{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy as sy\n",
    "from tbcontrol.symbolic import routh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "sy.init_printing()\n",
    "s = sy.Symbol('s')\n",
    "a_0, a_1, a_2, a_3, a_4 = sy.symbols('a_0:5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo 1 - Polinômio simbólico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\operatorname{Poly}{\\left( s^{4} + a_{3} s^{3} + a_{2} s^{2} + a_{1} s + a_{0}, s, domain=\\mathbb{Z}\\left[a_{0}, a_{1}, a_{2}, a_{3}\\right] \\right)}$"
      ],
      "text/plain": [
       "Poly(s**4 + a_3*s**3 + a_2*s**2 + a_1*s + a_0, s, domain='ZZ[a_0,a_1,a_2,a_3]'\n",
       ")"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = sy.Poly(a_0 + a_1*s**1 + a_2*s**2 + a_3*s**3 + s**4, s)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & a_{2} & a_{0}\\\\a_{3} & a_{1} & 0\\\\- \\frac{a_{1}}{a_{3}} + a_{2} & a_{0} & 0\\\\\\frac{a_{0} a_{3}^{2} + a_{1}^{2} - a_{1} a_{2} a_{3}}{a_{1} - a_{2} a_{3}} & 0 & 0\\\\a_{0} & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           1             a₂  a₀⎤\n",
       "⎢                               ⎥\n",
       "⎢          a₃             a₁  0 ⎥\n",
       "⎢                               ⎥\n",
       "⎢         a₁                    ⎥\n",
       "⎢       - ── + a₂         a₀  0 ⎥\n",
       "⎢         a₃                    ⎥\n",
       "⎢                               ⎥\n",
       "⎢     2     2                   ⎥\n",
       "⎢a₀⋅a₃  + a₁  - a₁⋅a₂⋅a₃        ⎥\n",
       "⎢───────────────────────  0   0 ⎥\n",
       "⎢       a₁ - a₂⋅a₃              ⎥\n",
       "⎢                               ⎥\n",
       "⎣          a₀             0   0 ⎦"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "routh(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo 2 - Polinômio de coeficientes numéricos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 3 & 1\\\\2 & 4 & 0\\\\1 & 1 & 0\\\\2 & 0 & 0\\\\1 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  3  1⎤\n",
       "⎢       ⎥\n",
       "⎢2  4  0⎥\n",
       "⎢       ⎥\n",
       "⎢1  1  0⎥\n",
       "⎢       ⎥\n",
       "⎢2  0  0⎥\n",
       "⎢       ⎥\n",
       "⎣1  0  0⎦"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = sy.Poly(s**4 + 2 * s**3 + 3 * s**2 + 4 * s + 1, s)\n",
    "routh(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & \\frac{1}{2} & 0 & 2 & 4\\\\2 & 0 & 2 & 4 & 0\\\\\\frac{1}{2} & -1 & 0 & 4 & 0\\\\4 & 2 & -12 & 0 & 0\\\\- \\frac{5}{4} & \\frac{3}{2} & 4 & 0 & 0\\\\\\frac{34}{5} & \\frac{4}{5} & 0 & 0 & 0\\\\\\frac{28}{17} & 4 & 0 & 0 & 0\\\\- \\frac{110}{7} & 0 & 0 & 0 & 0\\\\4 & 0 & 0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  1     1/2   0   2  4⎤\n",
       "⎢                      ⎥\n",
       "⎢  2      0    2   4  0⎥\n",
       "⎢                      ⎥\n",
       "⎢ 1/2    -1    0   4  0⎥\n",
       "⎢                      ⎥\n",
       "⎢  4      2   -12  0  0⎥\n",
       "⎢                      ⎥\n",
       "⎢ -5/4   3/2   4   0  0⎥\n",
       "⎢                      ⎥\n",
       "⎢ 34/5   4/5   0   0  0⎥\n",
       "⎢                      ⎥\n",
       "⎢  28                  ⎥\n",
       "⎢  ──     4    0   0  0⎥\n",
       "⎢  17                  ⎥\n",
       "⎢                      ⎥\n",
       "⎢-110/7   0    0   0  0⎥\n",
       "⎢                      ⎥\n",
       "⎣  4      0    0   0  0⎦"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = sy.Poly(s**8 + 2 * s**7 + sy.Rational(1, 2) * s**6 + 2 * s**3 + 2 * s**2 + 4 * s + 4, s)\n",
    "routh(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemplo 3 - Bicicleta de Whipple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\operatorname{Poly}{\\left( 1.0 s^{4} + 3.19038797723876 v s^{3} + \\left(3.5124784014838 v^{2} - 40.3985278400138\\right) s^{2} + \\left(3.48482071330788 v^{3} - 26.5613984620113 v\\right) s + 300.015050749107 - 8.26676015041851 v^{2}, s, domain=\\mathbb{R}\\left[v\\right] \\right)}$"
      ],
      "text/plain": [
       "Poly(1.0*s**4 + 3.19038797723876*v*s**3 + (3.5124784014838*v**2 - 40.398527840\n",
       "0138)*s**2 + (3.48482071330788*v**3 - 26.5613984620113*v)*s + 300.015050749107\n",
       " - 8.26676015041851*v**2, s, domain='RR[v]')"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = sy.Symbol('v')\n",
    "\n",
    "p = sy.Poly(300.0150507491072 - 40.39852784001377*s**2 + 1.*s**4 - 26.561398462011333*s*v +\n",
    "            3.1903879772387578*s**3*v - 8.266760150418511*v**2 + 3.5124784014837966*s**2*v**2 +\n",
    "   3.484820713307884*s*v**3, s)\n",
