koeficijenti_prijenosne_funkcije.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Koeficijenti prijenosne funkcije\n",
    "\n",
    "Za razne operacije proračuna stabilnosti sustava potrebno je prijenosnu funkciju pojednostaviti, rasčlaniti, odvojiti brojnik i nazivnik u zasebne varijable te potom odvojiti sve koeficijente uz potencije s-a u zasebne varijable.\n",
    "\n",
    "Bez toga nije moguće odraditi hurwitzov i routhov kriterij stabilnosti.\n",
    "\n",
    "Python funkcije koje se koriste za ove operacije dio su ```Sympy``` knjižnice.\n",
    "```python\n",
    "* symbols\n",
    "* poly\n",
    "* simplify\n",
    "* expand\n",
    "* fraction\n",
    "```\n",
    "\n",
    "### Primjer s numerickim koeficijentima"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za početak potrebno je obrisati sve varijable iz memorije."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "clear = lambda: os.system('cls')\n",
    "clear()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.interactive import printing\n",
    "printing.init_printing(use_latex=True)\n",
    "from sympy import symbols, poly, simplify, expand, fraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Potrebno je definirati sva imena matematičkih varijabli koje koristimo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = symbols('s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Potenciranje u pythonu vršimo s ```**``` u obliku ```VARIJABLA**POTENCIJA```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{1}{\\left(s + 6\\right) \\left(s^{2} + 2\\right)}$$"
      ],
      "text/plain": [
       "       1        \n",
       "────────────────\n",
       "        ⎛ 2    ⎞\n",
       "(s + 6)⋅⎝s  + 2⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf = (1 / ((s+6)*(s**2+2)))\n",
    "display(tf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Funkciju možemo razviti u polinom putem funkcije ```expand()```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAhCAYAAAAf+x+qAAAABHNCSVQICAgIfAhkiAAAAyRJREFUeJzt2l+oFFUcwPGPZdkfLbGIJAIhX4xCBSGIrEtELyJEBL0kIb1lRUQpKogg6EOIIORTD1uBEORTQS8iUqhYRH+Ril5KKOrGjaTootXt4TeLu9vcu2eu487gni8cZvcwZ/e75zfn7PnNHDKZMeBBvIsfMYMnmtVpjquaFhgxN+JzPNe0SKY58ojPjB858GNKDvyYkgM/puTAjykLmxYYMYuxsuf9CqzBFH5oQigzGiZEGjdYOs0pZTKZTCZzWVhQHGcatchkMu3ipHiq9RV2NexSxp04jjPC8/FGba4gbiqOV+OUyH3bxHKsLl7fhrO4oTmd9pN65+5ccby2KG3jJzHS4Rf8hlub02k/VW7ZnhadehSfXQaX5XgDk/gLX+KheXzOOlwjRn2dbMfHYhBMip0899T8HcNI2UGU5Fkl8PfhDjHNp/7gDnYnnLcUJ0SWsQF340VxoVXhFryJZ6RlKql+xF2/Q7gfD+NvMQiWVXS8FI+UHUQTKnouwFZ8g2nR6e+UnLcNLydIkv6D9orAz8Uwv0X4AJsS3ar4lbEY/2BjBcc6PVJ3EJV59j2keQWb8Sy+c3HBdLP4X5/EdXgUBypKDuMxvI/DeERMZa/jNRdH7mx+RId3cAxv1ew2G0vEjDnVUzeXY1OUefZxDPtL6lfgE3yhejrXkXYlTxdlH9aKzvsDWxL84AH8K9Ye3XJvjX5lvI1PRaaT4li3R+qIL/Ps43kxJRwVHT6fVfEOEbBuuYDzA3XrS9qdF2liL/tEXt4Gv0FeFZnEyoH6VMc6PFICP5vn/7gLL4kR8ztWDWswwLLiS7rlCA4O1F1f0u57MbX3sgl/tsSvl/34WSxAy0hxrMNjWOCHeZayUKQDT1ZpVEJH2hR2GB8O1O3RP+J7GbVfl4PSO7OKY1UP5g78UM/u4m5bceJHYvn/tJh6jleUmS8HxG3hneI/aS1eEFNiG/yIFOkpsRCdwu1FfXdqHoVjyg6iYZ597MLX4sbJr3hPPavRjvQreYPIUafxrQh89+lhG/zKdu7M9LS/FMdUj4lZHDoVPDOZTCaTyVzB/Ae7Zg89uO8IfwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{1}{s^{3} + 6 s^{2} + 2 s + 12}$$"
