Laba_7_2.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xPMLC3rBNfst"
      },
      "source": [
        "# Лабораторная работа 7. Библиотеки. Научный Python 1.\n",
        "# Линейные и нелинейные уравнения."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mQ3CZ6EjNfsz"
      },
      "source": [
        "Загрузим необходимые для работы библиотеки: "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "l38hK0yJNfs1"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import sympy as sm\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy import linalg\n",
        "from scipy.optimize import root # описание библиотеки: https://docs.scipy.org/doc/scipy/reference/optimize.html\n",
        "from scipy.optimize import minimize, rosen, rosen_der\n",
        "import math\n",
        "import time\n",
        "import pylab\n",
        "from sympy import pi, symbols, expand, collect, factor, cancel, together, simplify, apart, together, degree, limit, oo, diff\n",
        "sm.init_printing()\n",
        "%matplotlib notebook"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dBbFza2kNfs2"
      },
      "source": [
        "# 1. Линейная алгебра"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vraqU9VYNfs3"
      },
      "source": [
        "Массивы бывают 1-мерные (вектора) 2-мерные (матрицы) и многомерные.\n",
        "\n",
        "Все элементы массива должны принадлежать к одному типу данных.\n",
        "\n",
        "Создадим одномерный массив из списка при помощи функции array:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_CEC52VkNfs3",
        "outputId": "8684250f-30a1-47de-cd16-6c26f3751381"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "np.array([1, 2, 3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qj_vy_2BNfs4"
      },
      "source": [
        "Создадим двумерный массив из списка при помощи функции array. Обратите внимание на скобки."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SSsHwDTCNfs5",
        "outputId": "b5a3ad25-6134-47c7-cf28-292683712cf4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0xTEY64YNfs5"
      },
      "source": [
        "Для создания специфических массивов надо использовать специальные методы. Нарпимер, zeros создаёт массив нулей."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3BFoodQlNfs6",
        "outputId": "2ab9b836-a28b-45f2-f998-1a88635766b1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0., 0.],\n",
              "       [0., 0., 0., 0.],\n",
              "       [0., 0., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "np.zeros((3,4), order='F')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GN4vNdtiRobD",
        "outputId": "c8590743-5758-42c7-de63-c3c3519aa0d1"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([(0, 0), (0, 0)], dtype=[('x', '<i4'), ('y', '<i4')])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.zeros((2,3))# AAAAAAAAA"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xatA58VBSEX9",
        "outputId": "25ac96d0-5f9a-4e67-c5f5-e978364d20ac"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0.],\n",
              "       [0., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NxVu_qQbNfs7"
      },
      "source": [
        "Для создания единично матрицы используется функция eye."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uedFwJtxNfs9",
        "outputId": "1ba9518e-a24b-4a8e-f86b-db56fb740734"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0., 0., 0.],\n",
              "       [0., 1., 0., 0., 0.],\n",
              "       [0., 0., 1., 0., 0.],\n",
              "       [0., 0., 0., 1., 0.],\n",
              "       [0., 0., 0., 0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "np.eye(5)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.eye(3, k= -1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LX2e-BmyTzFL",
        "outputId": "5a5234f8-e0d9-4673-93e1-0a8e1a484a03"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0., 0., 0.],\n",
              "       [1., 0., 0.],\n",
              "       [0., 1., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.empty([2, 3], dtype=int)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eEiplW-cVhlz",
        "outputId": "7bd30715-8988-4cd9-97b8-fbeaff40dd95"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 0, 0],\n",
              "       [0, 0, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "57jkGOj2Nfs-"
      },
      "source": [
        "Для получения случайных чисел из нормального распределения используем функцию randn() из модуля random. Для создания матрицы случайных чисел надо передать функции два числа задающих диапазон случайных значений [10, 100] и размерность матрицы (3, 3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GIG9Z-3qNfs_",
        "outputId": "1fb79b6f-c2c2-4f8d-d366-ace8a0e30eae"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[32.42747063, 97.91476617, 62.81703973, 63.53473865, 79.48898528],\n",
              "       [61.12266378, 10.4775815 , 40.88528555, 11.63184654, 40.88720813],\n",
              "       [67.12724847, 61.60038478, 54.15334353, 95.38147019, 32.02512245]])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "arr = np.random.uniform(10, 100, (3, 5))\n",
        "arr"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NbsYAac8Nfs_"
      },
      "source": [
        "К эллементам массива можно обращаться по индексу "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bXRobOOZNftA",
        "outputId": "8d22ad15-1750-475c-9c3e-71281eccca2c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([97.91476617, 63.53473865])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "arr[0,1:5:2]  #  arr[номер строки , от столбца : до столбца : шаг]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-lnjIgkRNftA"
      },
      "source": [
        "Чтобы вывести все элементы строки или столбца можно написать [:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AvjXuIi6NftB",
        "outputId": "ea9cdbb5-d520-49c0-f805-6ce3ebc24d51"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[98.91476617, 64.53473865],\n",
              "       [11.4775815 , 12.63184654],\n",
              "       [62.60038478, 96.38147019]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "arr[:,1:5:2]+1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_I0pIGnkNftC"
      },
      "source": [
        "К массиву можно применять арифметические и логические операции (при этом эта операция будет применина к каждому эллементу):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z9zutJwXNftC",
        "outputId": "98847c85-6bb9-4d5e-8c31-34735a2779f7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True, False, False, False, False],\n",
              "       [False,  True,  True,  True,  True],\n",
              "       [False, False, False, False,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "arr < 50"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "26AMcfQ1NftD"
      },
      "source": [
        "# Основные операции над матрицами и решение СЛАУ"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TDYK7CDUNftD",
        "outputId": "ed919954-b836-4c02-e85e-362127de0949"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = \n",
            " [5.6 6.1]\n"
          ]
        }
      ],
      "source": [
        "# определение матрицы\n",
        "A = np.array([[1, 2], [3, 4]])\n",
        "x0 = [5.6, 6.1]\n",
        "b = np.dot(A,x0)\n",
        "\n",
        "\n",
        "# вычисление определителя матрицы\n",
        "detA = linalg.det(A)\n",
        "\n",
        "# вычисление ранга матрицы\n",
        "rankA = np.linalg.matrix_rank(A)\n",
        "\n",
        "# вычисление обратной матрицы\n",
        "B = linalg.inv(A)\n",
        "\n",
        "# вычисление суммы матриц\n",
        "C = A + B\n",
        "\n",
        "# вычисление произведения матриц\n",
        "D = np.dot(A,B)\n",
        "\n",
        "# решение СЛАУ A*x=b с помощью обратной матрицы \n",
        "x = np.dot(linalg.inv(A),b) \n",
        "print('x = \\n', x)\n",
        "\n",
        "# проверка решения\n",
        "errx = np.dot(A,x) - b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GeZ6bZBfNftE"
      },
      "source": [
        "# Упражнение 1. Норма в норме."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xXnTr6cyNftF"
      },
      "source": [
        "Напишите программу для вычисления норм вещественных матриц:\n",
        "\n",
        "$$ \\|A\\|_1 = \\underset{1 \\leq j \\leq n}{max}\\overset{n}{\\underset{i=1}{\\sum}}|a_{ij}|, \\quad\n",
        "\\|A\\|_E = \\left( \\overset{n}{\\underset{i,j=1}{\\sum}}|a_{ij}|^2 \\right)^{1/2}, \\quad\n",
        "\\|A\\|_\\infty = \\underset{1 \\leq i \\leq n}{max}\\overset{n}{\\underset{j=1}{\\sum}}|a_{ij}|. $$\n",
        "\n",
        "На основе экспериментов со случайными матрицами при различных $n$ убедитесь в выполнении неравенств \n",
        "\n",
        "\n",
        "$$ \\frac{1}{\\sqrt{n}} \\|A\\|_\\alpha \\leq \\|A\\|_E \\leq \\sqrt{n}\\|A\\|_\\alpha, \\quad \\alpha = 1, \\infty.$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "KQW5gyzcNftF",
        "outputId": "d7a820ac-35ea-4ae4-cb65-edf9b0f72901"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(170.54805538141494, 231.5618866547178, 336.18300045506015)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( 170.548055381415, \\  231.561886654718, \\  336.18300045506\\right)$"
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "from numpy import linalg as LA\n",
        "\n",
        "LA.norm(arr, 1),LA.norm(arr, 'fro'),LA.norm(arr, np.inf) #https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JdEkHMJnNftF"
      },
      "source": [
        "# 2. Символьные вычисления и исследование функций."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "Wl7Cx12XNftF"
      },
      "outputs": [],
      "source": [
        "from sympy import pi, symbols, expand, collect, factor, cancel, together, simplify, apart, together, degree, limit, oo, diff"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XWpFcwUINftG"
      },
      "source": [
        "# 2.1. Число $\\pi$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tJRyEDqxNftG",
        "outputId": "0baea477-cb36-4ab8-b470-7fda6c5a81a2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Выведем 70 знаков числа пи: 3.141592653589793238462643383279502884197169399375105820974944592307816\n"
          ]
        }
      ],
      "source": [
        "# Выыедем заданное колличество знаков числа pi\n",
        "npi=70;\n",
        "print('\\n Выведем %i знаков числа пи:' %npi ,pi.n(npi));"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OcGJ-wX8NftG"
      },
      "source": [
        "# 2.2. Многочлены и рациональные функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "-X652mUYNftH"
      },
      "outputs": [],
      "source": [
        "# Создадим несколько символьных переменных\n",
        "x,y,z,a,b=symbols('x y z a b')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ror3vsy2NftH"
      },
      "source": [
        "Проверим фомулу бинома Ньютона, пусть $x=(a+b)^n$\n",
        "\n",
        "SymPy умеет раскрывать скобки, для этого используется функция expand"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "Lriavdg5NftH",
        "outputId": "05cb67e5-a5a2-4921-8c17-b59c67619a3c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(a + b)**6 = a**6 + 6*a**5*b + 15*a**4*b**2 + 20*a**3*b**3 + 15*a**2*b**4 + 6*a*b**5 + b**6\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 6      5         4  2       3  3       2  4        5    6\n",
              "a  + 6⋅a ⋅b + 15⋅a ⋅b  + 20⋅a ⋅b  + 15⋅a ⋅b  + 6⋅a⋅b  + b "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}$"
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "n=6\n",
        "x=(a+b)**n\n",
        "y=expand(x)\n",
        "print(x, '=', y)\n",
        "y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "id": "BFcwCBK5NftH",
        "outputId": "961fb8d7-1532-445d-dd0a-3a3196bb58b8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Полином имеет порядок 6 по переменной b\n",
            "Члены с этой переменной имеют вид:\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛ 6      5         4  2       3  3       2  4        5    6   6      5        \n",
              "⎝a  + 6⋅a ⋅b + 15⋅a ⋅b  + 20⋅a ⋅b  + 15⋅a ⋅b  + 6⋅a⋅b  + b , a  + 6⋅a ⋅b + 15⋅\n",
              "\n",
              " 4  2       3  3       2  4        5    6⎞\n",
              "a ⋅b  + 20⋅a ⋅b  + 15⋅a ⋅b  + 6⋅a⋅b  + b ⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}, \\  a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}\\right)$"
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "# определим степень многочлена  по b\n",
        "print ('Полином имеет порядок %i по переменной b' %(degree(y,b)))\n",
        "# и сгрупируем члены со степенями  b\n",
        "print('Члены с этой переменной имеют вид:')\n",
        "collect(y,b),  collect(y,a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "xSFUdaU9NftH",
        "outputId": "66ed9d8f-49e5-4f3b-923f-415868a377ce"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       6\n",
              "(a + b) "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left(a + b\\right)^{6}$"
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "# раскрытое вырожение можно свернуть обратно\n",
        "z=factor(y)\n",
        "z"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gSQAWy8mNftI"
      },
      "source": [
        "SymPy умеет сокращать символьное отношение, для этого используется функция cancel"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 77
        },
        "id": "TJYKPXtxNftI",
        "outputId": "ed1892fc-7cb7-4cf8-82f2-f0e180fe69e5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(a**3 - b**3)/(a**2 - b**2) = (a**2 + a*b + b**2)/(a + b)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛ 3    3   2          2⎞\n",
              "⎜a  - b   a  + a⋅b + b ⎟\n",
              "⎜───────, ─────────────⎟\n",
              "⎜ 2    2      a + b    ⎟\n",
              "⎝a  - b                ⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( \\frac{a^{3} - b^{3}}{a^{2} - b^{2}}, \\  \\frac{a^{2} + a b + b^{2}}{a + b}\\right)$"
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "x,y,z,a,b=symbols('x y z a b')\n",
        "x=(a**3-b**3)/(a**2-b**2)\n",
        "print(x,'=',cancel(x))\n",
        "x, cancel(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dlu0hieVNftI"
      },
      "source": [
        "Можно приводить дроби к общему знаменателю, для этого используется функция together"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "lSJjcDa8NftI",
        "outputId": "854c2af3-f2d5-4319-f9e7-21f7480e7144"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  x       y  \n",
              "───── + ─────\n",
              "x + y   x - y"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{x}{x + y} + \\frac{y}{x - y}$"
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "x,y,z,a,b=symbols('x y z a b')\n",
        "a=y/(x-y)+x/(x+y)\n",
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "K7htCuRmNftJ",
        "outputId": "265aea0b-e2b5-4722-bb41-e713f4285620"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "x⋅(x - y) + y⋅(x + y)\n",
              "─────────────────────\n",
              "   (x - y)⋅(x + y)   "
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAnCAYAAADJovy3AAAABHNCSVQICAgIfAhkiAAAA3ZJREFUeJzt2k/oZWMcx/HX/Ch/NvKzsJzFNCnmZ1KURN0sNGRhYWOlKBsljSmykIWNLBhDmSRHKTEp2TFZMhbs1KTYyNAgIgsMxuI5N+d37r3nnnvuc855Ls+7bvc+f7+f++mef7cPmUwLLsdZ7BtbSI0TeGTE+qn6QiRvnsGr62uJzg5+xGUj1U/VFyJ4cyl+ws2xFEXmEzy4wvwCT0ao24cvhTjapsx4s1X5fDd+x95K31F8iStxB87jw9qmy9bF4GscrvXt4DdcXbbfxT2R6q1SO3VfWOLNHuGX8XLZPoLvsL9sH8XJDuticAJv1Po+wAuV9iH8gUta7llod1Qtq92HL7G0TVnqzW04h8fwC26ojL2D1zqsi8FhfFFp3yVct66o9F0rHHltb7AK7cxdVrsPX2Jpm9LKm4/wJ26v9b+H4x3WVXmqFND0msxZd1M5to2LhC/7cG3O/nLOgQW1H8evldc54Sio9t3SoXYMX/rSNmXGmwtrE27FQeE0dbY29oPw2DKPpnVVnsPrDePw1Zy+TwUjrsd1gpEv1uZsl+/fL9j3JbxVaT+NM3i+0nemQ+0YvvSlbUqjNwfxM+7D28IvucoRfNZhXSw+xjHhlHnnnPH7hZudthTa3zk31e7Dl1japiz0Zi++wRNl+wD+tvu0u4O/7L5+tFkXi2fLvRcZWOCVFfYrtDe3qXYfvsTSVt1vxpttnDZ7nXoTp2p9p/z7PLjKuhjcK5zKrpkzdrFwdN24wn6F9uY21Sa+LzG1dfFmhkP4HBess0lHTpp//SKY/v5ItUnXFyJ685Ddf0r0yZbwZ8ej+Nbim6gHcNVItaek6Av9eNM7E+H6dVp4dPm/1F7GRLraMplMJpMGe8r386OqyGQym0uqMaSmCNImak6OVGNITRGkTdScFJsYz4qtudBzbCoGW8unrMS8GNIQESS6x7PG0hwlNpUK82JIQ0Sz6B7Piq25MHBsKgUWxZD6jmbRPZ4VW3NhhNjU2DTFkPqMZtE9nrWu5sFjUzGoR6/WZVEMqe9oFt3jWetqHjU2lQrzYkhDRbPoFs+KrbkwUGwqJeoxpCGjWXSLZ8XWXBggNpUi0xjS0NEsusezYmouJBabGopUY0hNEaSxNA8WmxqKFGNIyyJIQ2n+z8emhmJis2JIE5ulN5PJZDKZTCaTOv8AG1i1ECACU9MAAAAASUVORK5CYII=\n",
            "text/latex": "$\\displaystyle \\frac{x \\left(x - y\\right) + y \\left(x + y\\right)}{\\left(x - y\\right) \\left(x + y\\right)}$"
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "together(a)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VnSiEBL_NftJ"
      },
      "source": [
        "Можно попытаться переписать выражение в наиболее простом виде, для этого используется функция simplify"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "AJVoexcWNftJ",
        "outputId": "e7345d32-d7be-41a8-ccb9-74c75b5d0cef"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 2    2\n",
              "x  + y \n",
              "───────\n",
              " 2    2\n",
              "x  - y "
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAADMAAAAsCAYAAADIIYBkAAAABHNCSVQICAgIfAhkiAAAAhRJREFUaIHt2M+LTWEcx/HXHemSlaGw0GzYYPIrm4m6zWJKURYsJf4CTWpkIQsLO/m1kM3dSVLKSlKyGBYSirFg42dZKEK4GIvnqNMxM53nnDudy5x3Pd37POc+38/nPOd5OrcPc5SVuIUneIQ9/7L+CmxIvi/HaywqU7CX9B8Kq1UVf+n3FSy0GfPwsqyjqvX78RhDOX/fxrGyonn0009mN75hIDV2Cs+xLOk3cRUnMN5Fg394hdHM2CC+Yk2MfgP3cCHpH8I7rE5dvyh+ldsRcy4nGmlu4mwR/RF0cBgfsSV1bSt+4UGqDeao2Y4wMIpnqf4uvMeSovrj+IHtOQ1kOYJPqdbB98zYtmnmDmFSOBdN4cYOFvRhGJ/xE5sK1ujHqlS7gtOZsYXTzG0K53YEY3iK+UVMrMcHHEgMXC9SZAra4s7ZXZwRtvmOIoIDeIOjSX+dsD9bRYplaIu7mZOJdqHF7McEzmfGL+FOkYIZ2uJuZp9wZtd2QbtybuBc1SbK0Ce8mMfwFourtVOOlnBOJuT/m1RTU1OSRvI5WamLCqgDjS5SBxp5mLOBRrfJpZ830LiNvd33iHyBRi792Qo0Yuj5QCOGngs0jgsv4Zlaa5q5pQKNRqY/jGtYIDyV+3kLpViatJl4gS9TjDeFHbETG7FfWP1OrInZCjRi6elAI5aeDjRiqQONXqIONGpqamr+T34DFyix9i04owoAAAAASUVORK5CYII=\n",
            "text/latex": "$\\displaystyle \\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$"
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "simplify(a)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ykhWN7rjNftJ"
      },
      "source": [
        "Разложить на элементарные дроби по отношению к x "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "oB8iI3xqNftJ",
        "outputId": "631bf214-f4b7-486e-d415-b54a9dbce0be"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    y       y      \n",
              "- ───── + ───── + 1\n",
              "  x + y   x - y    "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle - \\frac{y}{x + y} + \\frac{y}{x - y} + 1$"
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "b=apart(a,x)\n",
        "b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HarI4WPJNftJ"
      },
      "source": [
        "т.к."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "n6kNzuN5NftK",
        "outputId": "a8e2e5f5-c9bf-4132-eb40-ac34dab617f2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-y⋅(x - y) + y⋅(x + y) + (x - y)⋅(x + y)\n",
              "────────────────────────────────────────\n",
              "            (x - y)⋅(x + y)             "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{- y \\left(x - y\\right) + y \\left(x + y\\right) + \\left(x - y\\right) \\left(x + y\\right)}{\\left(x - y\\right) \\left(x + y\\right)}$"
          },
          "metadata": {},
          "execution_count": 27
        }
      ],
      "source": [
        "together(b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "UcPcNBD_NftK",
        "outputId": "85b1aec0-c62e-446d-8013-0fa5f05677db"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 2    2\n",
              "x  + y \n",
              "───────\n",
              " 2    2\n",
              "x  - y "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$"
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "cancel(together(b))"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x=(a**3+a+2)/(a**3 + 1)\n",
        "expand(x) \n",
        "apart(x,a), together(apart(x,a))\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "id": "kSJcvJY8N6RR",
        "outputId": "c8fd5683-a63e-4163-b0c6-1e8ff30f131b"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛   4      2  2      4    ⎛ 4    2  2      4⎞⎞\n",
              "⎜2⋅x  - 2⋅x ⋅y  + 4⋅y   2⋅⎝x  - x ⋅y  + 2⋅y ⎠⎟\n",
              "⎜─────────────────────, ─────────────────────⎟\n",
              "⎜       4      4               4      4      ⎟\n",
              "⎝      x  + 3⋅y               x  + 3⋅y       ⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( \\frac{2 x^{4} - 2 x^{2} y^{2} + 4 y^{4}}{x^{4} + 3 y^{4}}, \\  \\frac{2 \\left(x^{4} - x^{2} y^{2} + 2 y^{4}\\right)}{x^{4} + 3 y^{4}}\\right)$"
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aV1Dv75INftK"
      },
      "source": [
        "# 2.3 Решение алгебраических уравнений"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "1gitJABXNftK"
      },
      "outputs": [],
      "source": [
        "a,b,c,d,e,f,x = symbols('a b c d e f x')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Av6RubENftK"
      },
      "source": [
        "Как известно, алгеброические уравнения до 4 степени включительно имеют решение в радикалах:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "id": "0a_pH-w9NftK",
        "outputId": "82ad4a7f-1d22-4e5a-9c92-fb9d5471187d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡        _____________   ⎛       _____________⎞ ⎤\n",
              "⎢       ╱           2    ⎜      ╱           2 ⎟ ⎥\n",
              "⎢-b + ╲╱  -4⋅a⋅c + b    -⎝b + ╲╱  -4⋅a⋅c + b  ⎠ ⎥\n",
              "⎢─────────────────────, ────────────────────────⎥\n",
              "⎣         2⋅a                     2⋅a           ⎦"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ \\frac{- b + \\sqrt{- 4 a c + b^{2}}}{2 a}, \\  - \\frac{b + \\sqrt{- 4 a c + b^{2}}}{2 a}\\right]$"
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "sm.solve(a*x**2+b*x+c,x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 149
        },
        "id": "_YUC0x1yNftL",
