
        "sp.pprint(A[1:2,1:2])\n",
        "sp.pprint(A[:,1:2])"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "⎡1   2  5⎤\n",
            "⎢        ⎥\n",
            "⎢3   4  6⎥\n",
            "⎢        ⎥\n",
            "⎣-1  0  3⎦\n",
            "[4]\n",
            "⎡2⎤\n",
            "⎢ ⎥\n",
            "⎢4⎥\n",
            "⎢ ⎥\n",
            "⎣0⎦\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D47hKRi_MJZy"
      },
      "source": [
        "# **Visualização de Dados: Candle Sticks**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fYvPijlbVuVc"
      },
      "source": [
        "**Ver o pacote:** https://github.com/matplotlib/mplfinance\n",
        "\n",
        "**Sugestão de leitura:** https://www.infomoney.com.br/onde-investir/confuso-entre-os-candlestick-conheca-os-principais-padroes-de-reversao/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I63hGKYqMQr-",
        "outputId": "8a5da9f4-46ab-4f50-bcd6-3a8be43303c1"
      },
      "source": [
        "pip install mplfinance"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: mplfinance in /usr/local/lib/python3.7/dist-packages (0.12.7a17)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from mplfinance) (3.2.2)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from mplfinance) (1.1.5)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->mplfinance) (3.0.6)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->mplfinance) (0.11.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->mplfinance) (2.8.2)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->mplfinance) (1.3.2)\n",
            "Requirement already satisfied: numpy>=1.11 in /usr/local/lib/python3.7/dist-packages (from matplotlib->mplfinance) (1.19.5)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.1->matplotlib->mplfinance) (1.15.0)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas->mplfinance) (2018.9)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zi3ZowiWOv1I",
        "outputId": "12d0864f-cce3-43e4-b3fd-3070e79ec35d"
      },
      "source": [
        "!pip install yfinance --upgrade --no-cache-dir"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: yfinance in /usr/local/lib/python3.7/dist-packages (0.1.67)\n",
            "Requirement already satisfied: pandas>=0.24 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.1.5)\n",
            "Requirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.7/dist-packages (from yfinance) (1.19.5)\n",
            "Requirement already satisfied: lxml>=4.5.1 in /usr/local/lib/python3.7/dist-packages (from yfinance) (4.6.4)\n",
            "Requirement already satisfied: multitasking>=0.0.7 in /usr/local/lib/python3.7/dist-packages (from yfinance) (0.0.10)\n",
            "Requirement already satisfied: requests>=2.20 in /usr/local/lib/python3.7/dist-packages (from yfinance) (2.23.0)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24->yfinance) (2018.9)\n",
            "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas>=0.24->yfinance) (2.8.2)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas>=0.24->yfinance) (1.15.0)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.7/dist-packages (from requests>=2.20->yfinance) (2.10)\n",
            "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /usr/local/lib/python3.7/dist-packages (from requests>=2.20->yfinance) (1.24.3)\n",
            "Requirement already satisfied: chardet<4,>=3.0.2 in /usr/local/lib/python3.7/dist-packages (from requests>=2.20->yfinance) (3.0.4)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.7/dist-packages (from requests>=2.20->yfinance) (2021.10.8)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tPy0SLCjMbF-"
      },
      "source": [
        "import pandas as pd\n",
        "import yfinance as yf #Instalando e importando a API no código\n",
        "import matplotlib.pyplot as plt\n",
        "import mplfinance as mpf"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jf-4VCqubP5o",
        "outputId": "a065397a-0376-4bdf-902a-4141cfa01e0c"
      },
      "source": [
        "codigo = ['BTC-USD']\n",
        "#codigo = ['ABUD34.SA']\n",
        "df = yf.download(codigo[0], \n",
        "                 start='2021-09-01', \n",
        "                 end='2021-11-01',\n",
        "                 group_by=\"ticker\"); # \";\" serve para não exibir os dados"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\r[*********************100%***********************]  1 of 1 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "id": "JNEKNPQCbeMf",
        "outputId": "f0c124a6-1448-439e-f272-4f7cc4143927"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2021-09-01</th>\n",
              "      <td>47099.773438</td>\n",
              "      <td>49111.089844</td>\n",
              "      <td>46562.437500</td>\n",
              "      <td>48847.027344</td>\n",
              "      <td>48847.027344</td>\n",
              "      <td>39139399125</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-02</th>\n",
              "      <td>48807.847656</td>\n",
              "      <td>50343.421875</td>\n",
              "      <td>48652.320312</td>\n",
              "      <td>49327.722656</td>\n",
              "      <td>49327.722656</td>\n",
              "      <td>39508070319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-03</th>\n",
              "      <td>49288.250000</td>\n",
              "      <td>50982.273438</td>\n",