      ],
      "text/plain": [
       "         1          \n",
       "────────────────────\n",
       " 3      2           \n",
       "s  + 6⋅s  + 2⋅s + 12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf_poly = expand(tf)\n",
    "display(tf_poly)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Koeficijente uz ```S^n``` možemo dobiti putem funkcije ```poly(n, s)```\n",
    "No za to je prvo potrebno odvojiti brojnik i nazivnik"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$s^{3} + 6 s^{2} + 2 s + 12$$"
      ],
      "text/plain": [
       " 3      2           \n",
       "s  + 6⋅s  + 2⋅s + 12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "brojnik, nazivnik = fraction(tf_poly)\n",
    "display(brojnik)\n",
    "display(nazivnik)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sada kada smo odvojili brojnik i nazivnik u zasebne varijable možemo primjeniti ```poly()``` funkciju"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\operatorname{Poly}{\\left( s^{3} + 6 s^{2} + 2 s + 12, s, domain=\\mathbb{Z} \\right)}$$"
      ],
      "text/plain": [
       "Poly(s**3 + 6*s**2 + 2*s + 12, s, domain='ZZ')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_coeffs = poly(nazivnik, s)\n",
    "display(s_coeffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za matricu koeficijenata potrebno je primjeniti funkciju ```coeffs()```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ 1, \\quad 6, \\quad 2, \\quad 12\\right ]$$"
      ],
      "text/plain": [
       "[1, 6, 2, 12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_coeffs = s_coeffs.coeffs()\n",
    "display(s_coeffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Koeficijenti su zapisani u matricu obrnutim redoslijedom nego što inače zapisujemo, na prvom mjestu je koeficijent uz najviši eksponent s-a stoga treba paziti u izvlačenju koeficijenata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAASCAYAAABFGc6jAAAABHNCSVQICAgIfAhkiAAAAQ1JREFUOI3t1L8rhVEcx/EX+QuQ/AM2f8RlMSnFzMCglAxKKWVjv7sMbMomNsWoKOku0s1gMvgxGNA1PN+7cJ8fJ90sPnV6Tud8Pud9fjzn8EeaQR1neEELezneASzgELd4wzPOMY/eItBVDP6KRgloMfofsI8t7OAp2g/Qkwcaw0gYaiWgcUx2mPkw7iM7XbSqtspARVqPbL3dULiPv9B7fD+6CerDbNSPuwnaxiiOcFIlUJN+RsuRaaC/aigVtBT+G9mfV1kpoJXwXmMoBZICWgvfJQZTIVVBG+G5UHIm35+IqShk+zyBO9nbB49YjfocdvEpu5jPHcZvhueHNmOGeaWZ4G3hNG+F/6qsL7liU0twp8QzAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$12$$"
      ],
      "text/plain": [