        "outputId": "d29a1bcb-801b-4aae-e7b2-7166fb64fb9d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                                                                             \n",
              "⎢                                                                             \n",
              "⎢                                                                             \n",
              "⎢                                                                             \n",
              "⎢                                                                             \n",
              "⎢                                                                             \n",
              "⎢                                                 2                           \n",
              "⎢                                          3⋅c   b                            \n",
              "⎢                                        - ─── + ──                           \n",
              "⎢                                           a     2                           \n",
              "⎢                                                a                            \n",
              "⎢- ───────────────────────────────────────────────────────────────────────────\n",
              "⎢               ______________________________________________________________\n",
              "⎢              ╱        ____________________________________________          \n",
              "⎢             ╱        ╱                 3                        2           \n",
              "⎢            ╱        ╱      ⎛         2⎞    ⎛                  3⎞            \n",
              "⎢           ╱        ╱       ⎜  3⋅c   b ⎟    ⎜27⋅d   9⋅b⋅c   2⋅b ⎟            \n",
              "⎢          ╱        ╱    - 4⋅⎜- ─── + ──⎟  + ⎜──── - ───── + ────⎟            \n",
              "⎢         ╱        ╱         ⎜   a     2⎟    ⎜ a        2      3 ⎟            \n",
              "⎢        ╱       ╲╱          ⎝        a ⎠    ⎝         a      a  ⎠     27⋅d   \n",
              "⎢  3⋅   ╱        ─────────────────────────────────────────────────── + ──── - \n",
              "⎢    3 ╱                                  2                            2⋅a    \n",
              "⎣    ╲╱                                                                       \n",
              "\n",
              "                         _____________________________________________________\n",
              "                        ╱        ____________________________________________ \n",
              "                       ╱        ╱                 3                        2  \n",
              "                      ╱        ╱      ⎛         2⎞    ⎛                  3⎞   \n",
              "                     ╱        ╱       ⎜  3⋅c   b ⎟    ⎜27⋅d   9⋅b⋅c   2⋅b ⎟   \n",
              "                    ╱        ╱    - 4⋅⎜- ─── + ──⎟  + ⎜──── - ───── + ────⎟   \n",
              "                   ╱        ╱         ⎜   a     2⎟    ⎜ a        2      3 ⎟   \n",
              "                  ╱       ╲╱          ⎝        a ⎠    ⎝         a      a  ⎠   \n",
              "                 ╱        ─────────────────────────────────────────────────── \n",
              "              3 ╱                                  2                          \n",
              "              ╲╱                                                              \n",
              "─────────── - ────────────────────────────────────────────────────────────────\n",
              "___________                                            3                      \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "         3                                                                    \n",
              "9⋅b⋅c   b                                                                     \n",
              "───── + ──                                                                    \n",
              "    2    3                                                                    \n",
              " 2⋅a    a                                                                     \n",
              "\n",
              "____________________                                                          \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                  3                                                           \n",
              "  27⋅d   9⋅b⋅c   b                                                           3\n",
              "+ ──── - ───── + ──                                                        - ─\n",
              "  2⋅a        2    3                                                           \n",
              "          2⋅a    a      b                                                     \n",
              "──────────────────── - ───, - ────────────────────────────────────────────────\n",
              "                       3⋅a                              ______________________\n",
              "                                                       ╱        ______________\n",
              "                                                      ╱        ╱              \n",
              "                                                     ╱        ╱      ⎛        \n",
              "                                                    ╱        ╱       ⎜  3⋅c   \n",
              "                                                   ╱        ╱    - 4⋅⎜- ─── + \n",
              "                                                  ╱        ╱         ⎜   a    \n",
              "                                ⎛  1   √3⋅ⅈ⎞     ╱       ╲╱          ⎝        \n",
              "                              3⋅⎜- ─ - ────⎟⋅   ╱        ─────────────────────\n",
              "                                ⎝  2    2  ⎠ 3 ╱                              \n",
              "                                             ╲╱                               \n",
              "\n",
              "                                                                              \n",
              "                                                                             ╱\n",
              "                                                                            ╱ \n",
              "                                                                           ╱  \n",
              "                                                                          ╱   \n",
              "                                                                         ╱    \n",
              "      2                                                                 ╱     \n",
              "⋅c   b                                                ⎛  1   √3⋅ⅈ⎞     ╱      \n",
              "── + ──                                               ⎜- ─ - ────⎟⋅   ╱       \n",
              "a     2                                               ⎝  2    2  ⎠ 3 ╱        \n",
              "     a                                                             ╲╱         \n",
              "─────────────────────────────────────────────────── - ────────────────────────\n",
              "___________________________________________________                           \n",
              "______________________________                                                \n",
              "   3                        2                                                 \n",
              " 2⎞    ⎛                  3⎞                                                  \n",
              "b ⎟    ⎜27⋅d   9⋅b⋅c   2⋅b ⎟                                                  \n",
              "──⎟  + ⎜──── - ───── + ────⎟                                                  \n",
              " 2⎟    ⎜ a        2      3 ⎟                     3                            \n",
              "a ⎠    ⎝         a      a  ⎠     27⋅d   9⋅b⋅c   b                             \n",
              "────────────────────────────── + ──── - ───── + ──                            \n",
              "    2                            2⋅a        2    3                            \n",
              "                                         2⋅a    a                             \n",
              "\n",
              "_________________________________________________________________________     \n",
              "        ____________________________________________                          \n",
              "       ╱                 3                        2                           \n",
              "      ╱      ⎛         2⎞    ⎛                  3⎞                            \n",
              "     ╱       ⎜  3⋅c   b ⎟    ⎜27⋅d   9⋅b⋅c   2⋅b ⎟                            \n",
              "    ╱    - 4⋅⎜- ─── + ──⎟  + ⎜──── - ───── + ────⎟                            \n",
              "   ╱         ⎜   a     2⎟    ⎜ a        2      3 ⎟                     3      \n",
              " ╲╱          ⎝        a ⎠    ⎝         a      a  ⎠     27⋅d   9⋅b⋅c   b       \n",
              " ─────────────────────────────────────────────────── + ──── - ───── + ──      \n",
              "                          2                            2⋅a        2    3      \n",
              "                                                               2⋅a    a      b\n",
              "───────────────────────────────────────────────────────────────────────── - ──\n",
              "                        3                                                   3⋅\n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "\n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                           2                  \n",
              "                                                    3⋅c   b                   \n",
              "                                                  - ─── + ──                  \n",
              "                                                     a     2                  \n",
              "                                                          a                   \n",
              "─, - ─────────────────────────────────────────────────────────────────────────\n",
              "a                              _______________________________________________\n",
              "                              ╱        _______________________________________\n",
              "                             ╱        ╱                 3                     \n",
              "                            ╱        ╱      ⎛         2⎞    ⎛                 \n",
              "                           ╱        ╱       ⎜  3⋅c   b ⎟    ⎜27⋅d   9⋅b⋅c   2⋅\n",
              "                          ╱        ╱    - 4⋅⎜- ─── + ──⎟  + ⎜──── - ───── + ──\n",
              "                         ╱        ╱         ⎜   a     2⎟    ⎜ a        2      \n",
              "       ⎛  1   √3⋅ⅈ⎞     ╱       ╲╱          ⎝        a ⎠    ⎝         a      a\n",
              "     3⋅⎜- ─ + ────⎟⋅   ╱        ──────────────────────────────────────────────\n",
              "       ⎝  2    2  ⎠ 3 ╱                                  2                    \n",
              "                    ╲╱                                                        \n",
              "\n",
              "                                                     _________________________\n",
              "                                                    ╱        _________________\n",
              "                                                   ╱        ╱                 \n",
              "                                                  ╱        ╱      ⎛         2⎞\n",
              "                                                 ╱        ╱       ⎜  3⋅c   b ⎟\n",
              "                                                ╱        ╱    - 4⋅⎜- ─── + ──⎟\n",
              "                                               ╱        ╱         ⎜   a     2⎟\n",
              "                             ⎛  1   √3⋅ⅈ⎞     ╱       ╲╱          ⎝        a ⎠\n",
              "                             ⎜- ─ + ────⎟⋅   ╱        ────────────────────────\n",
              "                             ⎝  2    2  ⎠ 3 ╱                                 \n",
              "                                          ╲╱                                  \n",
              "────────────────────────── - ─────────────────────────────────────────────────\n",
              "__________________________                                                   3\n",
              "_____                                                                         \n",
              "   2                                                                          \n",
              " 3⎞                                                                           \n",
              "b ⎟                                                                           \n",
              "──⎟                                                                           \n",
              "3 ⎟                     3                                                     \n",
              "  ⎠     27⋅d   9⋅b⋅c   b                                                      \n",
              "───── + ──── - ───── + ──                                                     \n",
              "        2⋅a        2    3                                                     \n",
              "                2⋅a    a                                                      \n",
              "\n",
              "________________________________________________      ⎤\n",
              "___________________________                           ⎥\n",
              "3                        2                            ⎥\n",
              "    ⎛                  3⎞                             ⎥\n",
              "    ⎜27⋅d   9⋅b⋅c   2⋅b ⎟                             ⎥\n",
              "  + ⎜──── - ───── + ────⎟                             ⎥\n",
              "    ⎜ a        2      3 ⎟                     3       ⎥\n",
              "    ⎝         a      a  ⎠     27⋅d   9⋅b⋅c   b        ⎥\n",
              "─────────────────────────── + ──── - ───── + ──       ⎥\n",
              " 2                            2⋅a        2    3       ⎥\n",
              "                                      2⋅a    a      b ⎥\n",
              "──────────────────────────────────────────────── - ───⎥\n",
              "                                                   3⋅a⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎥\n",
              "                                                      ⎦"
            ],
            "image/png": 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\n",
            "text/latex": "$\\displaystyle \\left[ - \\frac{- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}}{3 \\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}} - \\frac{\\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}}{3} - \\frac{b}{3 a}, \\  - \\frac{- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}}{3 \\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}} - \\frac{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}}{3} - \\frac{b}{3 a}, \\  - \\frac{- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}}{3 \\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}} - \\frac{\\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{\\sqrt{- 4 \\left(- \\frac{3 c}{a} + \\frac{b^{2}}{a^{2}}\\right)^{3} + \\left(\\frac{27 d}{a} - \\frac{9 b c}{a^{2}} + \\frac{2 b^{3}}{a^{3}}\\right)^{2}}}{2} + \\frac{27 d}{2 a} - \\frac{9 b c}{2 a^{2}} + \\frac{b^{3}}{a^{3}}}}{3} - \\frac{b}{3 a}\\right]$"
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "sm.solve(a*x**3+b*x**2+c*x+d,x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WhtDq7SbNftL"
      },
      "source": [
        "Функция roots возвращает численное значение корней многочлена с их множественностями."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "3mtyZrF4NftL",
        "outputId": "3619f794-cc3c-4091-cda1-b68767792d28"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{-2: 1, 1: 2}"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left\\{ -2 : 1, \\  1 : 2\\right\\}$"
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "sol = sm.roots(x**3-3*x+2,x)\n",
        "sol"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uJvg76RwNftL",
        "outputId": "930b42f0-5ded-4598-b8c4-01d5d162a12e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "# обратите внимание на тип:\n",
        "type(sol)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B7bFkpRmNftM"
      },
      "source": [
        "# 2.4. Пределы"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LMSqMCylNftM"
      },
      "source": [
        "Пусть задана числовая последовательность\n",
        "$$x_{n}=\\frac{5n^2+2n}{7n^2-3n}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "id": "MqAtz-W2NftM",
        "outputId": "5d610103-021b-41fb-d92a-0b807a038aaf"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   2      \n",
              "5⋅n  + 2⋅n\n",
              "──────────\n",
              "   2      \n",
              "7⋅n  - 3⋅n"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{5 n^{2} + 2 n}{7 n^{2} - 3 n}$"
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "n=symbols('n')\n",
        "xn = (5*n**2+2*n)/(7*n**2-3*n)\n",
        "xn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qWsoxNowNftM"
      },
      "source": [
        "Рассмотрим разность двух членов последовательности $x_{n+1}-x_{n}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "EBRluyJLNftN",
        "outputId": "a90f1dce-dc2a-49ad-d82d-8e46e2292687"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      -29       \n",
              "────────────────\n",
              "    2           \n",
              "49⋅n  + 7⋅n - 12"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle - \\frac{29}{49 n^{2} + 7 n - 12}$"
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "xnn=simplify(xn.subs({n:n+1})-xn)\n",
        "xnn"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6bSdXlxDNftN"
      },
      "source": [
        "или, что то же самое"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "id": "yg-6jFL4NftN",
        "outputId": "95a68594-628c-4afa-9e0a-9a12bd29abcd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     29            29    \n",
              "─────────── - ───────────\n",
              "7⋅(7⋅n + 4)   7⋅(7⋅n - 3)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{29}{7 \\left(7 n + 4\\right)} - \\frac{29}{7 \\left(7 n - 3\\right)}$"
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "xnn=apart(xnn,n)\n",
        "xnn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7w8HyY6KNftN",
        "outputId": "62fb8114-0cd2-4c71-e48e-02b7f4fdeb77"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Последовательность является убывающей\n"
          ]
        }
      ],
      "source": [
        "print('Последовательность '+'не '*int(bool(xnn.subs({n:1}) > 0)) +'является убывающей')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E325BU1qNftN"
      },
      "source": [
        "Вычислим предел последовательности"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XZnbUG3tNftN",
        "outputId": "8c58cc1b-f973-4e25-b9b6-f7a054737a08"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Предел последовательности xn равен: 5/7\n"
          ]
        }
      ],
      "source": [
        "LimXn = limit(xn,n,oo);\n",
        "print('\\n Предел последовательности xn равен:', LimXn);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5jy8J_vMNftO"
      },
      "source": [
        "# Пример. Вычисление предела с помощью критерия Коши\n",
        "\n",
        "Критерий Коши: последовательность сходится если для любого $\\epsilon$ существует такое N, что для двух любых номеров $m,n>N$ верно $|x_{n}-x_{m}|<\\epsilon$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "1wYc3PX-NftO"
      },
      "outputs": [],
      "source": [
        "def Cauchy_convergence(xn, eps):\n",
        "    for j in range(100,1000): \n",
        "        xn1=xn.subs({n:j-1}).n()\n",
        "        xn2=xn.subs({n:j}).n()\n",
        "        if (abs(xn2-xn1)<eps): \n",
        "            break\n",
        "    return abs(xn2-xn1), j"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "CPUoWvNhNftO",
        "outputId": "9f6880e8-abca-47df-91f8-e7a2e1f98eaf"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.71505376344086, 9.98021920550762e-7, 771)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( 0.71505376344086, \\  9.98021920550762 \\cdot 10^{-7}, \\  771\\right)$"
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "# зададимся величиной эпсилон\n",
        "eps = 1.e-6\n",
        "\n",
        "XnXn, N = Cauchy_convergence(xn, eps)\n",
        "        \n",
        "LimXnNum = xn.subs({n:N}).n()\n",
        "LimXnNum, XnXn, N"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y51a4NAuNftO",
        "outputId": "48191d5b-bf3c-4680-8fef-51b1f2ced2e6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Предел числовой последовательности xn (аналитически) равен: 0.7142857142857143\n",
            "Предел числовой последовательности xn (по кр. Коши при eps = 1.00000e-06, N=771) равен: 0.715053763440860\n",
            "Разность этих значений равна: 0.000768049155145945\n"
          ]
        }
      ],
      "source": [
        "print('Предел числовой последовательности xn (аналитически) равен:', float(LimXn));\n",
        "print('Предел числовой последовательности xn (по кр. Коши при eps =%12.5e, N=%i) равен:' %(eps, N), LimXnNum);\n",
        "print('Разность этих значений равна:', abs(float(LimXn)-LimXnNum));"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2NSoQXniNftO"
      },
      "source": [
        "# 2.5. Произвадная"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DjSnGbNqNftO"
      },
      "source": [
        "Рассмотрим функцию $y = x^2$, и приращение аргумента $dx$, приводящее к приращению функции $dy$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 66
        },
        "id": "-_W50bVTNftO",
        "outputId": "405180cb-eeb6-4021-dbea-571e107f2d96"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y = x**2 ,  dy = -x**2 + (dx + x)**2\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛ 2     2           2⎞\n",
