10. Polynomial .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.poly1d((2,3,-1)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2\n",
      "2 x + 3 x - 1\n"
     ]
    }
   ],
   "source": [
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([1, 2, 2])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.poly1d([1,2,2])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2\n",
      "1 x + 2 x + 2\n"
     ]
    }
   ],
   "source": [
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b5d1dffd30>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(b)\n",
    "plt.plot(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.polynomial.polynomial import polyval\n",
    "polyval(1, [1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 6, 6])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyadd([1, 2], [9, 5, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([1, 2])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = np.poly1d([1, 2])\n",
    "p2 = np.poly1d([9, 5, 4])\n",
    "p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([9, 5, 4])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([9, 6, 6])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.polyadd(p1,p2)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2\n",
      "9 x + 6 x + 6\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.poly1d([1,1,1,1,1])\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   4     3     2\n",
      "1 x + 1 x + 1 x + 1 x + 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(p)\n",
    "p.order"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](https://lh3.googleusercontent.com/-sPq1TCnnNG0/XTsHa6jRPPI/AAAAAAAAgIY/4LxPFGigoSEQ84oWQ-gotopyQMrfX4b8gCK8BGAs/s0/Rootsofploy.PNG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.00000000e+00+0.j, -7.77156117e-16+1.j, -7.77156117e-16-1.j])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([1, 1, 1, 1])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2\n",
      "2 x + 3 x + 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "poly1d([4, 3])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.poly1d([2,3,1])\n",
    "print(p)\n",
    "p2 = np.polyder(p)\n",
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([4])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyder(p, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.5 , 1.75]), array([0.25]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([3.0, 5.0, 2.0])\n",
    "y = np.array([2.0, 1.0])\n",
    "np.polydiv(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([0.0, 1.0, 2.0, 3.0,  4.0,  5.0])\n",
    "y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])\n",
    "z = np.polyfit(x, y, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1b5d41cc5c0>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([0.33333333, 0.5       , 1.        , 0.        ])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.poly1d([1,1,1])\n",
    "P = np.polyint(p)\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([0.01666667, 0.04166667, 0.16666667, 0.        , 0.        ,\n",
       "       0.        ])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = np.polyint(p, 3)\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = np.polyint(p, 3, k=[6,5,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "poly1d([0.01666667, 0.04166667, 0.16666667, 3.        , 5.        ,\n",
       "       3.        ])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = np.poly1d([1, 2, 3])\n",
    "p2 = np.poly1d([9, 5, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2\n",
      "1 x + 2 x + 3\n",
      "   2\n",
      "9 x + 5 x + 1\n"
     ]
    }
   ],
   "source": [
    "print(p1)\n",
    "print(p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "Poly = np.polymul(p1,p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   4      3      2\n",
      "9 x + 23 x + 38 x + 17 x + 3\n"
     ]
    }
   ],
   "source": [
    "print(Poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = np.polysub(p1,p2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    2\n",
      "-8 x - 3 x + 2\n"
     ]
    }
   ],
   "source": [
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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