       "12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAMJJREFUKJHF0j9LQlEYB+DH6BNYhJ/HxcmpD9CgQxCImxAIbi5u7eLSJji5NzQGDRItDtHQ3J0aSnS4LxJytBMN/eBw4XCe+77nD3/MCdqYYYkPFLhHC0cpdIk13nCLIcZ4j/kpKruojmbijzW8Bjz/TevXgW7s6zORz/h+5VY5xiIqNXLRKMA8F3QCPKOaA64CPClP8Md0AyxwlgN6AR5xmgP6AR4c2MP3Z3GBCVbKSywS619izTaDqHJo3OW0+8/ZALBUMPfsVQVVAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAASCAYAAABrXO8xAAAABHNCSVQICAgIfAhkiAAAAP5JREFUOI3N0r8rxVEYx/FXftUtSordYEImQplkYeW/MSol+SfYMFjkx6K7KIMySl2KkqRrkd+u4fvcup3OvZPBs3xO53Pe5/k8p8Mf1wx2cY/30CPM1w+0Z6BlbKIf+wHcYTD841ynJdTC7Mn4nTmoDRW8RLeW1dGwno44O6hiASN4wxlOm4HjoQ84x2jSpIxFPKbdVxXzfeEKs+jGMA7CO8nFXgvzG2OJV8Jt+FMUD1KvamgFFwn4isNYT6TgZehzLk7DxaUULCvmG0JXBhwJvcnduqWYYyXZn8NPpOnNgQOKF61FgnVsR5JPxc9qWn3YwDU+8IQ9TLaC/nH9AnM2OpXemhB0AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$6$$"
      ],
      "text/plain": [
       "6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s0 = s_coeffs[3]\n",
    "s1 = s_coeffs[2]\n",
    "s2 = s_coeffs[1]\n",
    "s3 = s_coeffs[0]\n",
    "display(s0, s1, s2, s3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na ovaj način smo odvojili koeficijente uz eksponente s-a u zasebne varijable ```s0``` ```s1``` ```s2``` i ```s3```.\n",
    "U ovom slučaju radi se o numeričkim koeficijentima, no na isti način bi smo odvojili i koeficijente u obliku simboličkih varijabli."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Primjer s simboličkim koeficijentima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "k, m = symbols('k m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{1}{\\left(4 k^{2} + s^{2}\\right) \\left(2 k + 4 m + s\\right)}$$"
      ],
      "text/plain": [
       "             1             \n",
       "───────────────────────────\n",
       "⎛   2    2⎞                \n",
       "⎝4⋅k  + s ⎠⋅(2⋅k + 4⋅m + s)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf = (1 / ((s+(2*k+4*m))*(s**2+(k**2*4))))\n",
    "display(tf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{1}{8 k^{3} + 16 k^{2} m + 4 k^{2} s + 2 k s^{2} + 4 m s^{2} + s^{3}}$$"
      ],
      "text/plain": [
       "                      1                       \n",
       "──────────────────────────────────────────────\n",
       "   3       2        2          2        2    3\n",
       "8⋅k  + 16⋅k ⋅m + 4⋅k ⋅s + 2⋅k⋅s  + 4⋅m⋅s  + s "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf_simp = expand(tf)\n",
    "display(tf_simp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$8 k^{3} + 16 k^{2} m + 4 k^{2} s + 2 k s^{2} + 4 m s^{2} + s^{3}$$"
      ],
      "text/plain": [
       "   3       2        2          2        2    3\n",
       "8⋅k  + 16⋅k ⋅m + 4⋅k ⋅s + 2⋅k⋅s  + 4⋅m⋅s  + s "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "brojnik, nazivnik = fraction(tf_simp)\n",
    "display(brojnik)\n",