              "⎝x , - x  + (dx + x) ⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( x^{2}, \\  - x^{2} + \\left(dx + x\\right)^{2}\\right)$"
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "x,y,dx,dy=symbols('x y dx dy')\n",
        "y=x**2\n",
        "dy=y.subs({x:x+dx})-y.subs({x:x})\n",
        "print('y =', y,',  dy =', dy)\n",
        "y, dy"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ivuLhWfNftP"
      },
      "source": [
        "Найдём предел отношения $dy/dx$ при $dx$ стремящемся к 0:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "-3WNVl0NNftP",
        "outputId": "2a3c68db-1e6f-475a-f0a5-326613dc6d92"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "dydx = 2*x\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2⋅x"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 x$"
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "dydx = limit(dy/dx,dx,0)\n",
        "print('dydx =', dydx)\n",
        "dydx"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gl_5Q9ryNftP"
      },
      "source": [
        "Определение. Такой предел называют производной функции $y(x)$ по $x$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UedzTSbmNftP"
      },
      "source": [
        "# Упражнение 2. Производные как предел\n",
        "\n",
        "Найдите с помощью предела производные следующих функций:\n",
        "\n",
        "$$ y = sin(x), \\quad y=ln(x), \\quad y=6sin(3x)-tan(x^2)+e^{6x} $$"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "sm.cos(pi/4),sm.tan(5*pi/6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "id": "ekvTn-dS1Qvh",
        "outputId": "a1968194-049c-452e-d991-fefac0f05796"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛√2  -√3 ⎞\n",
              "⎜──, ────⎟\n",
              "⎝2    3  ⎠"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAAeCAYAAAA7HGznAAAABHNCSVQICAgIfAhkiAAABN5JREFUeJztmlmIHEUYx3+Z3cQVRY0mbvCMkTWKguIRg0TjekbZ9cDggxqz4kFAIyKCLx5BvDGKRiS+xHiCB+Qhmn2KiLvBQMRRk5BLcdUYNmDEC9cjGh++au2d6er6uqZwu039YJjZrq/+VfPfmuqqrxoikRKxz1h3IFIpJtgKao6KvcAsjwb3BH5Fmimrv6cAc4pWOgFY5tHYacACj3oRPWX3eDFwsja4BgwCUzwaug840qNeRE/ZPT4QWAO0pS/abqPzge3AsEdDRwFfe9SL6Cm7xz8AG4A+V+A4YCtwkUcjncCDHvUieqri8QxkwurIC+oGfgXaPRroA87yqBfR00d1PN4FXJ38kXUbnQusB3Z7iJ8JrPXrV0RJlTyuI+MJyB5ss01QUcYDfwJ/+fUroqBqHn+EjCegebBNQFIeQx7Cs5AdbCOHADcBK4DPgBFkATkI3JjRhzw6EbOXBNatCjaPAR4DViMbhxHgO2TSuB/xSkPa3xC6XwKHGt0mupAk363KzqV5FJiYcX2B0dwBvAo8guTvvjfX30I2JRpuMXW6A+tWBZvHAL8jt9dlJm4JsA7x4ht0qZK0vyF0rzNxM7MKZ5jCeTkCNbI3D89b4s9DTiIaZ5opwFemvaty2kvTD3yL5G9C6paNoh6Dfdf3EOLFc4p20/6G0L3MxMyB5n9Ucg76i6XyRGAVcG3D9WnA55Y67wIraV5nDANLzedzczqccAAywFYiU30o3bLh4zFIBiGLN8x7l6PdRn9D6CbjqAOaB9uIed/fUvlEYCfQ03C9B3gnp1Ebf5h3zc63B1lTrgisWzZCe9xr3j91xBXxV6ubjKORrMJpyLS3MEegC1mIj09dW2qJzaMdSbHsAS5WxL8J/IwjSeihW0Za8fguYBHwFDCA+PAJMNlRz+Wvj+71Ju70rMJ2ZFa4x9GxLcD55vN+yMFrUZ4wHdH8WjuAnxBDQuqWGV+Phxn9REc/lt1gCo2/ProLTaxtU0MdWO4QWYyMcIDLgUsc8Y3cbjqxCThYEd9r4q8JrBuCIYo9zvOKUrdVjzuBK5FBuwM4NSdW629R3aeBL/LEnsR9f+9Gzk9BDHHd2tLchnyxjeifKnkB+A15miCkbghWA5sLvB5X6rbicZqjEe825MRo/PXRHcDxmNpM5Fa6b05MO5LPmo5uS51wBzIg1iPJPg1tyHa8P7Bu2fH1OIs64s+kjDKNvz66NeBHFOvmtbhzVK8DLyOJQA13m47VLZ2z0W3q2drx1a0CRT22sRP72snlr6/uBcjJTltG2SjOAd52xMxDclxHKDp1r+nUhxRfSz2D5H2yFqNFdZeb+L6CfRgrtB4fR/YtsMa/ydc1lrp5/rai+xpwQ/qC7TGi95FbUxewzRKzCplNtlvKE+YDDyBfaABZxDcyRPamZBxwBfAB8itqVTfJK1Yl/6b1+FLkuG4QWZDvQgbPbCSdNQzcnFEvz99WdA8HDgNedPT7HyYji7u888WpCp1FuHdo71nqnmHK7wykW0fWEdateAmZqog5CXgW+BhZf+1G8nTrEJ9ss36ev63ovgQcq+j3KI4HLixaKSAPI2YcE0DrIGQW1O4G9wZC+ptwNqMP8gsxlk9ObEJ+VSHoRc75/su0SNkJ6W/C/+1Jm0gkEolEIpG9ir8B6Aur6AoTjJcAAAAASUVORK5CYII=\n",
            "text/latex": "$\\displaystyle \\left( \\frac{\\sqrt{2}}{2}, \\  - \\frac{\\sqrt{3}}{3}\\right)$"
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 47
        },
        "outputId": "a95161ac-d4f6-4a3f-8940-9ceffe4295d4",
        "id": "QR7Y7w48xMq2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛ 6⋅x                   ⎛ 2⎞     6⋅x    6⋅dx + 6⋅x                            \n",
              "⎝e    + 6⋅sin(3⋅x) - tan⎝x ⎠, - e    + e           - 6⋅sin(3⋅x) + 6⋅sin(3⋅dx +\n",
              "\n",
              "           ⎛ 2⎞      ⎛        2⎞⎞\n",
              " 3⋅x) + tan⎝x ⎠ - tan⎝(dx + x) ⎠⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( e^{6 x} + 6 \\sin{\\left(3 x \\right)} - \\tan{\\left(x^{2} \\right)}, \\  - e^{6 x} + e^{6 dx + 6 x} - 6 \\sin{\\left(3 x \\right)} + 6 \\sin{\\left(3 dx + 3 x \\right)} + \\tan{\\left(x^{2} \\right)} - \\tan{\\left(\\left(dx + x\\right)^{2} \\right)}\\right)$"
          },
          "metadata": {},
          "execution_count": 46
        }
      ],
      "source": [
        "\n",
        "x,y,dx,dy=symbols('x y dx dy')\n",
        "#y = math.sin(x)\n",
        "#y = np.sin(np.pi/2.)\n",
        "#y = np.sin(x)\n",
        "y = 6*sm.sin(3*x) - sm.tan(x**2) + e**(6*x)\n",
        "dy=y.subs({x:x+dx})-y.subs({x:x})\n",
        "\n",
        "y, dy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "outputId": "6220c407-6225-4c49-9364-e36b5f961316",
        "id": "LbH9toNA13YC"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   6⋅x                 2⎛ 2⎞                    \n",
              "6⋅e   ⋅log(e) - 2⋅x⋅tan ⎝x ⎠ - 2⋅x + 18⋅cos(3⋅x)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 6 e^{6 x} \\log{\\left(e \\right)} - 2 x \\tan^{2}{\\left(x^{2} \\right)} - 2 x + 18 \\cos{\\left(3 x \\right)}$"
          },
          "metadata": {},
          "execution_count": 47
        }
      ],
      "source": [
        "dydx = limit(dy/dx,dx,0)\n",
        "\n",
        "dydx"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AM5drreeNftP"
      },
      "source": [
        "В пакете символьных вычислений можно находить производную напрямую:"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        ""
      ],
      "metadata": {
        "id": "69xEIR3C9Eu9"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o-TdEbuwNftP",
        "outputId": "3f8b05f6-df51-40c1-d4ce-dde69bc6aae7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Производные функции f(x,y) по x: x*cos(x + y) + sin(x + y)\n",
            "\n",
            " Производные функции f(x,y) по y: x*cos(x + y)\n",
            "\n",
            " Производные функции f(x,y) по xx и y: 0\n"
          ]
        }
      ],
      "source": [
        "x,y=symbols('x y')\n",
        "\n",
        "f=x*sm.sin(x+y);\n",
        "\n",
        "# Вычислим частные производные функции:\n",
        "fx=diff(f,x);\n",
        "fy=diff(f,y);\n",
        "print('\\n Производные функции f(x,y) по x:', fx);\n",
        "print('\\n Производные функции f(x,y) по y:', fy);\n",
        "\n",
        "# Вторая производная по x и первая по y\n",
        "fxxy=diff(a,x,2,y);\n",
        "print('\\n Производные функции f(x,y) по xx и y:', fxxy);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9SvcjLfuNftQ"
      },
      "source": [
        "# Упражнение 3. Производные\n",
        "\n",
        "Проверьте правильность найденных ранее с помощью предела производных."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "outputId": "12c5990e-6b22-464a-d134-69a035ff1292",
        "id": "ZK7_astC9Rpz"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " Производные функции f(x,y) по x: 6*e**(6*x)*log(e) - 2*x*(tan(x**2)**2 + 1) + 18*cos(3*x)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛ 6⋅x                   ⎛ 2⎞     6⋅x              ⎛   2⎛ 2⎞    ⎞              \n",
              "⎝e    + 6⋅sin(3⋅x) - tan⎝x ⎠, 6⋅e   ⋅log(e) - 2⋅x⋅⎝tan ⎝x ⎠ + 1⎠ + 18⋅cos(3⋅x)\n",
              "\n",
              "⎞\n",
              "⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( e^{6 x} + 6 \\sin{\\left(3 x \\right)} - \\tan{\\left(x^{2} \\right)}, \\  6 e^{6 x} \\log{\\left(e \\right)} - 2 x \\left(\\tan^{2}{\\left(x^{2} \\right)} + 1\\right) + 18 \\cos{\\left(3 x \\right)}\\right)$"
          },
          "metadata": {},
          "execution_count": 49
        }
      ],
      "source": [
        "x,y=symbols('x y')\n",
        "\n",
        "f = 6*sm.sin(3*x) - sm.tan(x**2) + e**(6*x);\n",
        "\n",
        "# Вычислим частные производные функции:\n",
        "fx=diff(f,x);\n",
        "#fy=diff(f,y);\n",
        "print('\\n Производные функции f(x,y) по x:', fx);\n",
        "f, fx"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lNbaekhtNftQ"
      },
      "source": [
        "# 3. Нелинейные уравнения и системы."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqSp2AsoNftQ"
      },
      "source": [
        "# 3.1. Алгоритмы для решения нелинейного уравнения "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PYzhOkmkNftQ"
      },
      "source": [
        "Нас интересуют задачи вида: $f(x) = 0$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B5lVQv92NftQ"
      },
      "source": [
        "Пусть есть некоторая функция $f(x)=(1+x+x^2) \\cdot e^{-x}+sin(x+0.1)-1$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "gEU1zv3ANftQ"
      },
      "outputs": [],
      "source": [
        "def f(x):\n",
        "    return ((1.0 + x + x**2) * math.exp(-x) + math.sin(x+0.1) - 1.0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KpzDChD8NftQ"
      },
      "source": [
        "Построим график этой функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "Ur3XGmnfNftQ",
        "outputId": "5e11eafb-474a-488f-e6c4-d0f6aba8102f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.00000000e+00, -9.44723618e-01, -8.89447236e-01, -8.34170854e-01,\n",
              "       -7.78894472e-01, -7.23618090e-01, -6.68341709e-01, -6.13065327e-01,\n",
              "       -5.57788945e-01, -5.02512563e-01, -4.47236181e-01, -3.91959799e-01,\n",
              "       -3.36683417e-01, -2.81407035e-01, -2.26130653e-01, -1.70854271e-01,\n",
              "       -1.15577889e-01, -6.03015075e-02, -5.02512563e-03,  5.02512563e-02,\n",
              "        1.05527638e-01,  1.60804020e-01,  2.16080402e-01,  2.71356784e-01,\n",
              "        3.26633166e-01,  3.81909548e-01,  4.37185930e-01,  4.92462312e-01,\n",
              "        5.47738693e-01,  6.03015075e-01,  6.58291457e-01,  7.13567839e-01,\n",
              "        7.68844221e-01,  8.24120603e-01,  8.79396985e-01,  9.34673367e-01,\n",
              "        9.89949749e-01,  1.04522613e+00,  1.10050251e+00,  1.15577889e+00,\n",
              "        1.21105528e+00,  1.26633166e+00,  1.32160804e+00,  1.37688442e+00,\n",
              "        1.43216080e+00,  1.48743719e+00,  1.54271357e+00,  1.59798995e+00,\n",
              "        1.65326633e+00,  1.70854271e+00,  1.76381910e+00,  1.81909548e+00,\n",
              "        1.87437186e+00,  1.92964824e+00,  1.98492462e+00,  2.04020101e+00,\n",
              "        2.09547739e+00,  2.15075377e+00,  2.20603015e+00,  2.26130653e+00,\n",
              "        2.31658291e+00,  2.37185930e+00,  2.42713568e+00,  2.48241206e+00,\n",
              "        2.53768844e+00,  2.59296482e+00,  2.64824121e+00,  2.70351759e+00,\n",
              "        2.75879397e+00,  2.81407035e+00,  2.86934673e+00,  2.92462312e+00,\n",
              "        2.97989950e+00,  3.03517588e+00,  3.09045226e+00,  3.14572864e+00,\n",
              "        3.20100503e+00,  3.25628141e+00,  3.31155779e+00,  3.36683417e+00,\n",
              "        3.42211055e+00,  3.47738693e+00,  3.53266332e+00,  3.58793970e+00,\n",
              "        3.64321608e+00,  3.69849246e+00,  3.75376884e+00,  3.80904523e+00,\n",
              "        3.86432161e+00,  3.91959799e+00,  3.97487437e+00,  4.03015075e+00,\n",
              "        4.08542714e+00,  4.14070352e+00,  4.19597990e+00,  4.25125628e+00,\n",
              "        4.30653266e+00,  4.36180905e+00,  4.41708543e+00,  4.47236181e+00,\n",
              "        4.52763819e+00,  4.58291457e+00,  4.63819095e+00,  4.69346734e+00,\n",
              "        4.74874372e+00,  4.80402010e+00,  4.85929648e+00,  4.91457286e+00,\n",
              "        4.96984925e+00,  5.02512563e+00,  5.08040201e+00,  5.13567839e+00,\n",
              "        5.19095477e+00,  5.24623116e+00,  5.30150754e+00,  5.35678392e+00,\n",
              "        5.41206030e+00,  5.46733668e+00,  5.52261307e+00,  5.57788945e+00,\n",
              "        5.63316583e+00,  5.68844221e+00,  5.74371859e+00,  5.79899497e+00,\n",
              "        5.85427136e+00,  5.90954774e+00,  5.96482412e+00,  6.02010050e+00,\n",
              "        6.07537688e+00,  6.13065327e+00,  6.18592965e+00,  6.24120603e+00,\n",
              "        6.29648241e+00,  6.35175879e+00,  6.40703518e+00,  6.46231156e+00,\n",
              "        6.51758794e+00,  6.57286432e+00,  6.62814070e+00,  6.68341709e+00,\n",
              "        6.73869347e+00,  6.79396985e+00,  6.84924623e+00,  6.90452261e+00,\n",
              "        6.95979899e+00,  7.01507538e+00,  7.07035176e+00,  7.12562814e+00,\n",
              "        7.18090452e+00,  7.23618090e+00,  7.29145729e+00,  7.34673367e+00,\n",
              "        7.40201005e+00,  7.45728643e+00,  7.51256281e+00,  7.56783920e+00,\n",
              "        7.62311558e+00,  7.67839196e+00,  7.73366834e+00,  7.78894472e+00,\n",
              "        7.84422111e+00,  7.89949749e+00,  7.95477387e+00,  8.01005025e+00,\n",
              "        8.06532663e+00,  8.12060302e+00,  8.17587940e+00,  8.23115578e+00,\n",
              "        8.28643216e+00,  8.34170854e+00,  8.39698492e+00,  8.45226131e+00,\n",
              "        8.50753769e+00,  8.56281407e+00,  8.61809045e+00,  8.67336683e+00,\n",
              "        8.72864322e+00,  8.78391960e+00,  8.83919598e+00,  8.89447236e+00,\n",
              "        8.94974874e+00,  9.00502513e+00,  9.06030151e+00,  9.11557789e+00,\n",
              "        9.17085427e+00,  9.22613065e+00,  9.28140704e+00,  9.33668342e+00,\n",
              "        9.39195980e+00,  9.44723618e+00,  9.50251256e+00,  9.55778894e+00,\n",
              "        9.61306533e+00,  9.66834171e+00,  9.72361809e+00,  9.77889447e+00,\n",
              "        9.83417085e+00,  9.88944724e+00,  9.94472362e+00,  1.00000000e+01])"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ],
      "source": [
        "A = -1.0\n",
        "B =  10.0\n",
        "N =  200\n",
        "Y = np.zeros((N))\n",
        "X = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    Y[i] = f(X[i])\n",
        "\n",
        "plt.figure(figsize=(8,5))      \n",
        "plt.plot(X, Y)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "np.linspace(A, B, N)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5WoRydnqNftR"
      },
      "source": [
        "Очевидно, что корень может находиться толькро между точками a и b, для которых справедливо: $f(a)>0, f(b)<0$ или $f(a)>0, f(b)<0$, т.е. $f(a)\\cdot f(b)<0$. Найдём такие точки a и b переберая значения x в некотором интервале"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pyj81xvONftR",
        "outputId": "e1452354-d8df-426a-aaec-7f7373d92766"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t -1.0000000000e+00 \t -4.2105263158e-01\n",
            "\t 1 \t -4.2105263158e-01 \t 1.5789473684e-01\n",
            "\t 2 \t 2.4736842105e+00 \t 3.0526315789e+00\n",
            "\t 3 \t 7.1052631579e+00 \t 7.6842105263e+00\n",
            "\t 4 \t 7.6842105263e+00 \t 8.2631578947e+00\n",
            "Найдено 5 интервалов локализации корня.\n"
          ]
        }
      ],
      "source": [
        "n=20\n",
        "AB = np.zeros((2,n))\n",
        "xab = np.linspace(A, B, n)\n",
        "ia=0\n",
        "for i in range(n-1):\n",
        "    if f(xab[i])*f(xab[i+1])<0:\n",
        "        AB[0][ia]=xab[i]\n",
        "        AB[1][ia]=xab[i+1]\n",
        "        print ('\\t %i \\t %.10e \\t %.10e' %(ia, AB[0][ia], AB[1][ia]))\n",
        "        ia=ia+1\n",
        "print('Найдено %i интервалов локализации корня.' %(ia))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "6Y8ChJB9NftR",
        "outputId": "fedc04a7-4838-4f59-e495-d9be6f3e55d7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "for i in range(ia): \n",
        "    plt.plot(AB[0][i], 0, 'o')\n",
        "    plt.plot(AB[1][i], 0, 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CCLabdEbNftR"
      },
      "source": [
        "# 3.2 Метод деления отрезка пополам (Метод бисекции)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "sUlvSwIQNftR"
      },
      "outputs": [],
      "source": [
        "def bisection(f, x1, x2, pr=0, tol=1.0e-10):\n",
        "    \"\"\"\n",
        "    Ищет корень уравнения f(x)=0\n",
        "    на отрезке [x1, x2] методом дихотомии (бисекции).\n",
        "    Значения функций на концах отрезка не могут иметь один знак.\n",
        "    :param f: - функция\n",
        "    :param x1: - левая точка мнтервала\n",
        "    :param x2: - правая точка мнтервала\n",
        "    :param pr: - параметр выдачи итераций (pr=0 - не выводить итерации, pr=1 - выводить итерации)\n",
        "    :param tol: - точность\n",
        "    :return:\n",
        "    \"\"\"\n",
        "    f1 = f(x1)\n",
        "    f2 = f(x2)\n",
        "    if f1*f2 > 0.:\n",
        "        print('f(x1) and f(x2) can not have the same signs')\n",
        "    n = int(math.ceil(np.log(abs(x2-x1)/tol)/np.log(2.)))\n",
        "    \n",
        "    Error=abs(x1-x2)\n",
        "    for i in range(n):\n",
        "        Error0=Error\n",
        "        x3 = 0.5*(x1+x2)\n",
        "        f3 = f(x3)\n",
        "        if f2*f3 < 0.:\n",
        "            x1=x3\n",
        "            f1=f3\n",
        "        else:\n",
        "            x2=x3\n",
        "            f2=f3\n",
        "        Error=abs(x1-x2)\n",
        "        k=np.log(Error)/np.log(Error0)\n",
        "        if pr>0:\n",
        "            print('итерация:\\t%i \\t%.6e \\t%.3f' %(i, Error, k))\n",
        "    return (x1+x2)/2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cm4RdnykNftR",
        "outputId": "19177120-62de-4aec-bca5-1894bd7597d3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t root[0] =  -6.8256428205e-01 \t f(root[0]) =   4.0557335268e-11\n",
            "\t 1 \t root[1] =  -1.0653060478e-01 \t f(root[1]) =  -1.6943224601e-11\n",
            "\t 2 \t root[2] =   2.7584180781e+00 \t f(root[2]) =  -3.5366154449e-11\n",
            "\t 3 \t root[3] =   7.4839086268e+00 \t f(root[3]) =   2.9021229864e-13\n",
            "\t 4 \t root[4] =   7.9776600799e+00 \t f(root[4]) =  -1.9744206270e-12\n"
          ]
        }
      ],
      "source": [
        "xRoot = np.zeros((2,ia))\n",
        "\n",
        "for i in range(ia): \n",
        "    xRoot[0][i] = bisection(f, AB[0][i], AB[1][i], pr=0)\n",
        "    xRoot[1][i] = f(xRoot[0][i])\n",
        "    print('\\t %i \\t root[%i] = %18.10e \\t f(root[%i]) = %18.10e' %(i, i, xRoot[0][i], i, xRoot[1][i]))    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "IVqrIi8aNftS",
        "outputId": "3689f74f-3479-4803-e5fa-953b73294570"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "plt.plot(xRoot[0,:], xRoot[1,:], 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BP0XmDOvNftS"
      },
      "source": [
        "# 3.3 Метод Ньютона"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yesDWsNTNftS"
      },
      "source": [
        "Вычислим производную заданной функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "x2eQcdOYNftS",
        "outputId": "abb84917-7c0e-4d23-ee1c-50b622ddc010"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           -x   ⎛ 2          ⎞  -x               \n",
              "(2⋅x + 1)⋅ℯ   - ⎝x  + x + 1.0⎠⋅ℯ   + cos(x + 0.1)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left(2 x + 1\\right) e^{- x} - \\left(x^{2} + x + 1.0\\right) e^{- x} + \\cos{\\left(x + 0.1 \\right)}$"
          },
          "metadata": {},
          "execution_count": 57
        }
      ],
      "source": [
        "x=symbols('x')\n",
        "\n",
        "F = (1.0 + x + x**2) * sm.exp(-x) + sm.sin(x + 0.1) - 1.0;\n",
        "\n",
        "FX = diff(F,x)\n",
        "FX"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "M6ZfTnC-NftS"
      },
      "outputs": [],
      "source": [
        "def fx(a):\n",
        "    return FX.subs({x:a}).n()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "EZkvRWpiNftS"
      },
      "outputs": [],
      "source": [
        "def newton(f, x, pr=0, tol=1.0e-10):   \n",
        "    Error=2\n",
        "    i=0\n",
        "    while Error>tol:\n",
        "        Error0=Error\n",
        "        x0=x\n",
        "        x = x0 - f(x0)/fx(x0)\n",
        "        Error=math.fabs(x-x0)\n",
        "        k=np.log(Error)/np.log(Error0)\n",
        "        i=i+1\n",
        "        if pr>0:\n",
        "            if i>1: print('итерация:\\t%i \\t%.6e \\t ' %(i, Error), k)\n",
        "            else:   print('итерация:\\t%i \\t%.6e \\t ' %(i, Error))\n",
        "    return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QHdO5p0WNftT"
      },
      "source": [
        "Рассмотрим в качестве начального приближения левые точки отрезков локализации:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kesE_LR4NftT",
        "outputId": "cd59c915-c3ab-44d9-ee05-c6662052a417"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t root(0) =  -6.8256428202e-01 \t f(root[0]) =  -3.3306690739e-16\n",
            "\t 1 \t root(1) =   2.7584180781e+00 \t f(root[1]) =   0.0000000000e+00\n",
            "\t 2 \t root(2) =   2.7584180781e+00 \t f(root[2]) =   0.0000000000e+00\n",
            "\t 3 \t root(3) =   7.4839086268e+00 \t f(root[3]) =   2.2204460493e-16\n",
            "\t 4 \t root(4) =   7.4839086268e+00 \t f(root[4]) =  -1.1102230246e-16\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:9: RuntimeWarning: divide by zero encountered in log\n",
            "  if __name__ == '__main__':\n"
          ]
        }
      ],
      "source": [
        "xRootA = np.zeros((2,ia))\n",
        "\n",
        "for i in range(ia): \n",
        "    xRootA[0][i] = newton(f, AB[0][i], pr=0)\n",
        "    xRootA[1][i] = f(xRootA[0][i])\n",
        "    print('\\t %i \\t root(%i) = %18.10e \\t f(root[%i]) = %18.10e' %(i, i, xRootA[0][i], i, xRootA[1][i]))   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "Ox1iTMEcNftT",
        "outputId": "71ac659d-4ddc-45f3-c005-398b019f5c81"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "for i in range(ia): \n",
        "    plt.plot(xRootA[0][i], 0, 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fviVZcmHNftT"