    "\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 3.5124784014838 v^{2} - 40.3985278400138 & 300.015050749107 - 8.26676015041851 v^{2}\\\\3.19038797723876 v & 3.48482071330788 v^{3} - 26.5613984620113 v & 0\\\\2.42019096241065 v^{2} - 32.0730832071012 & 300.015050749107 - 8.26676015041851 v^{2} & 0\\\\\\frac{v \\left(8.43393159596917 v^{4} - 149.67842901189 v^{2} - 105.258467931569\\right)}{2.42019096241065 v^{2} - 32.0730832071012} & 0 & 0\\\\\\frac{69.7212896289135 v^{6} - 3767.66208811192 v^{4} + 44035.6349678579 v^{2} + 31579.124598263}{- 8.43393159596917 v^{4} + 149.67842901189 v^{2} + 105.258467931569} & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                       1.0                                   \n",
       "⎢                                                                             \n",
       "⎢                                                                             \n",
       "⎢                               3.19038797723876⋅v                            \n",
       "⎢                                                                             \n",
       "⎢                                       2                                     \n",
       "⎢                     2.42019096241065⋅v  - 32.0730832071012                  \n",
       "⎢                                                                             \n",
       "⎢           ⎛                  4                    2                   ⎞     \n",
       "⎢         v⋅⎝8.43393159596917⋅v  - 149.67842901189⋅v  - 105.258467931569⎠     \n",
       "⎢         ───────────────────────────────────────────────────────────────     \n",
       "⎢                                        2                                    \n",
       "⎢                      2.42019096241065⋅v  - 32.0730832071012                 \n",
       "⎢                                                                             \n",
       "⎢                  6                     4                     2              \n",
       "⎢69.7212896289135⋅v  - 3767.66208811192⋅v  + 44035.6349678579⋅v  + 31579.12459\n",
       "⎢─────────────────────────────────────────────────────────────────────────────\n",
       "⎢                              4                    2                         \n",
       "⎣          - 8.43393159596917⋅v  + 149.67842901189⋅v  + 105.258467931569      \n",
       "\n",
       "                        2                                                     \n",
       "       3.5124784014838⋅v  - 40.3985278400138    300.015050749107 - 8.266760150\n",
       "                                                                              \n",
       "                        3                                                     \n",
       "      3.48482071330788⋅v  - 26.5613984620113⋅v                    0           \n",
       "                                                                              \n",
       "                                            2                                 \n",
       "       300.015050749107 - 8.26676015041851⋅v                      0           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                         0                                        0           \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "8263                                                                          \n",
       "────                     0                                        0           \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "       2⎤\n",
       "41851⋅v ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎥\n",
       "        ⎦"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rhm = routh(p)\n",
    "rhm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/latex": [
       "$\\displaystyle \\left(\\left(-6.02426201538842 < v \\wedge v < -4.29238253634113\\right) \\vee \\left(-4.29238253634113 < v \\wedge v < 4.29238253634113\\right) \\vee \\left(4.29238253634113 < v \\wedge v < 6.02426201538842\\right)\\right) \\wedge \\left(\\left(-4.29238253634113 < v \\wedge v < -3.64037009499264\\right) \\vee \\left(4.29238253634113 < v \\wedge v < \\infty\\right) \\vee \\left(0 < v \\wedge v < 3.64037009499264\\right)\\right) \\wedge 3.64037009499264 < v \\wedge v < \\infty$"
      ],
      "text/plain": [
       "((-6.02426201538842 < v ∧ v < -4.29238253634113) ∨ (-4.29238253634113 < v ∧ v \n",
       "< 4.29238253634113) ∨ (4.29238253634113 < v ∧ v < 6.02426201538842)) ∧ ((-4.29\n",
       "238253634113 < v ∧ v < -3.64037009499264) ∨ (4.29238253634113 < v ∧ v < ∞) ∨ (\n",
       "0 < v ∧ v < 3.64037009499264)) ∧ 3.64037009499264 < v ∧ v < ∞"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = sy.solve([e > 0 for e in rhm[:, 0]], v)\n",
    "sol"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "P39",
   "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": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}