    "display(nazivnik)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$$\\operatorname{Poly}{\\left( s^{3} + \\left(2 k + 4 m\\right) s^{2} + 4 k^{2} s + 8 k^{3} + 16 k^{2} m, s, domain=\\mathbb{Z}\\left[k, m\\right] \\right)}$$"
      ],
      "text/plain": [
       "Poly(s**3 + (2*k + 4*m)*s**2 + 4*k**2*s + 8*k**3 + 16*k**2*m, s, domain='ZZ[k,\n",
       "m]')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_coeffs = poly(nazivnik, s)\n",
    "display(s_coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ 1, \\quad 2 k + 4 m, \\quad 4 k^{2}, \\quad 8 k^{3} + 16 k^{2} m\\right ]$$"
      ],
      "text/plain": [
       "⎡                 2     3       2  ⎤\n",
       "⎣1, 2⋅k + 4⋅m, 4⋅k , 8⋅k  + 16⋅k ⋅m⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_coeffs = s_coeffs.coeffs()\n",
    "display(s_coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$8 k^{3} + 16 k^{2} m$$"
      ],
      "text/plain": [
       "   3       2  \n",
       "8⋅k  + 16⋅k ⋅m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$4 k^{2}$$"
      ],
      "text/plain": [
       "   2\n",
       "4⋅k "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFIAAAATCAYAAAADKFpSAAAABHNCSVQICAgIfAhkiAAAA0hJREFUWIXt11uIlVUUB/CfOc0YGVgTIUE3gqKw1AmKHgIroiikSHoICk9UEBUivkQPwtBLUQbTWxDFdLGn0K5EGJFdCGJ0hhFmUCymoBIxMyOji04Pax/ma8/+xnNmdEZi/nDY5+z/3muvvfa6HeZxymADxnHvXCsylzit8r0bD2Er9uIP/Iov8GC2toqeNO44STrOBPeLRx4Xd5sVPJIO/BGb8TRewaE0/xYWFPaN4HANN5e4QOj+m1k25E1YbbLnLcX3SZk1GXcmjuLTE6hHI521agYyFuBjfIPnzIIhq0b7BO/hWLZmH15M31dl3IokIw/rs/GOuEAfTj8BuraDdcIxHsDvx1l7o9Bzk0hTb+OgSGtbhSPBlXgT+xP3Pi5sCqnLezn+TuM/2fw1aawa8joMJgXvwfrK/tnAFXgGL+CzFtY3c/xloh4cxcsiCu8S6W01vsZivIo9uAOvtaNYB3aJV7s14/rT/OXp9wb8heGk2HTQMP3Q7sAAduOMNNdr6tDenPh9uLoyfxZ+Ec7zE66vcJ3C0MewqFXlNqWDPihww6LQdJsI5f7KJaaDhukb8inhUdVL95rakKOJv63ADSbuvgK3LXHdrSi2Li0exTkZt0iE7A8YE+3Sw60IrWDMRHvSyqd/ClnXCu95NpvvVW/IZrH8tkbmQfysnOP3CCdChEIdHhN5ZgQ3J6FVLE/7u3A+3sBLU8groQ9LsrkVuFPkorGMG6qR04HXxeU2tnH+clEnthW4i0XR3GJyjl+MS/Hl8Q5YL15xF86rWfNoWrNWVPvxtG+maGg/tJdo3av7KvseT3OlSFqTuCcL3A25rJJHPiGq3hBuwYEa5ZvVbkA069vxvEjCW2r2nCz8KSptCT1YKSrybnyVcZT/lZU6kiZWpnFnnUIbhaUHTM6JOXbiCBam30tFKB7x32TfLhpm3pBX0as+Rw6JR+gscB+lfecWuP7ELWtOVD1yrYmq97koNDnGkpDOJGQwrSfah9tF3nhXGHNvQcapgi7RZA+Lli1HD75TjsgeUVxHmxNVQ16SxoXqc912YcirRCUbzPgR3C1e80NhzLrUMNdYJu5QCt2LhCeWGvou0fTvMOFE85jHPP6f+Bez0+J77UgVaQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$2 k + 4 m$$"
      ],
      "text/plain": [
       "2⋅k + 4⋅m"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAHZJREFUKJFjYKACCGFgYJjMwMBwmIGB4RMDA8N/BgaGJYQ0XYAq/MzAwHCdWE2ODAwMqgwMDIwMDAwOuDSxoPH3EzKVgYGBgYkYRaOaBlwTeuQGQDEDAwODBJS2ZGBgWABlv2FgYChBN6SBAZJ0cOEH5LiMzgAA6XoX52TB9a4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s0 = s_coeffs[3]\n",
    "s1 = s_coeffs[2]\n",
    "s2 = s_coeffs[1]\n",
    "s3 = s_coeffs[0]\n",
    "display(s0, s1, s2, s3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}