      },
      "source": [
        "Рассмотрим в качестве начального приближения правые точки отрезков локализации:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E1iIF1G-NftT",
        "outputId": "cd2edd86-4b56-4856-a4b8-7f180441c912"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t root(0) =   2.7584180781e+00 \t f(root[0]) =   0.0000000000e+00\n",
            "\t 1 \t root(1) =  -1.0653060476e-01 \t f(root[1]) =  -1.1102230246e-16\n",
            "\t 2 \t root(2) =   2.7584180781e+00 \t f(root[2]) =   0.0000000000e+00\n",
            "\t 3 \t root(3) =   7.4839086268e+00 \t f(root[3]) =  -1.1102230246e-16\n",
            "\t 4 \t root(4) =   7.9776600799e+00 \t f(root[4]) =   2.2204460493e-16\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:9: RuntimeWarning: divide by zero encountered in log\n",
            "  if __name__ == '__main__':\n"
          ]
        }
      ],
      "source": [
        "xRootB = np.zeros((2,ia))\n",
        "\n",
        "for i in range(ia): \n",
        "    xRootB[0][i] = newton(f, AB[1][i], pr=0)\n",
        "    xRootB[1][i] = f(xRootB[0][i])\n",
        "    print('\\t %i \\t root(%i) = %18.10e \\t f(root[%i]) = %18.10e' %(i, i, xRootB[0][i], i, xRootB[1][i])) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "id": "HodTSHU9NftT",
        "outputId": "9930ea4d-d525-44cb-8c3f-d6511b8ba815"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(10,7))  \n",
        "plt.plot(X, Y, '-')\n",
        "for i in range(ia): \n",
        "    plt.plot(xRootB[0][i], 0, 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eCxCf-NgNftU"
      },
      "source": [
        "Видно, что решение из крайних точек отрезков локализации корня сходится к разным решениям. Это обусловленно локальными свойствами функции - поведением производной. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qgx1RE4wNftU"
      },
      "source": [
        "# Решение системы нелинейных уравнений"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WTEUSL2gNftU"
      },
      "source": [
        "# 3.4. Методом Ньютона "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "5om9LalcNftU"
      },
      "source": [
        "Нас интересуют задачи вида:\n",
        "\\begin{cases}\n",
        "   f(x_1,x_2) = 0\n",
        "   \\\\\n",
        "   g(x_1,x_2) = 0\n",
        "\\end{cases}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l-CiQlhQNftU"
      },
      "source": [
        "Рассмотрим систему:\n",
        "\\begin{cases}\n",
        "   4(x_2-1)^2+(x_1-1)^2-1 = 0\n",
        "   \\\\\n",
        "   x_2 - x_1 sin(25x_1) = 0\n",
        "\\end{cases}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wEhjjpOUNftU"
      },
      "source": [
        "Построим график этой функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "id": "ES6oX6hINftV"
      },
      "outputs": [],
      "source": [
        "def f1(x1, x2):\n",
        "    return (4.0*(x2 - 1.0)**2 + (x1 - 1.0)**2 - 1.0)\n",
        "\n",
        "def f2(x1, x2):\n",
        "    return (x2 - x1*math.sin(25.0*x1))\n",
        "\n",
        "def X22(x1):\n",
        "    return x1*math.sin(25.0*x1)\n",
        "\n",
        "def X21p(x1):\n",
        "    return (math.sqrt((1.0 - (x1 - 1.0)**2)/4.0)+1.0)\n",
        "\n",
        "def X21m(x1):\n",
        "    return (-math.sqrt((1.0 - (x1 - 1.0)**2)/4.0)+1.0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "id": "qT3-k4dKNftV",
        "outputId": "4b043de7-d15b-4e9d-b922-4e4e759ba6c6"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "A = 0.0\n",
        "B = 2.0\n",
        "N = 500\n",
        "y21p = np.zeros((N))\n",
        "y21m = np.zeros((N))\n",
        "y22 = np.zeros((N))\n",
        "x = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    y21p[i] = X21p(x[i])\n",
        "    y21m[i] = X21m(x[i])\n",
        "    y22[i]  =  X22(x[i])\n",
        "    \n",
        "plt.figure(figsize=(10,5))  \n",
        "plt.plot(x, y21p, x, y21m, x, y22)\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "byCfEDCONftV"
      },
      "source": [
        "Вычислим производные этих функций и сформируем матрицу Якоби:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "id": "_SAmEoSwNftV"
      },
      "outputs": [],
      "source": [
        "x1, x2 = symbols('x1, x2')\n",
        "\n",
        "F1 = 4.0*(x2 - 1.0)**2 + (x1 - 1.0)**2 - 1.0;\n",
        "\n",
        "F2 = x2 - x1*sm.sin(25.0*x1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p7oGVpwvNftV"
      },
      "source": [
        "Найдём частные производные: \n",
        "$$\\frac{\\partial f_1(x_1,x_2)}{\\partial x_1}, \\frac{\\partial f_1(x_1,x_2)}{\\partial x_2}, \\frac{\\partial f_2(x_1,x_2)}{\\partial x_1}, \\frac{\\partial f_2(x_1,x_2)}{\\partial x_2}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "MXxvJgO4NftV",
        "outputId": "b4b6cf6f-97ff-4e0a-ce0c-0141479c48ec"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2⋅x₁ - 2.0"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2 x_{1} - 2.0$"
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "F1X1 = diff(F1,x1)\n",
        "F1X1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "dtOcLa_QNftV",
        "outputId": "8e6a2d28-158a-46e1-f13c-217352641b8f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8.0⋅x₂ - 8.0"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 8.0 x_{2} - 8.0$"
          },
          "metadata": {},
          "execution_count": 68
        }
      ],
      "source": [
        "F1X2 = diff(F1,x2)\n",
        "F1X2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "vwLwZIDuNftW",
        "outputId": "99e5bac2-71e6-4bf5-ad06-b23a344e886b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-25.0⋅x₁⋅cos(25.0⋅x₁) - sin(25.0⋅x₁)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle - 25.0 x_{1} \\cos{\\left(25.0 x_{1} \\right)} - \\sin{\\left(25.0 x_{1} \\right)}$"
          },
          "metadata": {},
          "execution_count": 69
        }
      ],
      "source": [
        "F2X1 = diff(F2,x1)\n",
        "F2X1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "64hn-O6YNftW",
        "outputId": "1c2d351f-8d01-4f73-b854-8e92bbcc667d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
            "text/latex": "$\\displaystyle 1$"
          },
          "metadata": {},
          "execution_count": 70
        }
      ],
      "source": [
        "F2X2 = diff(F2,x2)\n",
        "F2X2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2kjFj4xDNftW"
      },
      "source": [
        "Сформируем иэ них матрицу Якоби:\n",
        "$$J = \n",
        "\\begin{pmatrix}\n",
        "  \\frac{\\partial f_1(x_1,x_2)}{\\partial x_1} \\frac{\\partial f_1(x_1,x_2)}{\\partial x_2}\\\\\n",
        "  \\frac{\\partial f_2(x_1,x_2)}{\\partial x_1} \\frac{\\partial f_2(x_1,x_2)}{\\partial x_2}\n",
        "\\end{pmatrix}\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "IVpYRlYMNftW",
        "outputId": "3c30eeb0-0b0c-4327-96e6-fc91e392417f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡             2⋅x₁ - 2.0               8.0⋅x₂ - 8.0⎤\n",
              "⎢                                                  ⎥\n",
              "⎣-25.0⋅x₁⋅cos(25.0⋅x₁) - sin(25.0⋅x₁)       1      ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}2 x_{1} - 2.0 & 8.0 x_{2} - 8.0\\\\- 25.0 x_{1} \\cos{\\left(25.0 x_{1} \\right)} - \\sin{\\left(25.0 x_{1} \\right)} & 1\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 71
        }
      ],
      "source": [
        "J=sm.Matrix([[F1X1,F1X2],[F2X1,F2X2]])\n",
        "J"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nUFMPlcUNftW"
      },
      "source": [
        "Программа для решения систем нелинейных уравнений методом Ньютона:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "metadata": {
        "id": "X-pa8SJMNftW"
      },
      "outputs": [],
      "source": [
        "def NEWTON(n, fun, Jac, x0, pr=0, tol=1.0e-10): \n",
        "    x = np.zeros(n)\n",
        "    b = np.zeros(n)\n",
        "    A = np.zeros((n,n)) \n",
        "    dx = np.zeros(n)\n",
        "    xStep = np.zeros((1000,n))\n",
        "    Error=2\n",
        "    i=0\n",
        "    x[:]=x0[:]\n",
        "    xStep[i][:]=x[:]\n",
        "    while Error>tol and i<999:\n",
        "        Error0=Error \n",
        "#        x0[:]=x[:]\n",
        "        b=-fun(x)\n",
        "        A=Jac(x)\n",
        "        dx = np.dot(linalg.pinv(A),b)\n",
        "        x[:]=x[:]+dx[:]\n",
        "        Error=math.sqrt(np.dot(dx.T,dx))\n",
        "        k=np.log(Error)/np.log(Error0)\n",
        "        i=i+1\n",
        "        xStep[i][:]=x[:]\n",
        "        if pr>0:\n",
        "            if i>1: print('итерация:\\t%i \\t%.6e \\t ' %(i, Error), k)\n",
        "            else:   print('итерация:\\t%i \\t%.6e \\t ' %(i, Error))\n",
        "    return x, xStep, i"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yr9hLX39NftX"
      },
      "source": [
        "Программы для вычсления значения функций и Якобиана:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "id": "QiHTMCf6NftX"
      },
      "outputs": [],
      "source": [
        "def fun(x):\n",
        "    f = np.zeros(2)\n",
        "    f[0] = f1(x[0],x[1])\n",
        "    f[1] = f2(x[0],x[1])\n",
        "    return f \n",
        "\n",
        "def jac(x):\n",
        "    JJ = J.subs({x1:x[0],x2:x[1]}).n()\n",
        "    M = np.array( [[float(JJ[0,0]), float(JJ[0,1])], [float(JJ[1,0]), float(JJ[1,1])]] )\n",
        "    return M"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kroiBQlCNftX"
      },
      "source": [
        "Выберем начальное приближение:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "id": "n2dmmb4aNftX",
        "outputId": "a6286e16-3fc5-4a2d-f00f-2ba0fa7a356b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "x10=1.8\n",
        "x20=1.1\n",
        "\n",
        "# попробуйте:\n",
        "# x10=1.0\n",
        "# x20=1.0\n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(x, y21p, x, y21m, x, y22)\n",
        "plt.plot(x10, x20, 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "doHg_qibNftX"
      },
      "source": [
        "Значение Якобиана в начальное точке"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mNb078Y7NftX",
        "outputId": "611b41dd-37cf-4ca4-f2d4-d972f6d23530"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  1.6       ,   0.8       ],\n",
              "       [-24.49039302,   1.        ]])"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ],
      "source": [
        "jac([x10, x20])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "65F3jUnuNftY",
        "outputId": "a201d68f-b060-4a70-8f45-85d95875f5aa"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "итерация:\t1 \t4.023895e-01 \t \n",
            "итерация:\t2 \t1.588120e-01 \t  2.0212721369631175\n",
            "итерация:\t3 \t3.628891e-02 \t  1.8022726495201313\n",
            "итерация:\t4 \t2.102438e-03 \t  1.8589280899170557\n",
            "итерация:\t5 \t7.120488e-06 \t  1.9226589841743564\n",
            "итерация:\t6 \t8.159902e-11 \t  1.959851229426387\n",
            " x1 = 1.791933e+00 \t x2 = 1.305304e+00 \t f1(x1,x2) = 0.000000e+00 \t f1(x1,x2) = 4.662937e-15\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "X0 = np.array([x10, x20])\n",
        "sol, xStep, iStep = NEWTON(2, fun, jac, X0, pr=1, tol=1.0e-10)\n",
        "\n",
        "print(' x1 = %12.6e \\t x2 = %12.6e \\t f1(x1,x2) = %12.6e \\t f1(x1,x2) = %12.6e' \n",
        "      %(sol[0],sol[1], f1(sol[0],sol[1]), f2(sol[0],sol[1]))) \n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(x, y21p, x, y21m, x, y22)\n",
        "plt.plot(sol[0], sol[1], 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "_euUtt4PNftY",
        "outputId": "742ecc06-1269-48a4-e190-90c7fdf770ce"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "r = sol[:] - X0[:]\n",
        "R = 1.1*math.sqrt(np.dot(r.T,r))\n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(x, y21p, x, y21m, x, y22)\n",
        "plt.plot(xStep[0:iStep+1,0], xStep[0:iStep+1,1], '-o')\n",
        "plt.xlim(sol[0]-R, sol[0]+R)\n",
        "plt.ylim(sol[1]-R, sol[1]+R)\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yCglelT4NftY"
      },
      "source": [
        "# 3.5 Функция root "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 540
        },
        "id": "V_enEJHbNftY",
        "outputId": "2ac03781-8c34-4286-dabc-c0b7707ef5a4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    fjac: array([[-0.05025335,  0.9987365 ],\n",
            "       [-0.9987365 , -0.05025335]])\n",
            "     fun: array([4.44089210e-16, 3.21964677e-14])\n",
            " message: 'The solution converged.'\n",
            "    nfev: 10\n",
            "    njev: 1\n",
            "     qtf: array([-9.79928722e-11,  5.98241088e-12])\n",
            "       r: array([-31.50774661,   0.80310234,  -2.48516491])\n",
            "  status: 1\n",
            " success: True\n",
            "       x: array([1.79193318, 1.30530388])\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "SOL = root(fun, X0, jac=jac, method='hybr')\n",
        "\n",
        "print(SOL)\n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(x, y21p, x, y21m, x, y22)\n",
        "plt.plot(SOL.x[0], SOL.x[1], 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OXup5ndpNftY"
      },
      "source": [
        "# 4. Алгоритмы минимизации нелинейной функции одной переменной "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D9eT7jLdNftY"
      },
      "source": [
        "Нас интересуют задачи вида: $f(x) -> min$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lP7wcQdWNftZ"
      },
      "source": [
        "Пусть есть некоторая функция $f(x)=(1+x+x^2) \\cdot e^{-x}+sin(x+0.1)-1$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "id": "18kuWVuhNftZ"
      },
      "outputs": [],
      "source": [
        "def f(x):\n",
        "    return ((1.0 + x + x**2) * math.exp(-x) + math.sin(x+0.1) - 1.0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "82euXugkNftZ"
      },
      "source": [
        "Построим график этой функции"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "ONGIqVtBNftZ",
        "outputId": "c9c4139e-4b2a-4a64-8ee9-ee195945f056"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "A = -1.0\n",
        "B =  10.0\n",
        "N =  200\n",
        "Y = np.zeros((N))\n",
        "X = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    Y[i] = f(X[i])\n",
        "    \n",
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hLuwvyZ4NftZ"
      },
      "source": [
        "Очевидно, что экстремум может находиться толькро между точками a и b, для которых справедливо: $f'(a)>0, f'(b)<0$ - для максимума или $f'(a)>0, f(b)'<0$ - для минимума, т.е. $f'(a)\\cdot f'(b)<0$. Найдём такие точки a и b переберая значения x в некотором интервале"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8fpKtnzbNftZ"
      },
      "source": [
        "Вычислим производную:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "tbqbG7GKNftZ",
        "outputId": "a1cc49dc-1cb1-4db2-8fee-0f3d00a1df27"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           -x   ⎛ 2          ⎞  -x               \n",
              "(2⋅x + 1)⋅ℯ   - ⎝x  + x + 1.0⎠⋅ℯ   + cos(x + 0.1)"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left(2 x + 1\\right) e^{- x} - \\left(x^{2} + x + 1.0\\right) e^{- x} + \\cos{\\left(x + 0.1 \\right)}$"
          },
          "metadata": {},
          "execution_count": 81
        }
      ],
      "source": [
        "x=symbols('x')\n",
        "\n",
        "F = (1.0 + x + x**2) * sm.exp(-x) + sm.sin(x+0.1) - 1.0\n",
        "\n",
        "FX = diff(F,x)\n",
        "FX"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "metadata": {
        "id": "XW9sYOFiNfta"
      },
      "outputs": [],
      "source": [
        "def fx(a):\n",
        "    return FX.subs({x:a}).n()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yjZWn608Nfta",
        "outputId": "c6490b76-b35c-41ff-ae68-1371c4a59fb7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t -6.2068965517e-01 \t -2.4137931034e-01\n",
            "\t 1 \t 1.2758620690e+00 \t 1.6551724138e+00\n",
            "\t 2 \t 4.6896551724e+00 \t 5.0689655172e+00\n",
            "\t 3 \t 7.7241379310e+00 \t 8.1034482759e+00\n",
            "Найдено 4 интервалов локализации экстремума.\n"
          ]
        }
      ],
      "source": [
        "n=30\n",
        "AB = np.zeros((2,n))\n",
        "xab = np.linspace(A, B, n)\n",
        "ia=0\n",
        "for i in range(n-1):\n",
        "    if fx(xab[i])*fx(xab[i+1])<0:\n",
        "        AB[0][ia]=xab[i]\n",
        "        AB[1][ia]=xab[i+1]\n",
        "        print ('\\t %i \\t %.10e \\t %.10e' %(ia, AB[0][ia], AB[1][ia]))\n",
        "        ia=ia+1\n",
        "print('Найдено %i интервалов локализации экстремума.' %(ia))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "ZBrLOaYRNfta",
        "outputId": "a0ac1111-ce14-4bed-e9ce-5f7104ef5a27"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "for i in range(ia): \n",
        "    plt.plot(AB[0][i], 0, 'o')\n",
        "    plt.plot(AB[1][i], 0, 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "vRQSGmCHNfta",
        "outputId": "cefa584f-745d-4c67-e0c2-2f19d06e558b"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "Yx = np.zeros((N))\n",
        "for i in range(N): \n",
        "    Yx[i] = fx(X[i])\n",
        "\n",
        "plt.figure(figsize=(8,5))      \n",
        "plt.plot(X, Yx, '-')\n",
        "for i in range(ia): \n",
        "    plt.plot(AB[0][i], 0, 'o')\n",
        "    plt.plot(AB[1][i], 0, 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i5nXm-DINfta"
      },
      "source": [
        "# 4.1 Метод дихотомии"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "metadata": {
        "id": "fTLLO72WNfta"
      },
      "outputs": [],
      "source": [
        "def bisectionMin(f, x1, x2, mm=0, tol=1.0e-10):\n",
        "    \"\"\"\n",
        "    Ищет корень уравнения f(x)=0\n",
        "    на отрезке [x1, x2] методом дихотомии (бисекции).\n",
        "    Значения функций на концах отрезка не могут иметь один знак.\n",
        "    :param f: - функция\n",
        "    :param x1: - левая точка мнтервала\n",
        "    :param x2: - правая точка мнтервала\n",
        "    :param mm: - параметр типа экстремума (pr=0 - mim, pr=1 - max)\n",
        "    :param tol: - точность\n",
        "    :return:\n",
        "    \"\"\"\n",
        "    f1 = f(x1)\n",
        "    f2 = f(x2)\n",
        "    a = (1.0 + np.sqrt(5.0))/2.0\n",
        "    \n",
        "    Error=abs(x1-x2)\n",
        "    for i in range(n):\n",
        "        Error0=Error\n",
        "        d = (x2-x1)*(1.0/a - 1.0/2.0)\n",
        "        x3 = 0.5*(x1+x2)+d\n",
        "        x4 = 0.5*(x1+x2)-d\n",
        "        f3 = f(x3)\n",
        "        f4 = f(x4)\n",
        "        if mm==0:\n",
        "            if f3 > f4:\n",
        "                x2=x3\n",
        "                f2=f3\n",
        "            else:\n",
        "                x1=x4\n",
        "                f1=f4\n",
        "        else:\n",
        "            if f3 < f4:\n",
        "                x2=x3\n",
        "                f2=f3\n",
        "            else:\n",
        "                x1=x4\n",
        "                f1=f4\n",
        "        Error=abs(x1-x2)\n",
        "    return (x1+x2)/2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PjCir67WNftb",
        "outputId": "6d4eca01-741b-44c9-95ce-2997526e2ad0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t root[0] =  -4.3018957759e-01 \t f(root[0]) =  -1.6356739805e-01\n",
            "\t 1 \t root[1] =   1.6551723119e+00 \t f(root[1]) =   1.0137704728e+00\n",
            "\t 2 \t root[2] =   4.7658265912e+00 \t f(root[2]) =  -1.7457293412e+00\n",
            "\t 3 \t root[3] =   8.1034481739e+00 \t f(root[3]) =  -3.7827206420e-02\n"
          ]
        }
      ],
      "source": [
        "xRoot = np.zeros((2,ia))\n",
        "\n",
        "for i in range(ia): \n",
        "    xRoot[0][i] = bisectionMin(f, AB[0][i], AB[1][i])\n",
        "    xRoot[1][i] = f(xRoot[0][i])\n",
        "    print('\\t %i \\t root[%i] = %18.10e \\t f(root[%i]) = %18.10e' %(i, i, xRoot[0][i], i, xRoot[1][i]))    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "Fqlogz4mNftb",
        "outputId": "80b04ac3-fa79-4c2b-85f9-aa0f20df1619"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "plt.plot(xRoot[0,:], xRoot[1,:], 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AOu6FI4ANftb",
        "outputId": "b7b800d4-47f1-4e36-f7c2-3580344bb73f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\t 0 \t root[0] =  -6.2068955323e-01 \t f(root[0]) =  -7.5224927500e-02\n",
            "\t 1 \t root[1] =   1.3484834753e+00 \t f(root[1]) =   1.0743944863e+00\n",
            "\t 2 \t root[2] =   5.0689654153e+00 \t f(root[2]) =  -1.6978096976e+00\n",
            "\t 3 \t root[3] =   7.7311372238e+00 \t f(root[3]) =   2.9807497755e-02\n"
          ]
        }
      ],
      "source": [
        "xRoot = np.zeros((2,ia))\n",
        "\n",
        "for i in range(ia): \n",
        "    xRoot[0][i] = bisectionMin(f, AB[0][i], AB[1][i], mm=1)\n",
        "    xRoot[1][i] = f(xRoot[0][i])\n",
        "    print('\\t %i \\t root[%i] = %18.10e \\t f(root[%i]) = %18.10e' %(i, i, xRoot[0][i], i, xRoot[1][i]))    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "NYAbL8yKNftc",
        "outputId": "6f6fe298-7545-4e6e-fb44-0db61f60bb8f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(8,5))  \n",
        "plt.plot(X, Y, '-')\n",
        "plt.plot(xRoot[0,:], xRoot[1,:], 'o')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2pipokMNftd"
      },
      "source": [
        "# Экстремум функции несколькох переменных"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6F3LjahFNfte"
      },
      "source": [
        "Нас интересуют задачи вида:\n",
        "   $$f(x_1,x_2) -> extr$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3YEHLL6dNfte"
      },
      "source": [
        "# 4.2 Функция minimize "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "id": "a9ms4QpZNfte"
      },
      "outputs": [],
      "source": [