              "      <td>48386.085938</td>\n",
              "      <td>50025.375000</td>\n",
              "      <td>50025.375000</td>\n",
              "      <td>43206179619</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-04</th>\n",
              "      <td>50009.324219</td>\n",
              "      <td>50545.582031</td>\n",
              "      <td>49548.781250</td>\n",
              "      <td>49944.625000</td>\n",
              "      <td>49944.625000</td>\n",
              "      <td>37471327794</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-05</th>\n",
              "      <td>49937.859375</td>\n",
              "      <td>51868.679688</td>\n",
              "      <td>49538.597656</td>\n",
              "      <td>51753.410156</td>\n",
              "      <td>51753.410156</td>\n",
              "      <td>30322676319</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    Open          High  ...     Adj Close       Volume\n",
              "Date                                    ...                           \n",
              "2021-09-01  47099.773438  49111.089844  ...  48847.027344  39139399125\n",
              "2021-09-02  48807.847656  50343.421875  ...  49327.722656  39508070319\n",
              "2021-09-03  49288.250000  50982.273438  ...  50025.375000  43206179619\n",
              "2021-09-04  50009.324219  50545.582031  ...  49944.625000  37471327794\n",
              "2021-09-05  49937.859375  51868.679688  ...  51753.410156  30322676319\n",
              "\n",
              "[5 rows x 6 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LLL7nd1pMxzY",
        "outputId": "ac8ecff3-3433-47f9-ad3a-e45ca3fae5e0"
      },
      "source": [
        "codigo = ['PETR4.SA']\n",
        "#codigo = ['ABUD34.SA']\n",
        "df = yf.download(codigo[0], \n",
        "                 start='2021-09-01', \n",
        "                 end='2021-11-01',\n",
        "                 group_by=\"ticker\"); # \";\" serve para não exibir os dados"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\r[*********************100%***********************]  1 of 1 completed\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 237
        },
        "id": "v6Bv6teXPVv4",
        "outputId": "2a9e7cb6-c179-4200-ca66-b5d0090ae9f1"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Open</th>\n",
              "      <th>High</th>\n",
              "      <th>Low</th>\n",
              "      <th>Close</th>\n",
              "      <th>Adj Close</th>\n",
              "      <th>Volume</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Date</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>2021-09-01</th>\n",
              "      <td>27.320000</td>\n",
              "      <td>27.340000</td>\n",
              "      <td>26.330000</td>\n",
              "      <td>27.040001</td>\n",
              "      <td>27.040001</td>\n",
              "      <td>69430400</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-02</th>\n",
              "      <td>27.000000</td>\n",
              "      <td>27.350000</td>\n",
              "      <td>26.459999</td>\n",
              "      <td>26.600000</td>\n",
              "      <td>26.600000</td>\n",
              "      <td>56052000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-03</th>\n",
              "      <td>26.650000</td>\n",
              "      <td>26.780001</td>\n",
              "      <td>26.100000</td>\n",
              "      <td>26.330000</td>\n",
              "      <td>26.330000</td>\n",
              "      <td>58182700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-06</th>\n",
              "      <td>26.209999</td>\n",
              "      <td>26.709999</td>\n",
              "      <td>26.150000</td>\n",
              "      <td>26.459999</td>\n",
              "      <td>26.459999</td>\n",
              "      <td>26770700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2021-09-08</th>\n",
              "      <td>26.290001</td>\n",
              "      <td>26.350000</td>\n",
              "      <td>24.790001</td>\n",
              "      <td>24.969999</td>\n",
              "      <td>24.969999</td>\n",
              "      <td>80378400</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                 Open       High        Low      Close  Adj Close    Volume\n",
              "Date                                                                       \n",
              "2021-09-01  27.320000  27.340000  26.330000  27.040001  27.040001  69430400\n",
              "2021-09-02  27.000000  27.350000  26.459999  26.600000  26.600000  56052000\n",
              "2021-09-03  26.650000  26.780001  26.100000  26.330000  26.330000  58182700\n",
              "2021-09-06  26.209999  26.709999  26.150000  26.459999  26.459999  26770700\n",
              "2021-09-08  26.290001  26.350000  24.790001  24.969999  24.969999  80378400"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "-64-ZWpPPbo_",
        "outputId": "27e2053c-b300-423d-830a-2c5a0cce791c"
      },
      "source": [
        "plt.plot(df[\"Close\"])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 493
        },
        "id": "RSlBZ88IQXM3",
        "outputId": "099b72ee-fe65-4eae-9b6a-928f38f3f8d4"
      },
      "source": [
        "mpf.plot(df, type=\"candle\", volume=True, style=\"yahoo\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 800x575 with 4 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    }
  ]
}