day 12 - roots of polynomial.ipynb

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    "import numpy as np"
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   "source": [
    "## algorithm"
   ]
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   "source": [
    "def roots(*coeffs):\n",
    "    matrix = np.eye(len(coeffs) - 1, k=-1)\n",
    "    matrix[:,-1] = np.array(coeffs[:0:-1]) / -coeffs[0]\n",
    "    return np.linalg.eigvals(matrix)"
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   "source": [
    "## run"
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       "array([ 0.1])"
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   "source": [
    "# 10x - 1 = 0\n",
    "roots(10, -1)"
   ]
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       "array([ 1.,  1.])"
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     "execution_count": 4,
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   "source": [
    "# x^2 - 2x + 1 = 0\n",
    "roots(1, -2, 1)"
   ]
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   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "array([ 3., -3.])"
      ]
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     "execution_count": 5,
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   "source": [
    "# 2x^2 - 18 = 0\n",
    "roots(2, 0, -18)"
   ]
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   "execution_count": 6,
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      "text/plain": [
       "array([ 0.5+0.8660254j,  0.5-0.8660254j, -1.0+0.j       , -0.5+0.8660254j,\n",
       "       -0.5-0.8660254j])"
      ]
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     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "# x^5 + x^4 + x^3 + x^2 + x + 1 = 0\n",
    "roots(1, 1, 1, 1, 1, 1)"
   ]
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   "execution_count": null,
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