        "from scipy.optimize import minimize, rosen, rosen_der"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iF5aqttuNfte",
        "outputId": "53a1c8fe-49df-4bfd-9e28-e9f1bc57244b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1.00000002, 1.00000002, 1.00000007, 1.00000015, 1.00000028])"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ],
      "source": [
        "x0 = [1.3, 0.7, 0.8, 1.9, 1.2]\n",
        "res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)\n",
        "res.x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L7f5z4LiNfte"
      },
      "source": [
        "# Домашнее задание (базовое):"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LQHvxmIJNftf"
      },
      "source": [
        "# Задание 1. Матрица Паскаля.\n",
        "\n",
        "Напишите программу, вычисляющую матрицу Паскаля, эллементы которой определяются следующим соотношением:\n",
        "\n",
        "$$ a_{ij} = \\frac{(i+j-2)!}{(i-1)!(j-1)!}, \\quad i=1,2,..., n, \\quad j=1,2,..., n. $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "id": "lo5_T5LSNftf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7a8e699b-7a34-45f4-93b9-9be9075b3c12"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n",
            "[1, 1, 1]\n",
            "[1, 2, 3]\n",
            "[1, 3, 6]\n"
          ]
        }
      ],
      "source": [
        "from math import factorial\n",
        "n = int(input())\n",
        "a = []\n",
        "for i in range(n):\n",
        "    a.append([])\n",
        "    for j in range(n):\n",
        "        a[i].append(factorial(i+j)//factorial(i)//factorial(j))\n",
        "    print(a[i])"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "n = int(input())\n",
        "b = [[1]*n for i in range(n)]\n",
        "print(*b[0])\n",
        "for i in range(1,n):\n",
        "    for j in range(1,n):\n",
        "        b[i][j] = b[i-1][j] + b[i][j-1]\n",
        "    print(*b[i])\n"
      ],
      "metadata": {
        "id": "2MqU9IDSBFP7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3fe35ac4-a15a-4f28-b842-b19109471361"
      },
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n",
            "1 1 1\n",
            "1 2 3\n",
            "1 3 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ltd_pm9LNftf"
      },
      "source": [
        "# Задание 2.\n",
        "\n",
        "Напишите программу, вычисляющую обратную матрицу на основе решения матричного уравнения:\n",
        "\n",
        "$$ AX = E. $$\n",
        "\n",
        "Найдите таким образом обратную матрицу для матрицы Паскаля."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "id": "dgqmjeewNftf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a4791e9-ef8a-42f8-ea6b-2ef6a53c8ee6"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[32.42747063, 97.91476617, 62.81703973],\n",
              "        [63.53473865, 79.48898528, 61.12266378],\n",
              "        [10.4775815 , 40.88528555, 11.63184654]]),\n",
              " array([[-0.03139473,  0.02850234,  0.01977206],\n",
              "        [-0.00196631, -0.00560289,  0.04006085],\n",
              "        [ 0.03519082, -0.00598011, -0.07265078]]),\n",
              " array([[ 0.00162538, -0.00117276, -0.00091537],\n",
              "        [ 0.00148252, -0.00026422, -0.00317379],\n",
              "        [-0.00364969,  0.00147099,  0.00573436]]),\n",
              " (array([[-0.03139473,  0.02850234,  0.01977206],\n",
              "         [-0.00196631, -0.00560289,  0.04006085],\n",
              "         [ 0.03519082, -0.00598011, -0.07265078]]),\n",
              "  array([], dtype=float64),\n",
              "  3,\n",
              "  array([172.38599621,  27.66059097,  10.51716458])))"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ],
      "source": [
        "#linalg.inv(arr)\n",
        "\n",
        "a = np.reshape(arr, 15)\n",
        "a = np.reshape(a[0:9], (3,3))\n",
        "x = np.linalg.lstsq(a, np.eye(3), rcond = -1)\n",
        "\n",
        "\n",
        "a, np.linalg.inv(a), np.linalg.solve(a, np.linalg.inv(a)), x\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZJU7ggCdNftf"
      },
      "source": [
        "# Задание 3\n",
        "\n",
        "Напишите программу реализующую метод секущих (https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D1%85%D0%BE%D1%80%D0%B4)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "id": "Rv6GeKoeNftf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 576
        },
        "outputId": "ed9baf05-cae2-42e0-ccc4-36edc74e649b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Введите точность: 0.0001\n",
            "Введите начало отрезка: 1\n",
            "Введите конец отрезка: 5\n",
            "Введите шаг: 1\n",
            "Введите максимальное число итераций: 10\n",
            "\n",
            "\n",
            "|№ Корня|     A     |     B     |      X    |      f(x)      | Число итераций | Код ошибки |\n",
            "--------------------------------------------------------------------------------------------\n",
            "\n",
            "\n",
            "Расшифровка ошибок:\n",
            " 0 - Ошибок не обнаружено. \n",
            " 1 - Неправильное построение секущей.\n",
            " 2 - Превышен предел итераций.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "#from math import \n",
        "\n",
        "#Функция для функций\n",
        "def f(x):\n",
        "    a = x ** 3 - 18 * x - 83\n",
        "    return a\n",
        " \n",
        "#Функция вывода\n",
        "def out(k):\n",
        "    if k == '-':\n",
        "        return k\n",
        "    if k < 100000000 and (not 'e' in str(k)) :\n",
        "        if len(str(k))>9:\n",
        "            return str(k)[:9]\n",
        "        else:\n",
        "            return str(k)\n",
        "    else:\n",
        "        return '{:9.5e}'.format(k)\n",
        "             \n",
        "    \n",
        " \n",
        "#Метод секущих\n",
        "def sec(a, b, eps, m):\n",
        "    if f(a)*f(b) > 0 or f(a) == 0:  #наличие корня\n",
        "        return '-'\n",
        "    N = 0\n",
        "    x0 = b\n",
        "    x1 = b - (b - a)/1000\n",
        "    while(abs(x1-x0) > eps): \n",
        "        if N > m:\n",
        "            return [x1, N, '2']               # итерации закончились\n",
        "        tmp = x1\n",
        "        x1 = x1 - (x1 - x0) * f(x1)/(f(x1) - f(x0))\n",
        "        if not a <= x1 <= b:\n",
        "            x0 = a\n",
        "            x1 = a + (b-a)/1000\n",
        "            while(abs(x1-x0) > eps):\n",
        "                  tmp = x1\n",
        "                  x1 = x1 - (x1 - x0) * f(x1)/(f(x1) - f(x0))\n",
        "                  x0 = tmp\n",
        "                  N += 1\n",
        "                  if not a <= x1 <= b:\n",
        "                      return [x1, N, '1']        #секущая убежала\n",
        "            return [x1, N, '0']                         \n",
        "        x0 = tmp\n",
        "        N += 1\n",
        "    return [x1, N, '0']\n",
        " \n",
        " \n",
        "eps = float(input('Введите точность: '))\n",
        "a = float(input('Введите начало отрезка: '))\n",
        "b = float(input('Введите конец отрезка: '))\n",
        "step = float(input('Введите шаг: '))\n",
        "m = int(input('Введите максимальное число итераций: '))\n",
        " \n",
        "res = []\n",
        "tabl = []\n",
        "restabl = []\n",
        " \n",
        "#разбиение на участки\n",
        "h = a\n",
        "while h < b:\n",
        "    if h + step > b:\n",
        "        step = b - h\n",
        "        #tempA.append(h)          # массив из а\n",
        "        #tempB.append(h + step)   # массив из b\n",
        "        #roots.append(sec(h,h+step,eps,m)[0]) # массив из x\n",
        "        #froots.append(f(sec(h,h+step,eps,m)[0])) # массив из f(x)\n",
        "        #print(sec(h,h+step,eps,m))\n",
        "        \n",
        "    if sec(h,h+step,eps,m) != '-' and sec(h,h+step,eps,m)[2] != '1':\n",
        "        res = res + sec(h,h+step,eps,m)\n",
        "        tabl = [h, h + step, f(sec(h,h+step,eps,m)[0])]\n",
        "        restabl.append(tabl)\n",
        "        restabl.append(res)\n",
        "        tabl = []\n",
        "        res = []\n",
        "    \n",
        "    if sec(h,h+step,eps,m) != '-' and sec(h,h+step,eps,m)[2] == '1':\n",
        "        res = ['-','-','1']\n",
        "        tabl = [h, h + step, '-']\n",
        "        restabl.append(tabl)\n",
        "        restabl.append(res)\n",
        "        tabl = []\n",
        "        res = []\n",
        "    h += step\n",
        " \n",
        " \n",
        "#Вывод таблицы\n",
        "g = 0\n",
        "n = 0\n",
        "p = round(len(restabl)/2)\n",
        "print('\\n')\n",
        "tab = '|№ Корня|     A     |     B     |      X    |      f(x)      | Число\\\n",
        " итераций | Код ошибки |'\n",
        "print(tab)\n",
        "print('-'*len(tab))\n",
        "for i in range(p):\n",
        "    print('|  ',i + 1,'  |', out(restabl[g][n]).center(9),'|',\\\n",
        "          out(restabl[g][n + 1]).center(9),'|',out(restabl[g + 1][n]).center(9),'|',\\\n",
        "          out(restabl[g][n + 2]).center(13),' |',\\\n",
        "          out(restabl[g + 1][n + 1]).center(9),'     | ',\\\n",
        "          restabl[g + 1][n + 2].center(9),'|')\n",
        "    if restabl[g + 1][n + 2] == '0':\n",
        "        plt.scatter(restabl[g + 1][n],restabl[g][n + 2])\n",
        "    print('-'*len(tab))\n",
        "    g = g + 2\n",
        " \n",
        "print('\\n\\nРасшифровка ошибок:\\n 0 - Ошибок не обнаружено. \\n 1 - Неправильное \\\n",
        "построение секущей.\\n 2 - Превышен предел итераций.')\n",
        " \n",
        "#График\n",
        "x = np.linspace(a,b,100)\n",
        "y=[]\n",
        "for i in range(len(x)):\n",
        "    y.append(f(x[i]))\n",
        "plt.plot(x,y,'r',label = '$x^2 - 4$')\n",
        "plt.title('$x^2 - 4$')\n",
        "plt.grid(True)\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**VAR** 2"
      ],
      "metadata": {
        "id": "4GermZIbZ87-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "    return x ** 3 - 18 * x - 83"
      ],
      "metadata": {
        "id": "UisiXhM4ZGAH"
      },
      "execution_count": 97,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "epsilon = float(input('Задайте точность: '))\n",
        "xs = []\n",
        "xs.append(float(input('Введите нулевую координату начального приближения: ')))\n",
        "xs.append(float(input('Введите первую координату начального приближения: ')))\n",
        "\n",
        "i = 1\n",
        "while abs(xs[i] - xs[i - 1]) >= epsilon:\n",
        "    xs.append(xs[i - 1] - f(xs[i - 1]) * (xs[i] - xs[i - 1]) / (f(xs[i]) - f(xs[i - 1])))\n",
        "    i += 1\n",
        "    \n",
        "print(xs[-1])"
      ],
      "metadata": {
        "id": "QCZRcU0KaHQh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "783f8848-e453-42ee-f434-e2ce26113804"
      },
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Задайте точность: 0.001\n",
            "Введите нулевую координату начального приближения: 1\n",
            "Введите первую координату начального приближения: 1\n",
            "1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**#VAR3**"
      ],
      "metadata": {
        "id": "mGE8AexBaU54"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "6eP-O3YcZxyX"
      },
      "execution_count": 98,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fnon= lambda x: np.sin(x-np.pi)\n",
        "\n",
        "from scipy.optimize import root_scalar\n",
        "x0=0\n",
        "x1=5\n",
        "tol=1e-8\n",
        "x= root_scalar(fnon,method='secant',x0=x0,x1=x1,rtol=tol)\n",
        "print(x)"
      ],
      "metadata": {
        "id": "4md-zNqUNa6S",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bb49e960-4433-42bd-e40e-6819f5663f58"
      },
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      converged: True\n",
            "           flag: 'converged'\n",
            " function_calls: 3\n",
            "     iterations: 2\n",
            "           root: 3.592664133576027e-15\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**VAR4**"
      ],
      "metadata": {
        "id": "1qzRH2THaisG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def secant(f, x0, x1, eps):\n",
        "        f_x0 = f(x0)\n",
        "        f_x1 = f(x1)\n",
        "        iteration_counter = 0\n",
        "        while abs(f_x1) > eps and iteration_counter < 100:\n",
        "            try:\n",
        "                denominator = float(f_x1 - f_x0)/(x1 - x0)\n",
        "                x = x1 - float(f_x1)/denominator\n",
        "            except ZeroDivisionError:\n",
        "                print(\"Error! - denominator zero for x = \", x)\n",
        "                sys.exit(1)     # Abort with error\n",
        "            x0 = x1\n",
        "            x1 = x\n",
        "            f_x0 = f_x1\n",
        "            f_x1 = f(x1)\n",
        "            iteration_counter += 1\n",
        "        # Here, either a solution is found, or too many iterations\n",
        "        if abs(f_x1) > eps:\n",
        "            iteration_counter = -1\n",
        "        return x, iteration_counter\n",
        "    \n",
        "def f(x):\n",
        "  return x ** 3 - 18 * x - 83\n",
        "        \n",
        "    \n",
        "x0 = 1000;   x1 = x0 - 1\n",
        "    \n",
        "solution, no_iterations = secant(f, x0, x1, eps=1.0e-6)\n",
        "    \n",
        "if no_iterations > 0:    # Solution found\n",
        "    print(\"Number of function calls: %d\" % (2 + no_iterations))\n",
        "    print(\"A solution is: %f\" % (solution))\n",
        "else:\n",
        "    print(\"Solution not found!\")"
      ],
      "metadata": {
        "id": "aJ6QWsIZN_cW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0606ac87-7e16-414e-9891-5233f79baa0f"
      },
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of function calls: 26\n",
            "A solution is: 5.705116\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eTgrBhkANftf"
      },
      "source": [
        "# Задание 4\n",
        "\n",
        "Постройте график и решить систему уравнений с помощью метода Ньютона и втроенной функции root:\n",
        "\n",
        "\\begin{cases}\n",
        "   x_1^2+(x_2-\\sqrt{|x_1|})^2 - 1 = 0\n",
        "   \\\\\n",
        "   x_1^2 x_2^3 - 7 x_1^3 x_2^3 - 7 = 0\n",
        "\\end{cases}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "id": "d_aXGnziNftg"
      },
      "outputs": [],
      "source": [
        "x, x1, x2 = symbols('x, x1, x2')\n",
        "\n",
        "F1 = x1**2 + (x2 - abs(x1)**0.5)**2 - 1\n",
        "F2 = x1**2*x2**3  -  7*x1**3*x2**3  -  7\n",
        "\n",
        "F1x1b = x1**4/(4*x2**2) + x1**3/(2*x2**2) + x1**2*(2*x2**2 - 1)/(4*x2**2) + x1*(-x2**2 - 1)/(2*x2**2) + (x2**4 - 2*x2**2 + 1)/(4*x2**2)\n",
        "F1x1a = x1**4/(4*x2**2) + x1**3/(2*x2**2) + x1**2*(2*x2**2 - 1)/(4*x2**2) + x1*(3*x2**2 - 1)/(2*x2**2) + (x2**4 - 2*x2**2 + 1)/(4*x2**2)\n",
        "\n",
        "def f1r(x1):\n",
        "    return (1 - x1**2)**0.5 + abs(x1)**0.5 \n",
        "\n",
        "def f2r(x1):\n",
        "    return (7 / (x1**2 - 7*x1**3)) ** (1/3)\n",
        "\n",
        "def f1(x1, x2):\n",
        "    return x1**2  +  (x2 - abs(x1))**2  -  1\n",
        "\n",
        "def f2(x1, x2):\n",
        "    return x1**2*x2**3  -  7*x1**3*x2**3  -  7"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = (x1**2 + x1 + x2**2 - 1)**2/(4*x2**2) + x1\n",
        "b = (x1**2 + x1 + x2**2 - 1)**2/(4*x2**2) - x1\n",
        "simplify(a),\n",
        "together(a),\n",
        "simplify(b),together(b), apart(a, x1)"
      ],
      "metadata": {
        "id": "rnv_1PA5NZVX",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "outputId": "ae69d4d6-baf4-4c5f-e063-2be8f26c0924"
      },
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎛                          2                                   2              \n",
              "⎜      ⎛  2          2    ⎞            2   ⎛  2          2    ⎞      4       3\n",
              "⎜      ⎝x₁  + x₁ + x₂  - 1⎠   - 4⋅x₁⋅x₂  + ⎝x₁  + x₁ + x₂  - 1⎠    x₁      x₁ \n",
              "⎜-x₁ + ─────────────────────, ──────────────────────────────────, ───── + ────\n",
              "⎜                  2                            2                     2       \n",
              "⎝              4⋅x₂                         4⋅x₂                  4⋅x₂    2⋅x₂\n",
              "\n",
              "                                                      ⎞\n",
              "      2 ⎛    2    ⎞      ⎛    2    ⎞     4       2    ⎟\n",
              "    x₁ ⋅⎝2⋅x₂  - 1⎠   x₁⋅⎝3⋅x₂  - 1⎠   x₂  - 2⋅x₂  + 1⎟\n",
              "─ + ─────────────── + ────────────── + ───────────────⎟\n",
              "2            2                2                 2     ⎟\n",
              "         4⋅x₂             2⋅x₂              4⋅x₂      ⎠"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left( - x_{1} + \\frac{\\left(x_{1}^{2} + x_{1} + x_{2}^{2} - 1\\right)^{2}}{4 x_{2}^{2}}, \\  \\frac{- 4 x_{1} x_{2}^{2} + \\left(x_{1}^{2} + x_{1} + x_{2}^{2} - 1\\right)^{2}}{4 x_{2}^{2}}, \\  \\frac{x_{1}^{4}}{4 x_{2}^{2}} + \\frac{x_{1}^{3}}{2 x_{2}^{2}} + \\frac{x_{1}^{2} \\left(2 x_{2}^{2} - 1\\right)}{4 x_{2}^{2}} + \\frac{x_{1} \\left(3 x_{2}^{2} - 1\\right)}{2 x_{2}^{2}} + \\frac{x_{2}^{4} - 2 x_{2}^{2} + 1}{4 x_{2}^{2}}\\right)$"
          },
          "metadata": {},
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "apart(b, x1)"
      ],
      "metadata": {
        "id": "AjXtj_8ybY6_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 60
        },
        "outputId": "e1761937-6444-419d-8a09-9c0d27f674e7"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   4       3      2 ⎛    2    ⎞      ⎛    2    ⎞     4       2    \n",
              " x₁      x₁     x₁ ⋅⎝2⋅x₂  - 1⎠   x₁⋅⎝- x₂  - 1⎠   x₂  - 2⋅x₂  + 1\n",
              "───── + ───── + ─────────────── + ────────────── + ───────────────\n",
              "    2       2            2                2                 2     \n",
              "4⋅x₂    2⋅x₂         4⋅x₂             2⋅x₂              4⋅x₂      "
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\frac{x_{1}^{4}}{4 x_{2}^{2}} + \\frac{x_{1}^{3}}{2 x_{2}^{2}} + \\frac{x_{1}^{2} \\left(2 x_{2}^{2} - 1\\right)}{4 x_{2}^{2}} + \\frac{x_{1} \\left(- x_{2}^{2} - 1\\right)}{2 x_{2}^{2}} + \\frac{x_{2}^{4} - 2 x_{2}^{2} + 1}{4 x_{2}^{2}}$"
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "F1X1 = diff(F1,x1)\n",
        "F1X2 = diff(F1,x2)\n",
        "F2X1 = diff(F2,x1)\n",
        "F2X2 = diff(F2,x2)\n",
        "\n",
        "J = sm.Matrix([[F1X1,F1X2],[F2X1,F2X2]])\n",
        "J"
      ],
      "metadata": {
        "id": "K-lRRCsFbjWF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "4d959d55-f52f-40ed-9eb7-a1a9039fd948"
      },
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡       ⎛         0.5⎞ ⎛        d                    d         ⎞     -0.5     \n",
              "⎢       ⎝x₂ - │x₁│   ⎠⋅⎜re(x₁)⋅───(re(x₁)) + im(x₁)⋅───(im(x₁))⎟⋅│x₁│    ⋅sign\n",
              "⎢                      ⎝       dx₁                  dx₁        ⎠              \n",
              "⎢2⋅x₁ - ──────────────────────────────────────────────────────────────────────\n",
              "⎢                                           x₁                                \n",
              "⎢                                                                             \n",
              "⎢                                    2   3          3                         \n",
              "⎣                             - 21⋅x₁ ⋅x₂  + 2⋅x₁⋅x₂                          \n",
              "\n",
              "                              ⎤\n",
              "(x₁)                          ⎥\n",
              "                       0.5    ⎥\n",
              "────      2⋅x₂ - 2⋅│x₁│       ⎥\n",
              "                              ⎥\n",
              "                              ⎥\n",
              "             3   2       2   2⎥\n",
              "      - 21⋅x₁ ⋅x₂  + 3⋅x₁ ⋅x₂ ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}2 x_{1} - \\frac{1.0 \\left(x_{2} - \\left|{x_{1}}\\right|^{0.5}\\right) \\left(\\operatorname{re}{\\left(x_{1}\\right)} \\frac{d}{d x_{1}} \\operatorname{re}{\\left(x_{1}\\right)} + \\operatorname{im}{\\left(x_{1}\\right)} \\frac{d}{d x_{1}} \\operatorname{im}{\\left(x_{1}\\right)}\\right) \\operatorname{sign}{\\left(x_{1} \\right)}}{x_{1} \\left|{x_{1}}\\right|^{0.5}} & 2 x_{2} - 2 \\left|{x_{1}}\\right|^{0.5}\\\\- 21 x_{1}^{2} x_{2}^{3} + 2 x_{1} x_{2}^{3} & - 21 x_{1}^{3} x_{2}^{2} + 3 x_{1}^{2} x_{2}^{2}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 104
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "F1X1A = diff(F1x1a,x1)\n",
        "F1X1B = diff(F1x1b,x1)\n",
        "F1X2A = diff(F1x1a, x2)\n",
        "F1X2B = diff(F1x1b, x2)\n",
        "\n",
        "Ja = sm.Matrix([[F1X1A,F1X2A],[F2X1,F2X2]])\n",
        "Ja"
      ],
      "metadata": {
        "id": "mtejwRPBb6pd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "fb309662-5474-429e-debc-2debcab59000"
      },
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡  3       2      ⎛    2    ⎞       2           4      3     2     2 ⎛    2   \n",
              "⎢x₁    3⋅x₁    x₁⋅⎝2⋅x₂  - 1⎠   3⋅x₂  - 1     x₁     x₁    x₁    x₁ ⋅⎝2⋅x₂  - \n",
              "⎢─── + ───── + ────────────── + ─────────  - ───── - ─── + ─── - ─────────────\n",
              "⎢  2       2           2              2          3     3    x₂            3   \n",
              "⎢x₂    2⋅x₂        2⋅x₂           2⋅x₂       2⋅x₂    x₂               2⋅x₂    \n",
              "⎢                                                                             \n",
              "⎢               2   3          3                                              \n",
              "⎣        - 21⋅x₁ ⋅x₂  + 2⋅x₁⋅x₂                                               \n",
              "\n",
              " ⎞             ⎛    2    ⎞       3            4       2    ⎤\n",
              "1⎠   3⋅x₁   x₁⋅⎝3⋅x₂  - 1⎠   4⋅x₂  - 4⋅x₂   x₂  - 2⋅x₂  + 1⎥\n",
              "── + ──── - ────────────── + ──────────── - ───────────────⎥\n",
              "      x₂           3                2                3     ⎥\n",
              "                 x₂             4⋅x₂             2⋅x₂      ⎥\n",
              "                                                           ⎥\n",
              "       3   2       2   2                                   ⎥\n",
              "- 21⋅x₁ ⋅x₂  + 3⋅x₁ ⋅x₂                                    ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{x_{1}^{3}}{x_{2}^{2}} + \\frac{3 x_{1}^{2}}{2 x_{2}^{2}} + \\frac{x_{1} \\left(2 x_{2}^{2} - 1\\right)}{2 x_{2}^{2}} + \\frac{3 x_{2}^{2} - 1}{2 x_{2}^{2}} & - \\frac{x_{1}^{4}}{2 x_{2}^{3}} - \\frac{x_{1}^{3}}{x_{2}^{3}} + \\frac{x_{1}^{2}}{x_{2}} - \\frac{x_{1}^{2} \\left(2 x_{2}^{2} - 1\\right)}{2 x_{2}^{3}} + \\frac{3 x_{1}}{x_{2}} - \\frac{x_{1} \\left(3 x_{2}^{2} - 1\\right)}{x_{2}^{3}} + \\frac{4 x_{2}^{3} - 4 x_{2}}{4 x_{2}^{2}} - \\frac{x_{2}^{4} - 2 x_{2}^{2} + 1}{2 x_{2}^{3}}\\\\- 21 x_{1}^{2} x_{2}^{3} + 2 x_{1} x_{2}^{3} & - 21 x_{1}^{3} x_{2}^{2} + 3 x_{1}^{2} x_{2}^{2}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Jb = sm.Matrix([[F1X1B,F1X2B],[F2X1,F2X2]])\n",
        "Jb"
      ],
      "metadata": {
        "id": "AtRJ2DP0c9fn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "d679fc5a-eafe-47a7-dfb7-4cf82359deff"
      },
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡  3       2      ⎛    2    ⎞       2           4      3     2     2 ⎛    2   \n",
              "⎢x₁    3⋅x₁    x₁⋅⎝2⋅x₂  - 1⎠   - x₂  - 1     x₁     x₁    x₁    x₁ ⋅⎝2⋅x₂  - \n",
              "⎢─── + ───── + ────────────── + ─────────  - ───── - ─── + ─── - ─────────────\n",
              "⎢  2       2           2              2          3     3    x₂            3   \n",
              "⎢x₂    2⋅x₂        2⋅x₂           2⋅x₂       2⋅x₂    x₂               2⋅x₂    \n",
              "⎢                                                                             \n",
              "⎢               2   3          3                                              \n",
              "⎣        - 21⋅x₁ ⋅x₂  + 2⋅x₁⋅x₂                                              -\n",
              "\n",
              " ⎞           ⎛    2    ⎞       3            4       2    ⎤\n",
              "1⎠   x₁   x₁⋅⎝- x₂  - 1⎠   4⋅x₂  - 4⋅x₂   x₂  - 2⋅x₂  + 1⎥\n",
              "── - ── - ────────────── + ──────────── - ───────────────⎥\n",
              "     x₂          3                2                3     ⎥\n",
              "               x₂             4⋅x₂             2⋅x₂      ⎥\n",
              "                                                         ⎥\n",
              "      3   2       2   2                                  ⎥\n",
              " 21⋅x₁ ⋅x₂  + 3⋅x₁ ⋅x₂                                   ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{x_{1}^{3}}{x_{2}^{2}} + \\frac{3 x_{1}^{2}}{2 x_{2}^{2}} + \\frac{x_{1} \\left(2 x_{2}^{2} - 1\\right)}{2 x_{2}^{2}} + \\frac{- x_{2}^{2} - 1}{2 x_{2}^{2}} & - \\frac{x_{1}^{4}}{2 x_{2}^{3}} - \\frac{x_{1}^{3}}{x_{2}^{3}} + \\frac{x_{1}^{2}}{x_{2}} - \\frac{x_{1}^{2} \\left(2 x_{2}^{2} - 1\\right)}{2 x_{2}^{3}} - \\frac{x_{1}}{x_{2}} - \\frac{x_{1} \\left(- x_{2}^{2} - 1\\right)}{x_{2}^{3}} + \\frac{4 x_{2}^{3} - 4 x_{2}}{4 x_{2}^{2}} - \\frac{x_{2}^{4} - 2 x_{2}^{2} + 1}{2 x_{2}^{3}}\\\\- 21 x_{1}^{2} x_{2}^{3} + 2 x_{1} x_{2}^{3} & - 21 x_{1}^{3} x_{2}^{2} + 3 x_{1}^{2} x_{2}^{2}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def fun(x):\n",
        "    f = np.zeros(2)\n",
        "    f[0] = f1(x[0],x[1])\n",
        "    f[1] = f2(x[0],x[1])\n",
        "    return f \n",
        "\n",
        "def jac(x):\n",
        "    JJ = J.subs({x1:x[0],x2:x[1]}).n()\n",
        "    print(JJ[0,0], JJ[1,0], JJ[0,1], JJ[1,1])\n",
        "    M = np.array( [[float(JJ[0,0]), float(JJ[0,1])], [float(JJ[1,0]), float(JJ[1,1])]] )\n",
        "    return M\n",
        "\n",
        "def jacA(x):\n",
        "    JJ = Ja.subs({x1:x[0],x2:x[1]}).n()\n",
        "    print(JJ[0,0], JJ[1,0], JJ[0,1], JJ[1,1])\n",
        "    M = np.array( [[float(JJ[0,0]), float(JJ[0,1])], [float(JJ[1,0]), float(JJ[1,1])]] )\n",
        "    return M\n",
        "\n",
        "def jacB(x):\n",
        "    JJ = Jb.subs({x1:x[0],x2:x[1]}).n()\n",
        "    print(JJ[0,0], JJ[1,0], JJ[0,1], JJ[1,1])\n",
        "    M = np.array( [[float(JJ[0,0]), float(JJ[0,1])], [float(JJ[1,0]), float(JJ[1,1])]] )\n",
        "    return M\n",
        "\n",
        "def NEWTON(n, fun, jac, x0, pr=0, tol=1.0e-5): \n",
        "    x = np.zeros(n)\n",
        "    b = np.zeros(n)\n",
        "    A = np.zeros((n,n)) \n",
        "    dx = np.zeros(n)\n",
        "    xStep = np.zeros((1000,n))\n",
        "    Error=2\n",
        "    i=0\n",
        "    x[:]=x0[:]\n",
        "    xStep[i][:]=x[:]\n",
        "    while Error>tol and i<999:\n",
        "        Error0=Error \n",
        "#        x0[:]=x[:]\n",
        "        b=-fun(x)\n",
        "        A=jac(x)\n",
        "        print(A)\n",
        "        dx = np.dot(linalg.pinv(A),b) # ошибка\n",
        "        x[:]=x[:]+dx[:]\n",
        "        Error=math.sqrt(np.dot(dx.T,dx))\n",
        "        k=sm.log(Error)/sm.log(Error0)\n",
        "        i=i+1\n",
        "        xStep[i][:]=x[:]\n",
        "        if pr>0:\n",
        "            if i>1: print('итерация:\\t%i \\t%.6e \\t ' %(i, Error), k)\n",
        "            else:   print('итерация:\\t%i \\t%.6e \\t ' %(i, Error))\n",
        "    return x, xStep, i"
      ],
      "metadata": {
        "id": "ptUPscHddB3o"
      },
      "execution_count": 107,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x10=0\n",
        "x20=2\n",
        "\n",
        "X0 = np.array([x10, x20])\n",
        "#sol, xStep, iStep = NEWTON(2, fun, jac, X0, pr=1, tol=1.0e-10)\n",
        "solA, xStepA, iStepA = NEWTON(2, fun, jacA, X0, pr=1, tol=1.0e-10)\n",
        "#solB, xStepB, iStepB = NEWTON(2, fun, jacB, X0, pr=1, tol=1.0e-10)\n",
        "\n",
        "A = -2\n",
        "B = 2\n",
        "N = 1000\n",
        "f1p = np.zeros((N))\n",
        "f2p = np.zeros((N))\n",
        "x = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    f1p[i] = f1r(x[i])\n",
        "    f2p[i] = f2r(x[i])\n",
        "\n",
        "plt.figure(figsize=(6,5))\n",
        "plt.plot(x, f1p, x, f2p)\n",
        "plt.plot(solA[0], solA[1], 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "fiiZ0MnBdaYt",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "9c623543-e9d3-426a-f42c-aaae6a954817"
      },
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.37500000000000 0 0.937500000000000 0\n",
            "[[1.375  0.9375]\n",
            " [0.     0.    ]]\n",
            "итерация:\t1 \t1.802678e+00 \t \n",
            "0.287274940271424 -47.2934052219580 0.453745837984261 73.6999838375793\n",
            "[[  0.28727494   0.45374584]\n",
            " [-47.29340522  73.69998384]]\n",
            "итерация:\t2 \t2.941540e+00 \t  1.83095580396573\n",
            "-59.5209132540163 143.503142385463 110.880688409973 730.848909463086\n",
            "[[-59.52091325 110.88068841]\n",
            " [143.50314239 730.84890946]]\n",
            "итерация:\t3 \t8.015290e-01 \t  -0.205048982169989\n",
            "-33.0048163565550 57.4451219004209 49.2454506603938 271.601838157538\n",
            "[[-33.00481636  49.24545066]\n",
            " [ 57.4451219  271.60183816]]\n",
            "итерация:\t4 \t7.920376e-01 \t  1.05384455381405\n",
            "-10.7496529298987 21.8919243090673 8.89526059409724 87.6296001295150\n",
            "[[-10.74965293   8.89526059]\n",
            " [ 21.89192431  87.62960013]]\n",
            "итерация:\t5 \t1.133958e+00 \t  -0.539207331144927\n",
            "1.91126274849852 6.02483320471223 1.44475028340929 12.0777662011367\n",
            "[[ 1.91126275  1.44475028]\n",
            " [ 6.0248332  12.0777662 ]]\n",
            "итерация:\t6 \t4.526424e+00 \t  12.0108261567222\n",
            "-21.7394007678105 -4170.81409765540 -17.3218866746953 10025.9237453209\n",
            "[[  -21.73940077   -17.32188667]\n",
            " [-4170.81409766 10025.92374532]]\n",
            "итерация:\t7 \t1.448613e+00 \t  0.245446042902505\n",
            "-7.21094982120492 -1846.56896429807 -2.36035889588968 3239.27383065375\n",
            "[[-7.21094982e+00 -2.36035890e+00]\n",
            " [-1.84656896e+03  3.23927383e+03]]\n",
            "итерация:\t8 \t1.662868e+00 \t  1.37219249382812\n",
            "-0.319168190502898 -757.223052716844 1.11573109067618 605.239607444270\n",
            "[[-3.19168191e-01  1.11573109e+00]\n",
            " [-7.57223053e+02  6.05239607e+02]]\n",
            "итерация:\t9 \t2.797213e+00 \t  2.02268374993309\n",
            "-355.423004201250 1.73609045664502 1861.24892669369 27.0586852270868\n",
            "[[-3.55423004e+02  1.86124893e+03]\n",
            " [ 1.73609046e+00  2.70586852e+01]]\n",
            "итерация:\t10 \t1.341799e+00 \t  0.285829737515878\n",
            "-348.955455676448 -0.00421529509637246 -1427.74409640285 0.198049882518585\n",
            "[[-3.48955456e+02 -1.42774410e+03]\n",
            " [-4.21529510e-03  1.98049883e-01]]\n",
            "итерация:\t11 \t1.368792e+02 \t  16.7309907027513\n",
            "-2418.31418908388 -13148819884.3133 -4697.17109882183 54469714405.4539\n",
            "[[-2.41831419e+03 -4.69717110e+03]\n",
            " [-1.31488199e+10  5.44697144e+10]]\n",
            "итерация:\t12 \t2.304730e+01 \t  0.637829938473184\n",
            "-2016.38692454034 -5280873782.37558 -3918.67489790225 21903966821.2294\n",
            "[[-2.01638692e+03 -3.91867490e+03]\n",
            " [-5.28087378e+09  2.19039668e+10]]\n",
            "итерация:\t13 \t1.921418e+01 \t  0.942024793035032\n",
            "-1680.67263519768 -2120855942.34930 -3267.70088242043 8808541278.47812\n",
            "[[-1.68067264e+03 -3.26770088e+03]\n",
            " [-2.12085594e+09  8.80854128e+09]]\n",
            "итерация:\t14 \t1.602006e+01 \t  0.938488276875436\n",
            "-1400.11923974366 -851744403.249761 -2722.94314717718 3542357909.74719\n",
            "[[-1.40011924e+03 -2.72294315e+03]\n",
            " [-8.51744403e+08  3.54235791e+09]]\n",
            "итерация:\t15 \t1.335844e+01 \t  0.934497700380151\n",
            "-1165.51613708056 -342065931.527789 -2266.64576000384 1424552622.53875\n",
            "[[-1.16551614e+03 -2.26664576e+03]\n",
            " [-3.42065932e+08  1.42455262e+09]]\n",
            "итерация:\t16 \t1.114060e+01 \t  0.929960538362285\n",
            "-969.187422307432 -137381082.857149 -1884.01229483827 572859474.798404\n",
            "[[-9.69187422e+02 -1.88401229e+03]\n",
            " [-1.37381083e+08  5.72859475e+08]]\n",
            "итерация:\t17 \t9.292583e+00 \t  0.924757512515951\n",
            "-804.736330380315 -55179890.4978578 -1562.71449808827 230346258.203530\n",
            "[[-8.04736330e+02 -1.56271450e+03]\n",
            " [-5.51798905e+07  2.30346258e+08]]\n",
            "итерация:\t18 \t7.752793e+00 \t  0.918732267716044\n",
            "-666.832425485584 -22166640.1821673 -1292.48391721734 92608198.1851250\n",
            "[[-6.66832425e+02 -1.29248392e+03]\n",
            " [-2.21666402e+07  9.26081982e+07]]\n",
            "итерация:\t19 \t6.469901e+00 \t  0.911675938703655\n",
            "-551.034479225103 -8906835.15456800 -1064.77312213310 37223187.5770163\n",
            "[[-5.51034479e+02 -1.06477312e+03]\n",
            " [-8.90683515e+06  3.72231876e+07]]\n",
            "итерация:\t20 \t5.401155e+00 \t  0.903303426293288\n",
            "-453.643193523759 -3580187.96584953 -872.475581807900 14956118.5668775\n",
            "[[-4.53643194e+02 -8.72475582e+02]\n",
            " [-3.58018797e+06  1.49561186e+07]]\n",
            "итерация:\t21 \t4.510956e+00 \t  0.893215765091817\n",
            "-371.578944517658 -1439866.16669983 -709.695342503242 6006057.41529031\n",
            "[[-3.71578945e+02 -7.09695343e+02]\n",
            " [-1.43986617e+06  6.00605742e+06]]\n",
            "итерация:\t22 \t3.769683e+00 \t  0.880838196302112\n",
            "-302.280606100068 -579530.380578856 -571.559512530594 2410010.69565664\n",
            "[[-3.02280606e+02 -5.71559513e+02]\n",
            " [-5.79530381e+05  2.41001070e+06]]\n",
            "итерация:\t23 \t3.152713e+00 \t  0.865313770818495\n",
            "-243.622295075732 -233514.187377639 -454.068260277404 965954.553091295\n",
            "[[-2.43622295e+02 -4.54068260e+02]\n",
            " [-2.33514187e+05  9.65954553e+05]]\n",
            "итерация:\t24 \t2.639632e+00 \t  0.845310862121027\n",
            "-193.845624633576 -94240.8850350585 -353.978674168171 386531.637273567\n",
            "[[-1.93845625e+02 -3.53978674e+02]\n",
            " [-9.42408850e+04  3.86531637e+05]]\n",
            "итерация:\t25 \t2.213591e+00 \t  0.818652259507573\n",
            "-151.505852113018 -38120.0699391352 -268.720504832862 154305.424398472\n",
            "[[-1.51505852e+02 -2.68720505e+02]\n",
            " [-3.81200699e+04  1.54305424e+05]]\n",
            "итерация:\t26 \t1.860836e+00 \t  0.781541661491693\n",
            "-115.431346997051 -15470.5494822125 -196.343582063215 61383.0022583994\n",
            "[[  -115.431347     -196.34358206]\n",
            " [-15470.54948221  61383.0022584 ]]\n",
            "итерация:\t27 \t1.570426e+00 \t  0.726776300524534\n",
            "-84.6975141240560 -6309.62350795524 -135.498489121917 24287.3770949405\n",
            "[[  -84.69751412  -135.49848912]\n",
            " [-6309.62350796 24287.37709494]]\n",
            "итерация:\t28 \t1.334303e+00 \t  0.638995831926931\n",
            "-58.6197883866468 -2593.19724235044 -85.4530052210577 9527.40979006740\n",
            "[[  -58.61978839   -85.45300522]\n",
            " [-2593.19724235  9527.40979007]]\n",
            "итерация:\t29 \t1.148185e+00 \t  0.479119636790696\n",
            "-36.7786590726163 -1079.35375439116 -46.1419821507703 3682.03605513657\n",
            "[[  -36.77865907   -46.14198215]\n",
            " [-1079.35375439  3682.03605514]]\n",
            "итерация:\t30 \t1.015299e+00 \t  0.109878029801626\n",
            "-19.1119697079758 -459.458016395944 -18.2113830468940 1381.03431144870\n",
            "[[ -19.11196971  -18.21138305]\n",
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            "итерация:\t95 \t2.443726e+01 \t  0.965667066362147\n",
            "20407413433.4718 -5.36054817908987 -104587477525301. -54792.2469056101\n",
            "[[ 2.04074134e+10 -1.04587478e+14]\n",
            " [-5.36054818e+00 -5.47922469e+04]]\n",
            "итерация:\t96 \t2.199709e+01 \t  0.967085351480906\n",
            "23783445610.3703 -1.94925991917359 -139735629459935. -22833.2307787468\n",
            "[[ 2.37834456e+10 -1.39735629e+14]\n",
            " [-1.94925992e+00 -2.28332308e+04]]\n",
            "итерация:\t97 \t2.031636e+01 \t  0.974284663450492\n",
            "27955260593.7796 -0.675927172870204 -189601682746713. -9136.16007080129\n",
            "[[ 2.79552606e+10 -1.89601683e+14]\n",
            " [-6.75927173e-01 -9.13616007e+03]]\n",
            "итерация:\t98 \t2.031960e+01 \t  1.00005301192029\n",
            "33867801900.8463 -0.199113213230491 -271645021511038. -3181.01061118947\n",
            "[[ 3.38678019e+10 -2.71645022e+14]\n",
            " [-1.99113213e-01 -3.18101061e+03]]\n",
            "итерация:\t99 \t2.635219e+01 \t  1.08632172927591\n",
            "48203960096.8367 -0.0273816240515173 -515770625181392. -582.970242937191\n",
            "[[ 4.82039601e+10 -5.15770625e+14]\n",
            " [-2.73816241e-02 -5.82970243e+02]]\n",
            "итерация:\t100 \t4.254505e-11 \t  -7.29942911765808\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  # Remove the CWD from sys.path while we load stuff.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:13: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  del sys.path[0]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x360 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x10=-10\n",
        "x20=-1\n",
        "\n",
        "X0 = np.array([x10, x20])\n",
        "\n",
        "solB, xStepB, iStepB = NEWTON(2, fun, jacB, X0, pr=1, tol=1.0e-10)\n",
        "\n",
        "A = -2\n",
        "B = 2\n",
        "N = 1000\n",
        "f1p = np.zeros((N))\n",
        "f2p = np.zeros((N))\n",
        "x = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    f1p[i] = f1r(x[i])\n",
        "    f2p[i] = f2r(x[i])\n",
        "\n",
        "plt.figure(figsize=(6,5))\n",
        "plt.plot(x, f1p, x, f2p)\n",
        "plt.plot(solB[0], solB[1], 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "IBX3oFN0d4BS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "2d785888-dc1e-4228-b1c8-f34f5c44b25a"
      },
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-856.000000000000 2120.00000000000 3960.00000000000 21300.0000000000\n",
            "[[ -856.  3960.]\n",
            " [ 2120. 21300.]]\n",
            "итерация:\t1 \t1.250819e+00 \t \n",
            "-900.177872569010 801.559875508160 4581.40922216266 8953.95516942199\n",
            "[[-900.17787257 4581.40922216]\n",
            " [ 801.55987551 8953.95516942]]\n",
            "итерация:\t2 \t1.063588e+00 \t  0.275461131073017\n",
            "-965.029792490363 300.637070483214 5441.61751371878 3769.45049688705\n",
            "[[-965.02979249 5441.61751372]\n",
            " [ 300.63707048 3769.45049689]]\n",
            "итерация:\t3 \t9.118638e-01 \t  -1.49664117293612\n",
            "-1053.78072749797 111.369238781211 6628.60096993795 1582.73602350960\n",
            "[[-1053.7807275   6628.60096994]\n",
            " [  111.36923878  1582.73602351]]\n",
            "итерация:\t4 \t7.937325e-01 \t  2.50376374153665\n",
            "-1173.21016015701 40.1831234632528 8298.16295633635 654.939015586432\n",
            "[[-1173.21016016  8298.16295634]\n",
            " [   40.18312346   654.93901559]]\n",
            "итерация:\t5 \t7.169031e-01 \t  1.44070120902889\n",
            "-1341.76862919670 13.4841691498235 10818.8212335290 257.019510700093\n",
            "[[-1341.7686292  10818.82123353]\n",
            " [   13.48416915   257.0195107 ]]\n",
            "итерация:\t6 \t7.215138e-01 \t  0.980737489306750\n",
            "-1634.32120027350 3.52419119231052 15620.2496873338 82.7301210625622\n",
            "[[-1.63432120e+03  1.56202497e+04]\n",
            " [ 3.52419119e+00  8.27301211e+01]]\n",
            "итерация:\t7 \t1.047224e+00 \t  -0.141366401952349\n",
            "-2951.34741058680 0.211243941802733 42572.7350950261 8.30056565926903\n",
            "[[-2.95134741e+03  4.25727351e+04]\n",
            " [ 2.11243942e-01  8.30056566e+00]]\n",
            "итерация:\t8 \t9.249262e+00 \t  48.2102699276137\n",
            "762.519801194348 -108.715194368211 -4126.54784629726 -1116.10175217114\n",
            "[[  762.51980119 -4126.5478463 ]\n",
            " [ -108.71519437 -1116.10175217]]\n",
            "итерация:\t9 \t7.277148e-01 \t  -0.142881452426888\n",
            "848.506514123656 -39.7020882886271 -5140.45545534624 -454.035810644568\n",
            "[[  848.50651412 -5140.45545535]\n",
            " [  -39.70208829  -454.03581064]]\n",
            "итерация:\t10 \t6.682062e-01 \t  1.26840777384871\n",
            "968.635680770804 -13.3313712062767 -6658.37061910372 -172.312241473740\n",
            "[[  968.63568077 -6658.3706191 ]\n",
            " [  -13.33137121  -172.31224147]]\n",
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            "6230233362.97129 1050700271753.55 2738836292803.90 -923722795197974.\n",
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            "итерация:\t71 \t4.157968e+01 \t  0.968122594521876\n",
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            "итерация:\t72 \t3.641080e+01 \t  0.964388473406840\n",
            "403991174341.716 1.01500940165217 7.42021495993598e+15 -37218.2171044104\n",
            "[[ 4.03991174e+11  7.42021496e+15]\n",
            " [ 1.01500940e+00 -3.72182171e+04]]\n",
            "итерация:\t73 \t2.407710e-11 \t  -6.80130021192960\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  # Remove the CWD from sys.path while we load stuff.\n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:13: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  del sys.path[0]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x360 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "jacB(x)\n"
      ],
      "metadata": {
        "id": "-RE3iBwdLBo8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3ec437cb-d6d5-439a-dad1-63083b6a8b34"
      },
      "execution_count": 110,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-2.87650602258128 699.780231044220 -0.935121114587984 717.120002885769\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ -2.87650602,  -0.93512111],\n",
              "       [699.78023104, 717.12000289]])"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "SOLB = root(fun, X0, jac = jacB, method='hybr')\n",
        "#SOLB = root(fun, X0)\n",
        "print(SOLB)\n",
        "\n",
        "plt.figure(figsize=(6,5))\n",
        "plt.plot(x, f1p, x, f2p)\n",
        "plt.plot(SOL.x[0], SOL.x[1], 'o')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "35WFlaCHeEQd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 705
        },
        "outputId": "dff68dd6-ef46-45ca-cd32-8f3b23996568"
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-856.000000000000 2120.00000000000 3960.00000000000 21300.0000000000\n",
            "-856.000000000000 2120.00000000000 3960.00000000000 21300.0000000000\n",
            "87.8642949630796 0.0241425781935049 213.055406749909 -0.185705117621948\n",
            "61.4916240308842 0.0266504334629697 119.407341398034 -0.180693172369241\n",
            "-1.52640469798188 0.318788737582753 0.297144801439695 -0.307081242519296\n",
            "4.42046570700838 3.78794168013239 1.80955699730501 -5.91616743599028\n",
            "2.92442305767688 12.7420086962638 0.594419456580125 -14.7823116906800\n",
            "1.26300449325518 20.4712460294724 -0.346178751020507 -15.9401596169642\n",
            "    fjac: array([[-0.27181517, -0.96234948],\n",
            "       [ 0.96234948, -0.27181517]])\n",
            "     fun: array([ 3.86574763, -1.09272031])\n",
            " message: 'The iteration is not making good progress, as measured by the \\n  improvement from the last ten iterations.'\n",
            "    nfev: 62\n",
            "    njev: 7\n",
            "     qtf: array([-0.02444307,  4.01754282])\n",
            "       r: array([-21.44863437,  16.07960429,   0.31195044])\n",
            "  status: 5\n",
            " success: False\n",
            "       x: array([ 0.91061546, -1.09849556])\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2lsE3WnYNftj"
      },
      "source": [
        "# Задание 5\n",
        "\n",
        "Напишите программу реализующую метод золотого сечения (https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%B7%D0%BE%D0%BB%D0%BE%D1%82%D0%BE%D0%B3%D0%BE_%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 112,
      "metadata": {
        "id": "Ru_Qjdv-Nftj"
      },
      "outputs": [],
      "source": [
        "def f(x):\n",
        "    return x ** 2\n",
        "\n",
        "def lf(a, b, epsilon, phi):\n",
        "    while abs(b - a) >= epsilon:\n",
        "        x1 = b - (b - a) / phi\n",
        "        x2 = a + (b - a) / phi\n",
        "        y1 = f(x1)\n",
        "        y2 = f(x2)\n",
        "        if y1 >= y2:\n",
        "            a = x1\n",
        "        else:\n",
        "            b = x2\n",
        "    return (a + b) / 2\n",
        "\n",
        "def hf(a, b, epsilon, phi):\n",
        "    while abs(b - a) >= epsilon:\n",
        "        x1 = b - (b - a) / phi\n",
        "        x2 = a + (b - a) / phi\n",
        "        y1 = f(x1)\n",
        "        y2 = f(x2)\n",
        "        if y1 <= y2:\n",
        "            a = x1\n",
        "        else:\n",
        "            b = x2\n",
        "    return (a + b) / 2"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = float(input('Задайте начало отрезка: '))\n",
        "b = float(input('Задайте конец отрезка: '))\n",
        "epsilon = float(input('Задайте точность вычислений: '))\n",
        "\n",
        "phi = 0.5*(1 + 5 ** 0.5)\n",
        "\n",
        "print('Минимум равен', f(lf(a, b, epsilon, phi)))\n",
        "print('Максимум равен', f(hf(a, b, epsilon, phi)))"
      ],
      "metadata": {
        "id": "9pBR6cvNeXpH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5842c640-70e5-49ff-d88b-2331f226d4ac"
      },
      "execution_count": 113,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Задайте начало отрезка: 1\n",
            "Задайте конец отрезка: 5\n",
            "Задайте точность вычислений: 0.0001\n",
            "Минимум равен 1.0000624239208162\n",
            "Максимум равен 24.999687886240864\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4b7Z3SHNftj"
      },
      "source": [
        "# Задание 6\n",
        "\n",
        "Выполните Упражнение 8.2 (с. 213) из книги Численные методы. Вычислительный практикум (Вабищевич П.Н. - 2010)."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import math as mt\n",
        "def golden(f, a, b, tol=0.000000000001):\n",
        "\n",
        "  c1 = (mt.sqrt(5) - 1) / 2\n",
        "  c2 = 1. - c1\n",
        "  nit = int(mt.ceil(mt.log(tol / abs(b-a)) / mt.log(c1)))\n",
        "  \n",
        "  # First step\n",
        "  x1 = c1*a + c2*b\n",
        "  x2 = c2*a + c1*b\n",
        "  f1 = f(x1)\n",
        "  f2 = f(x2)\n",
        "  # Iteration\n",
        "  for i in range(nit):\n",
        "    if f1 > f2:\n",
        "      a = x1\n",
        "      x1 = x2\n",
        "      f1 = f2\n",
        "      x2 = c2*a + c1*b\n",
        "      f2 = f(x2)\n",
        "    else:\n",
        "      b = x2\n",
        "      x2 = x1\n",
        "      f2 = f1\n",
        "      x1 = c1*a + c2*b\n",
        "      f1 = f(x1)\n",
        "  if f1 < f2:\n",
        "    return x1,f1\n",
        "  else:\n",
        "    return x2,f2\n"
      ],
      "metadata": {
        "id": "eDTk9GnxbgaB"
      },
      "execution_count": 121,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as pit\n",
        "#from golden import golden\n",
        "def f(x):\n",
        "  return (x**2 - 6.*x + 12.) / (x**2 + 6.*x + 12.)\n",
        "a = 0.\n",
        "b = 20.\n",
        "x = np.linspace(a, b, 200)\n",
        "у = f(x)\n",
        "y= (x**2 - 6.*x + 12.) / (x**2 + 6.*x + 12.)\n",
        "pit.plot(x, y)\n",
        "pit.xlabel('x')\n",
        "pit.grid(True)\n",
        "pit.show()\n",
        "xMin, fMin = golden(f, a, b)\n",
        "print('xMin = ', xMin)\n",
        "print('fMin = ', fMin)\n",
        "xMin - 3.46410163303\n",
        "fMin = 0.0717967697245\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "151g_-mOdjYS",
        "outputId": "42dff8ec-eecf-4461-abde-638be75c021d"
      },
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "xMin =  3.4641016330255576\n",
            "fMin =  0.07179676972449077\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 117,
      "metadata": {
        "id": "i6VxFVyhNftj"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "#import math as mt\n",
        "\n",
        "#from golden import golden\n",
        "def grad(F, GradF, x, d=0.5, tol=1.e-10):\n",
        "\n",
        "  # Line function along h\n",
        "  def f(al):\n",
        "    return F(x + al*h)\n",
        "  grO = - GradF(x)\n",
        "  h = grO.copy()\n",
        "  F0 = F(x)\n",
        "  itMax = 50000000\n",
        "  for i in range(itMax):\n",
        "  # Minimization ID function\n",
        "    al, fMin = sc.optimize.golden(f, 0, d)\n",
        "    x = x + al*h\n",
        "    Fl = F(x)\n",
        "    grl = - GradF(x)\n",
        "    if (mt.sqrt(np.dot(grl,grl)) <= tol) or (abs(F0 - Fl) < tol):\n",
        "      return x, i+1\n",
        "    h = grl\n",
        "    grO = gr1.copy()\n",
        "    F0 = Fl\n",
        "    print(\"Gradient method did not converge (500 iterations)\")\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9oSGeD7-Nftj"
      },
      "source": [
        "# Задание 7\n",
        "\n",
        "Найти все максимумы и минимумы с помощью разработанных программ (методом градиентного спуска) рассматриваемой функции $f(x)=(1+x+x^2) \\cdot e^{-x}+sin(x+0.1)-1$ на отрезки [-1.0;25]. Определить глобальный максимум (наибольший локальный максимум) и минимум на этом отрезке."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 118,
      "metadata": {
        "id": "XKdexe8dNftj"
      },
      "outputs": [],
      "source": [
        "def f(x):\n",
        "    return (1 + x + x ** 2) * sm.exp(-x) + sm.sin(x + 0.1) - 1\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A = -1\n",
        "B = 25\n",
        "N = 1000\n",
        "fp = np.zeros((N))\n",
        "x = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    fp[i] = f(x[i])\n",
        "\n",
        "plt.figure(figsize = (10,  5))\n",
        "plt.plot(x, fp)\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "MyOphqkseqmn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "outputId": "6ca401f3-a3d5-4f79-a426-45d550e0bdc9"
      },
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ],
            "image/png": 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wJC0SdWm3hmeDm6pLpx4tZG+uEa0jc0KHQQghhMgGJWlhSr83khb+dGeoia2YN1Vfy54cI/qsi1hwRnb3BUIIISReUZIWJlOSBoxFZiStZcCOkrQkpIp4U/W17M4NLHRoG6PFA4QQQkgkUJIWJpVSAXOSJuwkze/nuDY4g8MS2K9zNbuzA0nanVGa8iSEEEIigZK0CLDotWE3tO2ZdmDe6ZXkVCcQWECRadBRkkYIIYRECCVpEZCWrMXkfHirO1sGgpuqS3QkDQB25xjRSkkaIYQQEhGUpEVAtjEBY7PhJWlXB+yw6DUoNCdGKKrYCy0ecLgi09iXEEIIiWeUpEVAdkoCrA4XXN7tb4t0pd+Ow4UmSWyqvpY9uQZwDrTT4gFCCCEkbJSkRUBWig4AMDm3vbo027Ifo7PLkl00EBJaPEBTnoQQQkj4KEmLgGxjAgBgdHZ5Wz/fNeMHAFQXSTtJSzfokJ6sRRslaYQQQkjYKEmLgOzgSNr43PaStLszPiRrVdiVZYhkWILYQ4sHCCGEkIigJC0CsoIjaeNz21s80DXjw8GCVCgV0q1HC9mdY0TvtANLblo8QAghhISDkrQISNAokZqo3tZ058yiG2MOLvmpzpA9OUb4afEAIYQQEjZK0iIkOyUB49tI0q4O2AFIvx4tZHcOLR4ghBBCIoGStAjJTU3A8Mz2kjSVAtgb3PtS6jIMWlj0WtwZpZE0QgghJByUpEVIoTkJQ7Yl+Px8Sz93pd+OYqMCWpUySpHFFmMMe3IMtD0UIYQQEiZK0iKk0JIEt8+PsS1MeTpcXtwZm8eOVHkkaCF7cozonlrAsnv7zX0JIYSQeEdJWoQUmpMAAAO2xU3/THOfDT4/R4VZXkna7tDigXGa8iSEEEK2S9AkjTH2KGPsLmOshzH2p6t8X8sYez74/WbGWGHso9ycIkswSbNuPkm70GOFVqVAaYq8cuXQ4oH2MZryFMqQbQk/vzaCZ5sG8HbnFI1qEkKIBKmEOjBjTAngOwAeAjAC4Cpj7GXOefuKp/0egBnOeSlj7EkAfwngN2Mf7cYyDFokqJXoty5t+mcudFtRXWSCRrm9JrhilWXUISVRTSNpAuiZcuAbr7TjfNf0ex5P1qrw1IliPHWyWDb1j4QQIneCJWkAqgH0cM77AIAx9hyAJwCsTNKeAPA/gn//GYB/YIwxzvnWqvNjgDGGAnPipqc7J+ed6J5y4OOHcgE+HOXoYosxhoosA/VKi7Ff3RrDf/7pLSRolPjqIzvxcEUGjIlq3J1YwI+aBvHXb3bh3N0pPPM7VUhL1godLokgv5/D7fNDp6YEXO48Pj+UjEEhg+bnZGNCJmk5AFZmJyMAatZ6DufcyxibA2AGYI1JhFtUmq7HzeHZTT33Yk/gn3C01AJrt7ySNACozDbg2aZBeH1+qJTyms4VoxdvjOA/Pn8L1YUm/MNvH0B6su7e99KTdTheloZXW8fxn164hSefacJzT9VRoiZxnHO82T6JH1waQMvADNw+Pyx6DR6qyMAfnSxFvjlR6BBJhCw4PfiXCwN46dYo+q2LUDCGymwDPlGVh9+syoNGRfdYuWJCDUoxxj4O4FHO+ReCX/8OgBrO+ZdWPOdO8Dkjwa97g895X5LGGHsKwFMAkJGRcei5556Lwb/ivV7pc+NnXR5854FEJKnX/5Tzz7ecaLP58HenErG0uAi9Xh+jKGPj0pgXz9x24ZtHE5CTLI0biMPhkOR5aLf58NctTuxIVeA/HtJBo1z7d++uPfDcQqMC/+WwDioRfhqX6nmIpUUPx/daXbgx5UNaAsPBdCX0GoZRhx/Xp3zw+4EnyzV4IF8FxrZ+jukciIPD4cCIOwH/dMuFORdHpVmB0hQlvH7gjs2HwXk/8pIVeHqfFll6adxnpSZW18KpU6eucc6r7n9cyJG0UQB5K77ODT622nNGGGMqAEYAttVejHP+DIBnAKCqqorX19dHOt6NZU3hZ11XYS7Zi9pi85pP8/j8+HLDm3h0Ty5On9qHhoYGCBJvFGVNLOCZ2+eRmLsD9QdyhQ5nU6R4Hibnnfj/vn0epenJeP6P6mDQqdd9fj2AzOJR/IfnbqJxIQ1//sTumMS5FVI8D7E0veDCp7/XjD6bH//tA7vw2SOF7xmtnpx34mu/aMW/dUwhMS0XX3usfMuJGp0DcfjbF97Cd266kG9OxLOf3I99eSn3vhcaSf3TX7TiL6978eznq7E3N2WdVyPbIfS1IGTqfRVAGWOsiDGmAfAkgJfve87LAD4T/PvHAZwTYz1aSGV2YFVj2wa1WFf67VhwevFgRUYswhJESVoSNCoF1aVFEeccX/3ZbTg9Pvzjpw9umKCFPLE/B58/WoQfNg3em3Yn0uD0+PCFZ1swZF/CDz5XjS8cL35fOUGGQYfv/W4Vfqe2AM+c78P/O98nULQkHBd7rPjODRcqsw345RePvidBAwK1vw9XZuLFp48gSaPC539wFSMzm1+4RqRBsCSNc+4F8CUAZwB0AHiBc97GGPsGY+zDwad9H4CZMdYD4I8BvK9Nh5ikJWuRlqzdMDF5s30SWpUCx8ssMYos9lRKBcozk2mFZxT99NoIzndN4+uP70JJ2taG4//LoztRZEnC137RSu05JIJzjj/5+W3cHpnFt5/cj6Ola98/FAqGbzxRiQ/szcJfvt6JhrtTMYyUhGtizokv/+QGMpIYnv18zbofwArMSfjh56vh8vrxhR+20PUsM4JOYnPOX+Wc7+Ccl3DOvxl87M845y8H/+7knH+Cc17KOa8OrQQVs8psA26PrL14IDREfbzMgkSNkLPN0VeRZUDb2DxEPPgpWfNOD771eicOFaTi07UFW/55nVqJ//3RPRiyL+EfG3qiECGJtJdvjeGlm2P44wd34JHKzA2fzxjDX318L3ZmJOM/vXAL9kV3DKIk4fL5Ob7y3A04PT58cb8OxsSNR8hL0/X4h986iM6JBXzrTGcMoiSxQpWGEVZTZEb3lAPTC65Vv39zeBajs8t4uGLjm6zUVWYbMLvkwficU+hQZOf/nu2GbdGN//Ghym0VhgNAbbEZH9ybhe819mNqns6RmE0tOPHfX27DgfwUPH2qdNM/l6hR4e+ePIB5pwf/85X2jX+ACO7HV4Zwpd+OP/9wJbK3sBjg5I40fKauAD+4NIAr/fYoRkhiiZK0CDtSElgw0NS36voG/OL6KLQqBR7dI/8krSLbAABUlxZh43PL+OGlQXz8YC725BrDeq2vPrITXr8f3z7bHaHoSDT8xWudWHL58Fcf3wflFlfk7sxMxtP1pXjxxigau6c3/gEimOkFF771eieOlJgDPTS36E8eK0duagK+/mIrvD5/FCIksUZJWoTtzjEiWafCpVUKsp0eH351ewyPVGZuushbysozDWBs44UUZGv+8e1e+DnHVx4oC/u1CsxJ+K3qfDx/dZiKjkXqzugcfnF9FJ87VojS9O21Anj6VAnyTAn4X692wuen8gOx+j9n7sLp8eEbT+ze1gh5okaFrz9ege4pB55vkV//zXhESVqEKRUMR0rMONc59b5PMi/dHMXskge/eThvjZ+WlyStCkXmJLSP0x6ekTI2u4znrw7jE1V5yDNFplnpH9aXQMGA79IqQNHhnOObv+6AKUmDL25hmvN+WpUSX32kHB3j8/jljfs7HREx6Jt24GfXR/Dp2oJtJ+MA8EhlBqoLTfjbN7vgcHkjGCERAiVpUfDRg7mYWnDhnRX7J/r9HN9t7EdFluHelGg82JVtoBWeEfSvF/vh4xxfPFUSsdfMMibgN/bn4Lmrw7A6Vq+lJMJo7rejqc+GL58uDXv0/YN7srA314i/ebMLHpoKE51vv9UNjVKBp+u3n4wDgQUjX3u8HFaHGz9qGoxQdEQolKRFwenydFj0Wvx789C9x/79yhB6phz4o/qSbRd6S1FFlgHD9mXMLXuEDkXyHC4vnrs6jMd2ZyI3NbJb/vxhfQncPj/d1EXmH871wKLX4lPV+WG/lkLB8JXTZRidXcavbo1FIDoSKb3TDvzq9hg+e7QwItu1HchPxfEyC75/oY9ackgcJWlRoFYq8Jm6ApzrnMKZtgl0TszjW6914lipBR/cmyV0eDFVGVw80EGjaWH7+bURLDi9+Pyxooi/dkmaHid3pOEnV4ZolEUkbg7P4kKPFb9/vChiG6efLk/Hzoxk/FNDL/xUmyYa/3KhH2qlAr8XwWv7S6dKYXW48dzVoY2fTESLkrQo+f0TxdiTY8Qf/OgaHvu7RiRoAn2p4mkUDaAVnpHi93P84NIA9uel4GB+alSO8emaAkwtuPBW+2RUXp9szfca+2DQqfDb2+iDtxaFguHpUyXonnLgXCc1uBUD+6IbP78+go8eyIFFH/4oWkhNsRlVBan4/oV+WiwiYZSkRYlOrcSPf78GX31kJ758qhSvfPlYxAq9pSQ9WQeLXksrPMP0Ttc0+q2L+NzRwqgd41R5OnJSEvBvzTTlKbSpeSdevzOBT1blQa+NbNPrD+zJQqZBh2cv03kWgx83D8Lp8UdlhPxzR4swMrNMO05IGCVpUZSsU+OLp0rxxw/vRLpBJ3Q4gqmkxQNh+8mVIVj0Gjy2O3rT5UoFw6eq83Cxx4a+aUfUjkM29uMrQ/D6+bZ2k9iISqnAk9V5ON81jUHbYsRfn2ye2+vHD5sGcXJHGnZkJEf89R+uzECGQYtnqdZUsihJI1FXkW1Az9QC3F6qddoOq8OFc51T+OjBXGhU0b1kP3k4DyoFw3NXqceSUDw+P37cPISTO9JQaEmKyjE+VZ0PpYLhx81UrySkN9snMb3gwmejNEKuVirwqep8vNM1jQErJeRSREkaibqKLAM8Po6uyQWhQ5GkX94YhdfP8YltdCDfqvRkHep3puGlm6NUxyKQN9omMbXgwu/WRX4ULSTDoMPDFRl4oWUYTg+t/hPK8y3DyDbqcKIsLWrH+K3qfKgUDP9G09uSREkaibrQCk+a8tw6zjmevzqMA/kpKIvCdMhqPnIgF5PzLjT1rr61GYmuF1qGkZOSgPqd6VE9zqdrCzCz5MHrdyaiehyyurHZZTR2T+Pjh3K3vNXXVqQbdHi4MgO/uDFKK7cliJI0EnUF5iQkapS0wnMbbo3MoXvKgU9WxW6Xigd2pSNZq8KL1Jk+5ibnnWjsnsZHDuRE9Y0bAOqKzchNTcDPr49E9ThkdT+7NgLOgU/E4Nr+2MFc2BfdeOcu7d0qNZSkkahTKhjKM5MpSduGF6+PQKtSxLS/nk6txON7svD6nXFqhBljL90chZ8DHzmYE/VjKRQMHzmQg4s9VkzNO6N+PPIuv5/jhZZhHCkxx2TV/4kdaTAnafCLG5SQSw0laSQmKrONaB+fpwaaW+Dzc7x6ZwKny9ORHOaWQFv1GwdysOj24Y12mgqLFc45fn5tFPvzUlCStv29G7fiIwdy4OfASzdpB4JYujpgx8jMcsxGyNVKBT68PxtvtU9hbol2f5ESStJITFRkG+BweTE8syR0KJLR3G/D9IILH9ybHfNj1xSZkGXU4ZXb4zE/drxqH5/H3ckFfCwGo2ghxWl67MtLwS9oajumfnV7DAlqJR6uzIjZMT92MBdunx+vtFJCLiWUpJGYqMiinQe26pXb40jUKHG6PLoF5KtRKBgeqczEO13TcLi8MT9+PPrljVGolSzmSflH9mejY3wenRN0bcaC1+fHq60TeGBXOhI1kW1UvJ7KbAN2ZOjxi+uUkEsJJWkkJnZmJkOpYLTCc5M8Pj9eax3HA7sykKCJzL6NW/X4niy4vX68TdsHRR3nHK+2TuB4WRpSkzQxPfaH9mVDqWB4maY8Y+JSrw32RTc+tC+2yThjDB/am41rgzOYmKMaRKmgJI3EhE6tRElaEm0PtUmXem2YWfLEdMHA/Q4VpMKi1+K1OzTlGW2to3MYnV3Go7szY35ss16LumIzXrszAc6pZjTafnVrDMlaFU7uiF5vtLU8HryfvE7XtGRQkkZipiLLgLaxOaHDkIRXBLyRhygVDI9UZuDtzmla5Rllr7ZOQKVgeLgidjVKKz26OxP91kXcpYbTUeXy+nCmbQIPVWZAp479CHlJmh47M5LxaistCPkJNtUAACAASURBVJIKStJIzFRmGzE574LN4RI6FFHz+PyC3shXenxPFpY9PrzTRf2VooVzjtfvjKOuxIyUxNhOdYY8UpkJxoDX6M07qi712DDv9OJDAiwGCnlsTyauDtqp7YpEUJJGYqaCdh7YlCv9dsw7vXi0MvZTX/erKTIhJVGNM2305h0tHeMLGLAt4bHdwk1tpyVrcbjQRFPbUfZG+ySSNEocKTULFsMH9mSBc9A1LRGUpJGYCW0PRXVp63uzfRI6tQLHo7if32aplAqc2pmOhrtTtJdnlLx+ZxwKhpi2Y1jN47sz0TXpQM+UQ9A45Mrv53irYxL1O9OhVQk3Ql6WkYzSdD1+3UoJuRRQkkZiJiVRg5yUBErS1sE5x5vtkzhWmibYqs77nS5Px8ySBzeHZ4QORZZevTOB6iITLHqtoHE8GhzJoxGW6Lg1MovpBRceEqjucKVHKjNwdWCGGttKACVpJKZ2ZRnQTosH1tQ+Po/R2WU8VBH73mhrObEjDUoFw9kOasURab3TgZErIac6QzKNOuzJMeJsx6TQocjSm+2TUCoYTu0U/tp+YFcGfH6Ohi66psWOkjQSU5XZBvRZF7Hkpgapq3mzfRKMAafLhf+0HWJMUONwYSrOUb+0iAv1oHtgl/Bv3EBg1PTG8Czm3TS1HWlvtE+ipsgEY2Jst3hbzf7cFFj0GvrgJQGUpJGYqsw2gPNAsTR5v7c6JnEwPxVpycJOfd3vgfIMdE4sYHR2WehQZOVsxxR2ZOiRmxr9TbY348FdGeAcaJ2mD1GR1G9dRM+UQxRTnUBgR5FQranH5xc6HLKOdZM0xpiBMVayyuN7oxcSkTNa4bm2sdll3BmdF82NfKXTwZEeGk2LnHmnB1cH7KIaNa3MNiA9WYub09QXL5LebA/U+Ynp2n5gVzrmnV60DFCtqZitmaQxxj4JoBPAzxljbYyxwyu+/YNoB0bkKSclAcYENdWlrSJUCySmG3lIsSUJheZEnKN6pYi50G2F188F2Zt1LQoFw+nydNyx+uD20ghLpLzVMYVdWQbRjJgCwPGyNGiUCqpBFLn1RtL+K4BDnPP9AD4H4EeMsY8Ev8eiHhmRJcYYKrMNtNH6Ks51TqHQnIiSNL3QobwPYwynyzNwsddGuw9EyNmOKRgT1DiYnyJ0KO9xujwdy16gZcAudCiyMO/04PrgDE6XC99SZ6UkrQq1JWYaHRe59ZI0Jed8HAA451cAnALw3xhjXwEQVlUpY8zEGHuTMdYd/G/qGs/zMcZuBv+8HM4xiXhUZBnQObEAL9VC3OP0+NDUZ0O9CFZ+raV+ZxrcXj+a+21ChyJ5fj9Hw90pnNyRBpVSXKXBR0stUCmAs/TmHRGXemzw+jlOiKDv4f0e3JWOPusi+qapN55YrXd3WFhZjxZM2OoBPAGgMszj/imAs5zzMgBng1+vZplzvj/458NhHpOIRGWOAS6vH73Ti0KHIhrN/XY4PX6c3Cm+G3lIdZEJGpUCjd1WoUORvFsjs7AtukU11RmSpFVhl0lJ02AR8k7XNPRaFQ4WrDoWIajQ7x+NponXeknaHwFQMMYqQg9wzhcAPArgC2Ee9wkAPwz+/YcAfiPM1yMSUpltBAC0j1NdWsg7d6ehVSlQVyzcdjEb0amVqC404QIlaWF7u3MKCgac3CHOpHxfmhIDtiUM2uiDVDg45zjfNY2jpWaoRTZiCgC5qYkoTkvChR66psVqzd8azvktznk3gBcYY3/CAhIA/A2Ap8M8bkZoKhXABIC1KqV1jLEWxthlxhglcjJRbEmCVqVA2yjVpYU0dE2hptgs+IbqGzleZsHdyQVM0ubMYXmn24p9eSlITRJmQ/WN7LYEfg9p1DQ8vdMOjM4u4+QO8Y2YhpwoS8PlPhucHqo1FSPVJp5TA+AvAVwCkAzg3wEc3eiHGGNvAVhth+ivr/yCc84ZY2vVuBVwzkcZY8UAzjHGWjnnvWsc7ykATwFARkYGGhoaNgpRNBwOh6TijYTsJOBi+yAa9OIZZhfqPEwv+dE3vYxas0f0vwe6+cCN/Lu/asSxnOg05ZT79eBwc9weXsKHS9Si/Xcm+Zdg1inwYlMHcp39QocjWWcGAtsuaew9aGjo2/LPx+JaSHF64fT48S8vN6DCLO4PiUIQ+n60mSTNA2AZQAIAHYB+zvmGFd+c8wfX+h5jbJIxlsU5H2eMZQFY9Z2acz4a/G8fY6wBwAEAqyZpnPNnADwDAFVVVby+vn6jEEWjoaEBUoo3Es7YW/Fq6zhOnjwJxsSxWFio8/CjpgEAbfjCB+pQLMKVnSv5/Rz/9/ZbsCotqK8/EJVjyP16eLV1HBzX8TsPVaGq0CR0OKtqaGjAw3tNeOXWOI4dPyG6xQ1S8f3vN6MkbRkff6x+Wz8fi2vhsMuL79x6A3OJ2aiv3xXVY0mR0PejzVx5VxFI0g4DOA7gU4yxn4Z53JcBfCb4988AeOn+JzDGUhlj2uDfLQiM3rWHeVwiEhXZBswte6iDPYCGu9PINyWiyJIkdCgbUigYjpZacKHHCr+ftg7ajsZuK/RaFfbliav1xv2Ol6VhweXFrZFZoUORpGW3D839dlFPdQKBhSKHClJxvoumtsVoM0na73HO/4xz7uGcj3POn0AgyQrHXwB4iDHWDeDB4NdgjFUxxr4XfM4uAC2MsVsA3gbwF5xzStJkojK480BbnPdLc3p8uNRrQ/3ONNGMKG7keFkarA43Oidoa6+t4pyjsXsadSXiLCRf6UiJGQpGdWnbdbnfBrdX3Cu2Q46XpaFjfB5TC1RrKjYb3iU45y2rPPajcA7KObdxzh/gnJdxzh/knNtDx+KcfyH490uc8z2c833B/34/nGMScdmVaYCCIe6b2rYMzGDZ40O9BG7kIcdKLQCAxu5pgSORnkHbEkZmlnG8zCJ0KBtKSdRgT24KJWnbdL4rsGK7pkicU9orhVYZX6RVnqIj7o9yRLYSNEoUp+njfiTtna4paJQK1Iq49cb9Mo067MjQ05v3NjQG3wSPi7Cx6WpOlFlwc3gWc8seoUORnMZuK6qLTKJfsQ0EGoybkjRopClP0aEkjQimIsuAjjjfaL2x24qqwlQkajazhkc8jpWm4cqAnZbtb1Fj1zRyUhJQaBbPHo7rOV6WBp+fo6mXdpnYiukFF3qmHDhSIv4RUyBQa3qs1ILz3VRrKjaUpBHBVGYbMDq7jJlFt9ChCGJ6wYXOiQUck8DU1/2Ol1ng9vrRMjAjdCiS4fX50dRrw/Eyi2TqDw/kpyBJo6Sp7S260h/Y97S2WPxTnSHHyyywOlxUayoylKQRwby780B8jqZd6g1MLYRqvKTkcJEJSgXD5T4aYdmsWyOzWHB5JTPVCQBqpQJ1JRaa2t6iy302JGqU2J1jFDqUTTsRrEu70EMJuZhQkkYEUxFc4RmviwcudFthTFDfS1alRK9VYU+OEU2UpG1aY7cVjAVWTUrJ8TILhuxLGLYvCR2KZFzus6Gq0CT6FbwrZRh0KE5LoqltkZHObxCRHVOSBllGHdrG4m8PT845LvZYcaTEDKVCGlNf96srMePW8CwWXV6hQ5GESz027M42inYrqLXUBZNKevPeHKvDhe4ph6SmOkOOlJhxpd8Oj2/DfvUkRihJI4KqzDbE5QrPfusixuacOCrBqc6QumIzvH6OlkGqS9vIstuHG8MzkhtFA4CydD0seg2Nmm7Su/Vo0jvXdcUWLLp9aB2Nvw/OYkVJGhFURZYBvdOOuFslePFeKwbpJmlVhalQKxmNsGzCtcEZeHwctRJM0hhjqCk2o6nXBs5p5d9GQvVoeyRUjxYSGv2ja1o8KEkjgqrINsLPEXcrihq7rchNTUC+SRqtGFaTqFFhX24KjbBswuU+G5QKhsMi3atzI0dKzJiYd2LARnVpG7ncZ8OhglRJ1aOFmPValGcmU5ImItL7LSKyUhmHiwe8Pj+a+mw4ViqdVgxrqSsx487oHBac1Ox0PU19NuzJMUKvlVY/vJC64NRdaEUyWZ3N4ULXpEOSU50htcVmtAza4fLG1+yGWFGSRgSVm5oAg04VV4sHWkfnsOD0SroeLaSu2Ayfn1O/tHUsury4NTx7rwBfioosScgwaGmEZQNSrkcLOVJihtPjx63h+LknixklaURQjDFUxNnigVA9mhSLyO93sCAVGqWCpjzXcW1wBl4/vzcaJUWMMdQVm3G5z051aeu43GdDglqJvbnSq0cLqSkygzEaNRULStKI4CqzjeicmIc3TpZ9N3ZbUZltgFmvFTqUsOnUShzIT6ERlnU09dmgUjAcKkgVOpSw1JWYYXUEtjsiq2vutwcX1Ej3rdWYqMbubCNd0yIh3d8kIht7coxwevzonV4UOpSoW3J7cX1oRpK7DKylrsSMtrE52oR7DU29NuzLS0GSROvRQuqKA7+zNGq6OvuiG50TC5Ke6gypKzHjxtBs3K26FyNK0ojgQlun3B6ZFTiS6As0iuSyqEcLqS02w8/frcch73K4vGgdnZP0VGdInikBOSkJNMKyhiv9gf8vNUXSXMG7Ul2xGW6fH9eoB6LgKEkjgiu2JCFJo8SdOGigeLHHCo1SIdlWDKs5kJ8CrUpBb96ruDpgh8/PJb1oIIQxhroSM5r6bPD7qS7tfpf77NCpFdibmyJ0KGEL7c1L17TwKEkjglMoGHbnGHE7DpK0xm4rDhWkIkGjFDqUiNGqlDhUkIrmfrqh3+9yrw0apQIH86VdjxZSV2zG7JIn7voabsblPhuqCkzQqKT/tqrXqrA310iLB0RA+r9NRBb25BjRPjYv6z3jrA4XOicWcEzCuwyspabIjPbxecxTv7T3aOqzYX9eimyS8nv7eFJd2nvM3KtHk88IeV2xGbdH5mhvXoFRkkZEYU+uES6vH92T8l05dik4dSCnerSQ6iITOAeuUb+0e+adHtwZnZPkVlBryU5JQIE5kabB7tMcrMeskUHtYUhNcG/e60N0TQuJkjQiCqE6DjnXpV3qsSJZp8Lu4C4LcnIgPwVqJbv3ZkWAq/12+DlksWhgpdoiM64O2KkubYXmfluwHk26/dHud6ggFUoFowVBAqMkjYhCgSkRyVoVbo/Kd4XnxV4raorMUEm4h9JadGol9uWm3FvhRgKtNzQqBQ7kS7+QfKXaEhPmlj3omIifBtQbudxnx6GCVGhV8pjWBgJ1abuzDWjuoyRNSPJ7tyCSFFo80Doiz5G0YfsShu3LOFoqr1GVlaqLTLg9ModlN/VWAoDL/TYczE+BTi2fN24gUH8IBBITAswuudE5MY/aIvld2zXFZtwcpn5pQqIkjYjG3lwjOiYW4PbKb/FAaCsoOdajhVQXmeD1c9ygGhbMOz1oH5u/l9DISagurZkWDwAI1KNxLq96tJCaIhPcPj9uDst3hkPsKEkjorE7xwi314+uSfkt77/Ya0NashZl6XqhQ4maQwWpUDDgMtWw4NrADPwcqJHRar+VaovMaO6nujQAaO6zQ6tSYF+efOrRQqoKTWCMGlULiZI0IhqhottWmS0e4JyjqdeKIyVmMMaEDidqknVqVGYbqS4NgdEVtZLhQJ48+qPdr6Y4UJdG/dIC/dHkVo8WYkxQY1emgXogCoiSNCIa+aZEGHQq3JZZXdrdyQVYHW4cLZHvVGdIdZEJN4Zm4fLGdw1Lc78N+3Ll0x/tfqGpvctxPuU5txRYQCGH/TrXUl1kwrXBGVmWoUgBJWlENBhj2JNrlF0bjks9gTeyIzJeNBBSXWSCy+uX7QKQzVhye9E6ModqGezhuJaclATkmxLjPkm7MhCsR5Pxua4tNsHp8ctuhkMqKEkjorInJwWdE/OyGom51GtFgTkRuamJQocSddXBPUnjuV/a9cFZeP1cloXkK9UWm+K+Lu1yny1YjyavNisrHb53Tcd3Qi4UStKIqOzJMcLj47grk1oXr8+P5j47jsTBVCcApCZpsDMjOa4LjZv7bVAqGA4VyLMeLaS22Bz3dWmX+2w4mJ8quzYrK5n1gQVP8XxNC4mSNCIqcls8cHt0Dgsur6z7o90vVMPilfE+rOtp7rdjd7YBeq1K6FCiKjRSGK8jLHNLHrSPy7seLaS6yISWgfi9poVESRoRldzUBKQmqnFzSB59eS4F+6PJbWug9VQXmeBwedExHn8jLE6PDzeHZ2U/1QlQXdrVUD2aTNusrFRTbI7ba1pogiRpjLFPMMbaGGN+xljVOs97lDF2lzHWwxj701jGSITBGMP+vBTZNE+82GPDriwDzHqt0KHETKhgPh5HWG4Oz8Lt9d+rzZO7mqL4rUu73BfY9mu/jOvRQmri+JoWmlAjaXcAfBTA+bWewBhTAvgOgMcAVAD4FGOsIjbhESEdyE9Fz7QD806P0KGExenx4drQDI6WyH9UZaUMgw6F5sS4XDxwpd8OxoDDMl7tt1JtsRmzSx7clWED6o3Idduv1cTzNS00QZI0znkH5/zuBk+rBtDDOe/jnLsBPAfgiehHR4R2ID8FnAO3h6Vdl9YyEOgtJOetoNZSXWTC1YH4G2Fp7rdhV6YBxgS10KHERGiqL96mPOeWA9t+xUM9WkhNkTkur2mhibkmLQfA8IqvR4KPEZnbmxuYPpD6HpAXe61QKZis+2WtpbooMMLSPeUQOpSYcXv9uDY4E1fnOzc1EXmmhLhL0loG7IFtv2S4N+taqotMmF3yoGsq/kZNhRS15UeMsbcAZK7yra9zzl+KwvGeAvAUAGRkZKChoSHSh4gah8MhqXhjITuJ4a2bvdijHI3ZMSN9Hl6/sYwiA8PVpgsRe02p4EuBVWD/9sZlPJC/tVElqV4PPTM+OD1+6JfG0dAwLXQ4YdnKOShM8OBC1yTOvf02FDLe9myln3a6oFIACwO30TAcvX+zmK4Fvhy8ps8048GC+BgpBoQ/B1FL0jjnD4b5EqMA8lZ8nRt8bK3jPQPgGQCoqqri9fX1YR4+dhoaGiCleGPh6PQtnO2cwsmTJ2O232Ukz8PcsgeDZ97Al06Xob5+R0ReU0o45/jbW+cwo0pFff3BLf2sVK+H9oYeAHfxuQ8el/xCka2cA1vyCBp/egvZuw6hPNMQ3cBE4q9bL+BQgRIPP1AX1eOI7VoIXNMpW76mpWpu2YPmSxcEPQdinu68CqCMMVbEGNMAeBLAywLHRGLkQH4q7ItuDNmXhA5lWy732eDniLtFAyGMBaZ5r/TbwXl81LBc6bejLF0v+QRtq+7VpfXGx5TnvNODtrG5uKpHCwms5rXFzTX93fN9+PK5JTg9wu2AI1QLjo8wxkYA1AH4NWPsTPDxbMbYqwDAOfcC+BKAMwA6ALzAOW8TIl4SewfyQ3Vp0mzFcanHigS1Egfy5d11fj3VRWZMLbgwaJNmor0VXp8fLQMzcdEz6365qYnITU3A5b74WPl3rx4tDs91dZEJVocbvdOLQocSE839NmTrFYKu4BVqdeeLnPNczrmWc57BOX8k+PgY5/zxFc97lXO+g3Newjn/phCxEmHsyEhGokYp2X5pl3ptOFxkgkYl5sHq6AoV0MfDdjId4wtwuLyojqNC8pVqi81o7rfFxcq/y312aJQKHIzDD2ChJs3xcE07PT7cGp7DzlRhW6zE7zsIETWlgmFvrlGSKzyn5p3onnLE7VRnSElaEsxJmrjorRRq8lkTRys7V6otNmMmTlb+NffZsD9O+qPdr9CciLRkbVw0tb0xNAu3z49yk7BpEiVpRLQO5KeifXxe0HqA7bgQ3AoqHvujrRSqS4uHG/rlPjsKzYnIMOiEDkUQoeRU7nVpC04PWkfnUBunyThjLFCX1if/WtPmfhsYA8poJI2Q1R3IS4HHx9E2Ni90KFtyvmsa5iQNKrLiY6XbeqqLTBiZWcbo7LLQoUSN389xdcAeVz2z7pdnCtSlyX3UtGVgBn6OuFw0EFJTZMLEvBPDdvle00BgSndXpgFJamHbylCSRkRrf770mtr6/RwXeqw4VmaBQhEfPaPWE6pLuyrjN++7kwuYW/bEZSH5SoG6NHl3pL/cZ4NGqYjrBUGhujQ5j5C7vX5cHxLHQiBK0ohopSfrkJuagGuD0knS2sfnYXW4caIsTehQRKE804BknUrWIyyhIup42mlgNTVFJtgX3bLeZeJyvx3781KQoIm/erSQsnQ9TDKvNb09Mgunxy+K0XFK0oioHS404erAjGTqHxq7A/Vox8viux4tRKlgqC6Ud11ac78NOSkJyE1NFDoUQYWmAOW6RdSC04M7o3OiGF0REmMMhwtTZb3Cs1lEH7woSSOidrjQBKvDhQGJ9No63zWN8sxkpMdpAflqaopN6JtexNSCU+hQIo5zjiv99rhd1blSnikROSny3cezZXAGPj+P63q0kJoiM4bsSxiTaa1pc78dOzICI4ZCoySNiFp1UaD2Qwo1TUtuL1oG7Tixg6Y6Vwq9qTXLsNlp7/QirA533I+uhMi5Lq25zw61ksVlf7T7yXnU1Ovz45qIFgJRkkZErSQt8GnmyoD43+Cb++zw+DhNdd6nIsuAZK1Kljf0d/ujieOGLrTaYvnWpV3us8V9PVpIeWYyUhLVsrym28bmsej2ieaDFyVpRNQYY6gqSMVVCSRp73RNQ6tS4HChOC5usVApFThcZJLlDf1Kvx3pyVoUmOO7Hi2kVqYr/xwuL1pH5ygZD1IoAv3SmmR4TYd+d8VQjwZQkkYkoLrIhEHbEqbmxV3T1Ng9jZpic1x2It9IbbEJvTKrS+Oco7nPjppiMxijdiuAfOvSWgbsVI92n9piM4btyxiZkUa98GY199lRbElCerI46oopSSOiFxqZEvOU5+jsMnqnF3GCpjpXJce6tCH7EibmnaL5xC0WNcUmXJZZR/rLoXq0ghShQxGNupJQXZp8rmmfn+PKgF00U50AJWlEAiqzDUjUKEW9eKCxaxoAaNHAGuRYlxZKOON1i6C11BabZVeX1tRnw77cFCRqVEKHIho70pORKrO6tI7xeSw4vaKa1qYkjYieSqnAwfxUXBkQb1Pb893TyDToUJauFzoUUZJjXVpTnw0WvQaldM7fo05mK/9C/dFCI0ckIFCXZkaTjPZrDf3OiulcU5JGJOFwoQmdE/OYW/YIHcr7eHx+NHZZcWKHhWqT1nGvLk3ktYWbwTnHpV4raqke7X1yUxNkVZd2NViPVkf1aO9TV2LG6Owyhu3yqEu71GtDsSUJGSLqc0lJGpGEmmITOAeaRXjjbxmYwYLLi9PlGUKHImr3eiuJeNp6s/qti5icd+FICdUg3o8xhppiE5plUpfW1BvYr/NgAfVHu1/ompbDKk+vz48r/XbUimgUDaAkjUjEgfwUJKiVuCTCofVznZPQKBU4RosG1iWnurQmEU6LiEltsRm2RTd6ZFCX1tRnw4H8FFq1vYpQV345XNN3xubhcHlxRGTXNCVpRBK0KiUOF5lwoccqdCjvc65zCjXFJui1VFS8HjnVpV3qtSHToEMh9UdblVzq0uaWPGgbm6dkfA2MMdTKZNQ0VFsntjYrlKQRyThWakbPlAOTIqppGrAuond6EafL04UORRJqQ/t4iugcbhXnHJd7bThSQvVoa8lNTUC2USf59gzN/TZwDqpHW0dtcaguTdr7eF7qtWJHhh4WvVboUN6DkjQiGaH6n4siGk071zkFAJSkbZIc6tK6Jh2wLbpFV7siJoERFjMu99kkPcLS1GeDVqXA/nzqj7YWOYyaur1+tAzMiDIZpySNSEZFlgGpiWpc7BHPzeDtu1MoSUtCgTlJ6FAkQQ51aU29gQ8JYryhi4kc6tKaem2oKkyFVkX1aGspTdfDotdIevHA7ZFZLHt8qBPhQiBK0ohkKBQMR0osuNhjFcWnc4fLi8t9Njywi1Z1bpYc6tKa+mzIMyUgz0T1aOuplfgIi33Rjc6JBUrGNxBYzSvtUdNLvTYwFijHEBtK0oikHC21YGLeiT7rotCh4EL3NDw+jlM7aapzK6Rcl+b3c1zus9Mb9ybkmaRdl9ZMK3g3rbbYjPE5JwZt0uyX1tRrw65MA1ISNUKH8j6UpBFJOVoauGGKoS7ttTsTSE1U43Ah9U/aCin3VmofDzRUpjfujYXq0gLF99IbYWnqsyFRo8TeXKpH24iU69KcHh+uDc2I9pqmJI1ISr4pEbmpCTjfJWyS5vL6cK5jCg9VZEClpMtoKyqzjUjWqXBJRLWFm3Vv25hi8dWuiFFNsQlWhxu909KrSwvUo5mgput7QyVpSUhL1oqyj+VGbgzNwu31i64/Wgj99hFJYYzh1M50XOyxwunxCRbHpR4bFlxePLY7S7AYpEqpYDhSYsYFkdQWbkVo25hMo3i2jRGzd0dNpTXlOTXvRPeUQ7Rv3GLDGMPREjMu9ljh90vrmm7qtULBgMNF4qtHAyhJIxJ0elc6lj0+NAvYxuG1O+NI1qpwpJRu4ttxrCwNo7PL6BdBbeFmeYLbxoh1WkSM8k2JyDLqJDcNFmqafayURkw361hZGmyLbnRMzAsdypZc7LVhT24KDDq10KGsipI0Ijl1xWbo1Aqc65gU5Phenx9vtk/i9K50Wpq/TceDb35i3EFiLTeGZuFweXG8LE3oUCTjXl2axFb+NXZbYU7SoCLLIHQokhFKaC90S+eanlv24ObwLE6IeEs/StKI5OjUShwrteBs55QgN/4r/XbMLHnwaGVmzI8tFwXmQG2hlG7ojd3TUCoYjaRtUa3E6tI452jstuJoqQUKBe0osVmZRh3K0vWS+uDV1GuDz89F/cGLkjQiSafLMzAysyxIo8zX2yagUytwcqd4L2yxY4zhWKkFTb02eH1+ocPZlPPdVuzPS4ExQZzTImIltbq0zokFWB0uHBfx6IpYHS9Lw5V+u6D1wlvR2D2NJI0SB0S8owQlaUSSQtswnQ1uyxQrPj/Ha3cmcHJHGhI1tKF6OI6VO5boOQAAGoVJREFUWbDg8uLWyJzQoWxodsmN2yOz9Ma9DVKrS2vsngYAUY+uiNXxMgtcXj+uDkgjIW/stqKuxCLqFbyCRMYY+wRjrI0x5meMVa3zvAHGWCtj7CZjrCWWMRJxyzTqUJltwBttEzE97qVeK6YXXHhif05MjytHR0ssYEwcPe82crEnsNE2vXFvHWMMdcVmXOqxwieBlX+N3VaUpetpBe821BSboFYySZQxDNoWMWRfwokd4v7gJVT6eAfARwGc38RzT3HO93PO10zmSHx6fE8Wrg/NYmx2OWbH/OWNMSRrVbShegSkJmmwO9soiRt6Y/c0knUq7Ms1Ch2KJJ3cmYaZJQ9aR8U9aur0+HCl307J+DYlalQ4mJ+KRglc0+eDMYr9XAuSpHHOOzjnd4U4NpGPx/cEepS92joek+Mtu314/c44HtuTCZ2aVnVGwtFSC64PzcDh8godypo45zjfNY1jpRZqXLxNx8vSwBjQcDe25Qlb1TIwA5fXT9PaYTheZkH7+DysDpfQoayrsWsauakJKDSLew9esd9xOIA3GGPXGGNPCR0MEZciSxIqsw0xS9Le6pjEotuH3zhAU52RcrzMAq+f39snUYx6pxcxNucU/SduMTMlabAvNwUNd6eFDmVdjd3TUCsZakS40bZUhK4TMZcxeH1+NPXagh8exL2CN2qVz4yxtwCs1qPg65zzlzb5Msc456OMsXQAbzLGOjnnq06RBpO4pwAgIyMDDQ0N2wlbEA6HQ1LxismuJDd+1u3Bz187B3NCeJ85NjoP37vmhEnH4BxqRcOwuC9sqXD7ODQK4Mdv34RyUgtAfNfDmwMeAIDa1oOGhj6Bo4mNaJyDQq0bL/V48Mobb0OvEef189qNZZQYGa5cuiB0KADEdy1shp9zJKmBF87fgXG2W+hwVtU948OCywuTexINDet/QBT6HEQtSeOcPxiB1xgN/neKMfYigGqsUcfGOX8GwDMAUFVVxevr68M9fMw0NDRASvGKSeHuRfzs/zRgRl+Ijx0vDuu11jsPk/NO3HnjHH7/eDFOnyoP6zjkvY4PX0XX1AJOnjwJxpjorodnf3AVRZZFfOLxeqFDiZlonANj8Qx+2XMJvvQdqBfhwpupBSeGXj+Lrz6yE/X1pUKHA0C67w2nxq/jcp8dJ06cFGWvuRtvdkHBuvHUh0/CmLh+Sx2hz4FopzsZY0mMseTQ3wE8jMCCA0LuKbQkYXeOAS/dHIvqcZ6/Ogyfn+PJw3lRPU48OlWejmH7siibnTo9vuC0CNUohWtvbgpSE9V4R6RTng2dgbhO7aRFQeE6XZ4Oq8OFO2PiXCjS0DWNfXkpGyZoYiBUC46PMMZGANQB+DVj7Ezw8WzG2KvBp2UAuMAYuwXgCoBfc85fFyJeIm4fO5iL1tE5dIxHZ884n5/juStDOFZqQaElKSrHiGengitl3+4U35t3U58Nyx7fvRjJ9ikVDCd2pOGdrmlRbsJ9rnMKWUYddmUlCx2K5J3cEVgoci7GfSw3Y2rBiVvDs3hAIte0UKs7X+Sc53LOtZzzDM75I8HHxzjnjwf/3sc53xf8U8k5/6YQsRLx+439OdAoFfhpy0hUXv+drimMzTnxWzX5UXn9eJeTkoCdGcmivKGf65hCokaJumLaCioSTu4IbMLdNiauTbhdXh8au6dxujxd9IXkUmDWa7E/L0WU13RoxPR0eYbAkWyOaKc7Cdms1CQNHqrIwC9vjsLtjfwWQz9uHoJFr8VDFdK4qKXoVHk6rg7YseD0CB3KPZxznO2YxLFSC7VciZATOwIr/8TWiuNKvx2Lbh/1P4yg0zvTcXtkDlMLTqFDeY+znZPIltCIKSVpRBY+UZUL+6IbZyK8A8GAdRFnO6fw5OE8UW8dInWndqbB6+eiamzbMb6AsTknHthFb9yRYtFrsTfXiIYucU1tn+2YglalwJESqj2MlNPB60ZMbVecHh8au604vUs6I6b0rkNk4URZGgrNifjXi/0Rfd3vNvZBrVDgd48URPR1yXsdKkhFsk6Ft0U0wnKucxIAqB4twk6Xp+P60AymF8TR7JRzjnOdUzhaakGChkZMI6Uiy4BMgw5vi2jKs7nfjiW3Dw9IZKoToCSNyIRCwfDZI4W4PjSLG0MzEXlNq8OFn10bwUcP5iA9mfbxiyaVUoETO9Lw9t1p+Lk4isrf6pjCvrwUOvcR9nBFJjgHznZMCh0KgECz4iH7EiXjEcYYw6nyNDR2W6NShrId5zomoVMrUFcinRpTStKIbHy8Kg/JWhW+fyEyo2n/cqEfLq8fXwiz/xrZnIcrMjC94ELvrPA39OkFF26NzOJBeuOOuF1ZycgzJUS8NGG7QiOmVI8WeafLM+BwedHcL/yOIpxzvNUxJbkaU0rSiGzotSr8Vm0+ft06jp6phbBea2rBiX+9OIAP78tGabo+QhGS9ZwqT4dayXBtUvh9PN/unALn79bVkMhhjOHhikxc7LGJYs/WN9omUZ6ZjJyUBKFDkZ3jZRYkapR4/Y7wCfndyQWMzi7jgV3SmeoEKEkjMvMHJ0qQqFbib98KbzuS75zrgdvnxx8/tCNCkZGNGHRqHCu1oGXSBy7wlOeZtgnkpCSgIssgaBxy9UhlJtw+v+CNbafmnbg2NIPH92QJGodc6dRKnNqZjjNtE/AJ3Bvv9TsTYAyS6Y8WQkkakRVTkgafO1qEX98eR9s2u113Ty7gx1eG8Mmq/7+9O4+vqrzzOP755WYjCQRCIAlkAQQkGASSCK4UW7TEtqK4VFq3qtU6OtrX1NdYdZxpO13U2r76qlotrbZaUbSuiLjVHSs7hF2IEcgCCQEDCWQlz/yROGUYoCy555x7833/k9yTe8/z4/XkyfnxrDnavNZjUwsyqWtyvu6jtbu5jQ831nHemMyIWQEWaYry+pGWHO/7kOcba7bhHJQUHOyYaekOUwsyqWtsZcmmnb7G8dqqbZySl8bAPpE1x1RJmkSd7541jP7J8dz90uqj3tncOcddL60mKT6W285VL5rXzhmdiYGvD++319XQuq+DEvWuhE0oxpiSP5B319f6Oqn8tdXbOGFAMiMyImPPrEh09qiBxMfG8JqPQ55ltY18UtNAyZjIS8aVpEnUSU2K487z8lm2pZ7ZiyuO6rOzF1ew6LOd3FEyiv4pCWGKUA4lLTmeUWn+/kGft2obWamJjMvu61sMPcFXT8qkoaWdj8v9mVS+c08rCz/bSUmBkvFwSkmI5UsjB/DGmm2+HQf2+uqtQGevXqRRkiZRaXrhYE4dlsbP562jrPbIDu6uaOjgR3PWcMbw/lxarIPU/VKUEUtZbeNxL/44Fo0t7by/YTtTCzKJidFQZzidMTyd3gmxzC2t9qX8t9Z2zpOKxAd3pCkpyGTrrmZWVNb7Uv5rq7dRmNuXrNTIWxyiJE2ikpnx60vHkRAbw/eeXPpPjxva0djCg8ubSe0Vx2++OV4PaB8VZXQuj5+3yvvetLfX1dDa3qGJ5B5IjAvx1YJMXl+9jea2fZ6XP3flVnLTkjhpkBaHhNtX8jOIC5kvqzw379jDmurdEdumlaRJ1BrUtxcPzBjPZ3V7+M6fFrOr6eCJWs3uZi5/dBGfNzsevryQAb01zOmnfokxTByaxksrqjxf5TlnRTUZfRIoyu3nabk91fljB9HQ0u750UG1u5v5qKyOaeMGaXGIB1J7da7cfnXlVs+HPF9e0dlTG6lzTJWkSVQ7fXg6D84Yz4qKer7xwHze37D9fx/87fs6eKW0mq8/MJ/NO/ZwS2ECRXlpPkcsABeOH0z59j2srDy2FbrHoq6xhfc3bOeC8YPVk+qR00/oT3pKPHNKqzwtd05pNR0Opo0b7Gm5PdkF4wdTVd/Ews+8W+XpnOPF5VWcOiwtYvfBi/U7AJFwKxmTxTN9Erh19gquemwRmX0SyeqbyJYde9mxp5XRWX144poJ1HyyzO9QpUvJmCz+c84aXlxexdgcbybwv1JaTXuHY/r4bE/Kk87jwL42JounF1fQ0NxG78Q4T8p9aUUVJ2enaqNqD507OpOUhFheWFbp2bFMKyrq+axuDzd+6QRPygsH9aRJj1CUl8bbP/gS918yllOGppEUH2LyiQN55PJC5tx8BvnatDRQUnvFcU5+Bq+UVtO2z5stGl5YVsVJg/pwYqa2Y/DS+eMG09re4dl8pY01Dayu2s0F6kXzVK/4ECUFmcxbtZWmVm/mIL6wrIqE2JiI3HrjC0rSpMdIiA1xcVE2D8wYz6zrTuVXl45lakEWsSE1gyC6cPxgduxp5YMN4Z+vtLGmgVVVu5heqF40rxXm9mVYejLPLjm67XKO1YvLqwjFGN8YO8iT8uQfphdms6d1H2+uDX9C3trewSsrqzlndIZnPbThoKeTiATSpJED6J8c78nD+7mllYRijPP14PacmfHNU3JYvOnzsG+70ravg+eWVjJpRLoWCPlg4tDOuWHPLa0Me1nvrK+hfm8b0wsju8dUSZqIBFJ8bAyXFOfwt3W1bN3VFLZymtv28eySCqbkD9SD2ycXFWUTFzJmLwpvQv63tTXUNrTw7Yl5YS1HDi4mxri4KJv5ZXVs3rEnrGU9uWALg1ITmTRiQFjLCTclaSISWN+emEuHczwdxof3qyu38vneNq48bUjYypDDS09J4JzRGTy/rJKW9vDNV5q1sPPBfXaEHbIdTb41MZcYM2Yt3BK2Msq3NzK/rI5vTcyN+OkskR29iES1nLQkJo8cwOxFW8K2gOCJBZsZNiCZ0z1acSYHd9kpuXy+t4031tSE5f6f1e1hflkdMybkEtIWK77J6JPIV0/K4NklFWHbxHjWwi3EhYxLT4n8k2OUpIlIoF1+ah61DS28tbb7H94rK+sprajnilPztKmpz84cns7Q9GQe/bA8LJsYz1qwmdiYzvlv4q8rTh1C/d425oThSLCm1n38dUkFUwuyGNg7sdvv7zUlaSISaJNPHEhOWi/+GIaH958/2kSvuBAXFWlVp99iYozrzhpKaeUuFpR374anu5vbeGZxBVMLMhnYJ/If3JHu1GFpjBiYwuN/39TtbfqF5ZXsbm7n8om53XpfvyhJE5FAC8UY1581jGVb6rt1t/ItO/bycmk1Mybk0ieCl+hHk4sKs+mfHM/MDz7t1vs+uWAzDS3tfC+CNzWNJmbGtWcOZU31bj7YWNdt923f18Ej73/K2Jy+TBgaHafHKEkTkcC7pDiH9JR4Hnq3rNvu+cgHnxIy4/pJw7rtnnJ8EuNCXH36EN79ZDufbOue7Tia2/bx2PxNnDUinYLBqd1yTzl+0wuzyUpN5KF3uq9Nv7pqKxU7m7hp8glRM31BSZqIBF5iXIhrzxzGhxvrWLr5+HvTquubeG5JJRcVZZOZquGvILnitDyS4kP89u2N3XK/WQu3UNfYwo2T1YsWJPGxMVw/aRiLNu1kQfmO475f+74OHnynjJEZKUzJz+iGCINBSZqIRISrTs9jQO8Efj5v/XHPY7n/jU/A4Kaz9eAOmr5J8Vx31jBeXbWV0or647rX7uY2HnxnI2cOT+f0E9K7KULpLpedkktmn0R+8drxt+nnl1WysbaR708ZSUwUrd5VkiYiESEpPpZ/O2ckSzd/zhtrjv1YmdVVu3hheRXXnjmU7H5J3RihdJfvnjWU/snx3HOcD++Z75fz+d42bp86qhujk+7SKz7ED84dSWlFPXNXbj3m++xtbefXb22gMLcvJQWRe07nwShJE5GIcUlRNiMzUvjvuetobGk/6s/v63Dc/fJq0pLjNfwVYL0T47h1ygg+Lt9xzNs0lNU2MvODcqaNG8SYbM1FC6rphdnkZ/XhntfWH1ObBnjwnTJqdrdw53n5UTMX7QtK0kQkYsSGYvjF9JOp3tXEfa+vP+rPPzq/nOVb6vmvb4zWis6A+/bEPMbm9OXHr6xl557Wo/psR4fjzhdW0Ss+xH98bXSYIpTuEIoxfnrBSVTvauKe19Yd9edXVe7i9x+Uc2lxNsVDomNF5/6UpIlIRCnK68fVpw/hiY838/a6I9/gdk31Lu5/cwPnjs7QQeoRIBRj3HvRGHY3tXH78yvp6DjyYc+ZH5azaNNO7jovX+exRoCivDSuOWMoTy7Ywvsbth/x5/a2tnPbX0vpnxzPXVGajCtJE5GIc/vUUYwZnMqts1dQVvvPt2qobWjmuseXkJ4cz88uHBN1QyLRalRmH+44L5+31tbwu/eObKuG+RvruO/19Xzt5CwuKdYmxZHitnNP5MSM3vzrU8so3974T9/vnOO2v5aysbaB+y8ZS2qv6OwZ9yVJM7Nfmtl6M1tpZi+aWd9DvG+qmX1iZmVm9kOv4xSRYEqMC/H7K4pIjAtxxaOLDvtHfXtDC1c+uoj6vW384api9axEmGvOGMK0cYO4/80N/OXjTYd974qKem58cinDB6Zw30UnKxmPIL3iQ/zxqmJiQzFc8+fFVNc3HfK9zjl+Mnct81Zt446SfCaNHOBhpN7yqyftLaDAOXcysAG448A3mFkIeAgoAUYDM8wsOvszReSoDerbi79cO4HW9g4ueOgj5pRW/7+VgB+V1THtwfls3rGXmVcWcdIgTSCPNGbGvRedzJT8DO5+eQ33vr6e1vaO//Me5xwvLq9kxswF9EuO58/fmUByQqxPEcuxyklL4o9XFbOjsZXpv/s7Cw+yf9qupjZufno5f/poE985YwjXnTXUh0i948tvsXPuzf1eLgAuPsjbJgBlzrlyADObDUwD1oY/QhGJBPlZfXjxX87gpqeWccvTy/nt2517YoVijCWbdlJauYu8/kk8e8NpWuEXwRLjQjx8eSF3v7Sah9/7lFdKq7mkKIdhA5KpbWhh7spqlm+ppyivHw9fXhgVB2v3VIW5/XjmhtO4cdZSvjlzAVPyB/LlURkkJ4RYU72bZ5dU0NDczg9LRnHDpGFR31tq3X246VEHYPYK8Ixz7skDrl8MTHXOXdf1+gpgonPu5kPc53rgeoCMjIyi2bNnhzfwbtTY2EhKSorfYfR4qodgOJZ66HCOj6ramV/VzubdHXQAg1NiOC0rlsk5scSHovsPeXcLcltYub2dueVtbPy8gy+eXpnJxrl5cUzOiSUmih7aQa6HcGtqd7z+WRvvV7ZT39JZ0yGDkweEuGB4HHl9Qp7E4VUdnH322Uudc8UHXg9bT5qZ/Q042K5ydznnXu56z11AOzDreMtzzs0EZgIUFxe7yZMnH+8tPfPee+8RSfFGK9VDMBxrPXy5+0PpsYLcFiYDtwC79rZR09BM36Q4BqQkRGWPSpDrwQsldG6nUlXfRHPbPgb360VSvLcDgH7XQdj+tc65KYf7uZldDXwd+Io7eHdeFZCz3+vsrmsiItLDpSbFkZoUnSv65B9iYoyctJ57MohfqzunAv8OnO+c23uIty0GRpjZUDOLBy4D5ngVo4iIiIif/Frd+SDQG3jLzFaY2SMAZjbIzOYBOOfagZuBN4B1wLPOuTU+xSsiIiLiKb9Wdw4/xPVq4Lz9Xs8D5nkVl4iIiEhQ6MQBERERkQBSkiYiIiISQErSRERERAJISZqIiIhIAClJExEREQkgJWkiIiIiAaQkTURERCSAfD9gPRzMbDuw2e84jkI6UOd3EKJ6CAjVg/9UB8GgevCfV3WQ55wbcODFqEzSIo2ZLXHOFfsdR0+neggG1YP/VAfBoHrwn991oOFOERERkQBSkiYiIiISQErSgmGm3wEIoHoICtWD/1QHwaB68J+vdaA5aSIiIiIBpJ40ERERkQBSkuYzM5tqZp+YWZmZ/dDveHoqM9tkZqvMbIWZLfE7np7AzB4zs1ozW73ftTQze8vMNnZ97ednjD3BIerhR2ZW1dUeVpjZeX7GGO3MLMfM3jWztWa2xsxu7bqu9uChw9SDb+1Bw50+MrMQsAE4B6gEFgMznHNrfQ2sBzKzTUCxc057EnnEzCYBjcATzrmCrmv3ATudc/d0/aeln3Pudj/jjHaHqIcfAY3Oufv9jK2nMLMsIMs5t8zMegNLgQuAq1F78Mxh6uFSfGoP6knz1wSgzDlX7pxrBWYD03yOScQTzrkPgJ0HXJ4GPN71/eN0/oGUMDpEPYiHnHNbnXPLur5vANYBg1F78NRh6sE3StL8NRio2O91JT7/QvRgDnjTzJaa2fV+B9ODZTjntnZ9vw3I8DOYHu5mM1vZNRyqYTaPmNkQYDywELUH3xxQD+BTe1CSJtLpTOdcIVAC3NQ1BCQ+cp1zMTQfwx8PAycA44CtwK/8DadnMLMU4Hng+8653fv/TO3BOwepB9/ag5I0f1UBOfu9zu66Jh5zzlV1fa0FXqRzKFq8V9M1L+SL+SG1PsfTIznnapxz+5xzHcAfUHsIOzOLozMxmOWce6HrstqDxw5WD362ByVp/loMjDCzoWYWD1wGzPE5ph7HzJK7JoliZsnAucDqw39KwmQOcFXX91cBL/sYS4/1RWLQ5ULUHsLKzAx4FFjnnPv1fj9Se/DQoerBz/ag1Z0+61rK+xsgBDzmnPuZzyH1OGY2jM7eM4BY4CnVQ/iZ2dPAZCAdqAH+C3gJeBbIBTYDlzrnNKk9jA5RD5PpHNpxwCbghv3mRkk3M7MzgQ+BVUBH1+U76ZwPpfbgkcPUwwx8ag9K0kREREQCSMOdIiIiIgGkJE1EREQkgJSkiYiIiASQkjQRERGRAFKSJiIiIhJAStJERI6Qmb1uZvVmNtfvWEQk+ilJExE5cr8ErvA7CBHpGZSkiYgcwMxO6TpMObHrRIo1ZlbgnHsbaPA7PhHpGWL9DkBEJGicc4vNbA7wU6AX8KRzTkcjiYinlKSJiBzcT+g8X7cZuMXnWESkB9Jwp4jIwfUHUoDeQKLPsYhID6QkTUTk4H4P3A3MAu71ORYR6YE03CkicgAzuxJoc849ZWYh4O9m9mXgx8AoIMXMKoFrnXNv+BmriEQvc875HYOIiIiIHEDDnSIiIiIBpCRNREREJICUpImIiIgEkJI0ERERkQBSkiYiIiISQErSRERERAJISZqIiIhIAClJExEREQmg/wGuazjudI2ozQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "epsilon = float(input('Задайте точность вычислений: '))\n",
        "\n",
        "phi = .5 * (1 + 5 ** .5)\n",
        "\n",
        "mx = []\n",
        "mn = []\n",
        "\n",
        "# 1\n",
        "mx.append(f(hf(-1, 0, epsilon, phi)))\n",
        "mn.append(f(lf(-1, 0, epsilon, phi)))\n",
        "\n",
        "# 2\n",
        "mx.append(f(hf(0, 2, epsilon, phi)))\n",
        "mn.append(f(lf(4, 5, epsilon, phi)))\n",
        "\n",
        "#3\n",
        "mx.append(f(hf(6, 8, epsilon, phi)))\n",
        "\n",
        "# 4\n",
        "mn.append(f(lf(10, 12, epsilon, phi)))\n",
        "mx.append(f(hf(13, 15, epsilon, phi)))\n",
        "\n",
        "# 5\n",
        "mn.append(f(lf(16, 18, epsilon, phi)))\n",
        "\n",
        "# 6\n",
        "mx.append(f(hf(19, 21, epsilon, phi)))\n",
        "mn.append(f(lf(22, 24, epsilon, phi)))\n",
        "mx.append(f(hf(24, 25, epsilon, phi)))\n",
        "\n",
        "print('Максимумы:', mx)\n",
        "print('Минимумы:', mn)\n",
        "\n",
        "print('\\nГлобальный максимум:', max(mx))\n",
        "print('Глобальный минимум:', min(mn))"
      ],
      "metadata": {
        "id": "IxXszoAoe6o8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1e154119-780e-465c-ffa4-3a3ca381e76d"
      },
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Задайте точность вычислений: 0.0001\n",
            "Максимумы: [0.934795775705125, 1.07439448618161, 0.0298074977250666, 0.000169926484709038, 6.49687582843228e-7, -1.03276840603742]\n",
            "Минимумы: [-0.163567397916976, -1.74572934111995, -1.99758048780143, -1.99998915292961, -1.99999996278905]\n",
            "\n",
            "Глобальный максимум: 1.07439448618161\n",
            "Глобальный минимум: -1.99999996278905\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4adLCnDHNftk"
      },
      "source": [
        "# Домашнее задание (дополнительное):"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qKCVqk0pNftk"
      },
      "source": [
        "# Задание Штрафы. \n",
        "\n",
        "Напишите программу для нахождеиия минимума функции одной переменной f(x) на интервале [а, b] при ограничениях g(х) > 0 \n",
        "методом штрафа с использованием метода золотого сечения для решения задачи безусловной минимизации. \n",
        "\n",
        "С ее помощью найдите минимум функции $e^{-x}x$ при $x >= 2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 128,
      "metadata": {
        "id": "f04IiWjvNftk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6336b976-bb53-416a-9b1a-4ce8fa633f63"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "start interval - a = 1\n",
            "end interval - b = 5\n",
            "Задайте точность вычислений: 0.00001\n",
            "Минимумы: [1.00003858024691, 0.00673797949249438, 6.14423498873849e-6, 1.52300358522851e-8, 3.77514845195585e-11]\n",
            "Глобальный минимум: 3.77514845195585e-11\n"
          ]
        }
      ],
      "source": [
        "def f(x):\n",
        "  if x >=2:\n",
        "    return  sm.exp(-x)\n",
        "  else:\n",
        "    return sm.exp(-x)**8\n",
        "\n",
        "\n",
        "A = int(input(\"start interval - a = \"))\n",
        "B = int(input(\"end interval - b = \"))\n",
        "N = 1000\n",
        "fp = np.zeros((N))\n",
        "x = np.linspace(A, B, N)\n",
        "for i in range(N): \n",
        "    fp[i] = f(x[i])\n",
        "\n",
        "\n",
        "epsilon = float(input('Задайте точность вычислений: '))\n",
        "\n",
        "phi = .5 * (1 + 5 ** .5)\n",
        "\n",
        "mx = []\n",
        "mn = []\n",
        "\n",
        "# 1\n",
        "mx.append(f(hf(-1, 0, epsilon, phi)))\n",
        "mn.append(f(lf(-1, 0, epsilon, phi)))\n",
        "\n",
        "# 2\n",
        "mx.append(f(hf(0, 2, epsilon, phi)))\n",
        "mn.append(f(lf(4, 5, epsilon, phi)))\n",
        "\n",
        "#3\n",
        "mx.append(f(hf(6, 8, epsilon, phi)))\n",
        "\n",
        "# 4\n",
        "mn.append(f(lf(10, 12, epsilon, phi)))\n",
        "mx.append(f(hf(13, 15, epsilon, phi)))\n",
        "\n",
        "# 5\n",
        "mn.append(f(lf(16, 18, epsilon, phi)))\n",
        "\n",
        "# 6\n",
        "mx.append(f(hf(19, 21, epsilon, phi)))\n",
        "mn.append(f(lf(22, 24, epsilon, phi)))\n",
        "mx.append(f(hf(24, 25, epsilon, phi)))\n",
        "\n",
        "#print('Максимумы:', mx)\n",
        "print('Минимумы:', mn)\n",
        "\n",
        "#print('\\nГлобальный максимум:', max(mx))\n",
        "print('Глобальный минимум:', min(mn))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8PGqu9eUNftk"
      },
      "source": [
        "# Задание. Определитель.\n",
        "\n",
        "Напишите программу для вычисления определителя матрицы произвольной размерности методом разложения по строке или столбцу (https://ru.wikipedia.org/wiki/%D0%9E%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B8%D1%82%D0%B5%D0%BB%D1%8C)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 129,
      "metadata": {
        "id": "-HpGbZy-Nftk"
      },
      "outputs": [],
      "source": [
        "def getMinor(matrix, i1, j1):\n",
        "    minor = np.zeros((len(matrix) - 1, len(matrix) - 1))\n",
        "    i2 = 0\n",
        "    for i in range(len(matrix)):\n",
        "        j2 = 0\n",
        "        if i == i1:\n",
        "            continue\n",
        "        for j in range(len(matrix)):\n",
        "            if j == j1:\n",
        "                continue\n",
        "            minor[i2][j2] = matrix[i][j]\n",
        "            j2 += 1\n",
        "        i2 += 1\n",
        "    return minor"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "matrix = np.array([[1, 2, 3],\n",
        "                   [3, 4, 5],\n",
        "                   [5, 6, 7]])\n",
        "getMinor(matrix, 0, 0)"
      ],
      "metadata": {
        "id": "_B2n0q5pz-5n",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fee27d21-fd16-47b9-8ef3-fac6b2802a8d"
      },
      "execution_count": 130,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4., 5.],\n",
              "       [6., 7.]])"
            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def determinant_R(matrix):\n",
        "    if len(matrix) == 1:\n",
        "        return matrix[0][0]\n",
        "    s = 0\n",
        "    for i in range(len(matrix)):\n",
        "        s += (-1) ** i * matrix[0][i] * determinant_R(getMinor(matrix, 0, i))\n",
        "    return s"
      ],
      "metadata": {
        "id": "p_KgEgsk0Dpf"
      },
      "execution_count": 131,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "K = np.eye(3)\n",
        "A = np.array([[1, 2, 3],\n",
        "              [3, 4, 5],\n",
        "              [5, 6, 7]])\n",
        "print(determinant_R(K))\n",
        "print(determinant_R(A))"
      ],
      "metadata": {
        "id": "-bkez5eD0MlL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b3339b07-0b66-4bcf-b6a8-23b0a248b232"
      },
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n",
            "0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqGcdRlCNftk"
      },
      "source": [
        "# Задание. Области притяжения.\n",
        "\n",
        "Как мы уже поняли у каждого корня есть своя область притяжения (окрестность выбирая начальное приближение из которой можно получить этот корень с помощью итерационного метода, например метода Ньютона). Постройте для системы уравнений из задания 4 область притяжения каждого корня.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "import numpy as np\n",
        "\n",
        "x, x1, x2 = symbols('x, x1, x2')\n",
        "\n",
        "F1 = x1**2 + (x2 - abs(x1)**0.5)**2 - 1\n",
        "F2 = x1**2*x2**3  -  7*x1**3*x2**3  -  7\n",
        "\n",
        " \n",
        "class Function():\n",
        "    def f(self, x):\n",
        "        return sm.log(abs(x+1)) - 2*math.pow(x, 2) + 1\n",
        " \n",
        "class NewtonMethod():\n",
        "    def derrirative(self, x):\n",
        "        return 1/(x+1) - 4*x\n",
        " \n",
        "    def newtonsMethod(self, f, a, b,derrirative):\n",
        "        try:\n",
        "            x0 = (a+b)/2\n",
        "            xn = x0\n",
        "            xn1 = xn - f(xn) / derrirative(xn)\n",
        "            while abs(xn1-xn) > math.pow(10,-3):\n",
        "                xn = xn1\n",
        "                xn1 = xn - f(xn) / derrirative(xn)\n",
        "            return xn1\n",
        "        except:\n",
        "            print(\"Error!\")\n",
        " \n",
        "func = Function()\n",
        "\n",
        "nm = NewtonMethod()\n",
        "\n",
        "\n",
        "x1 = nm.newtonsMethod(func.f, -0.6, -0.4, nm.derrirative)\n",
        "y1 = nm.newtonsMethod(func.f, 0.8, 1., nm.derrirative)\n",
        "print(\"NM The first solution on such interval [-0.6; -0.4] x1 is: \" + str(x1))\n",
        "print(\"NM The second solution on such interval [0.8; 1] x2 is: \" + str(y1))\n",
        "print(\"F(x1) is: \" + str(func.f(x1)))\n",
        "print(\"F(x2) is: \" + str(func.f(y1)))\n"
      ],
      "metadata": {
        "id": "3tuMMyA87Kgm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0c01be30-c7d5-4038-bfea-40999ac15b1f"
      },
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "NM The first solution on such interval [-0.6; -0.4] x1 is: -0.449215282932589\n",
            "NM The second solution on such interval [0.8; 1] x2 is: 0.907075175897678\n",
            "F(x1) is: -1.44191991680032e-10\n",
            "F(x2) is: -2.59174015582175e-9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 134,
      "metadata": {
        "id": "q1-h7yfcNftk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "outputId": "6c6f4e1c-c997-46d1-92c7-698085fd0812"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "6\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.4494943716069653"
            ],
            "image/png": "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\n",
            "text/latex": "$\\displaystyle 2.44949437160697$"
          },
          "metadata": {},
          "execution_count": 134
        }
      ],
      "source": [
        "def sqrt(x):\n",
        "    \n",
        "    def sqrtIter(guess):\n",
        "        if goodEnaugh(guess):\n",
        "            return guess\n",
        "        else:\n",
        "            return sqrtIter(improve(guess))\n",
        "        \n",
        "    def improve(guess):\n",
        "        return average(guess, x/guess)\n",
        "    \n",
        "    def average(x, y):\n",
        "        return (x+y)/2\n",
        "    \n",
        "    def goodEnaugh(guess):\n",
        "        if(abs(guess**2-x)<0.001):\n",
        "            return 1\n",
        "        else:\n",
        "            return 0\n",
        "        \n",
        "    return sqrtIter(1.0)\n",
        "\n",
        "\n",
        "sqrt(int(input()))"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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        "version": 3
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      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.9"
    },
    "colab": {
      "name": "Laba 7.ipynb",
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