Solving Inequalities

solvingInequalities.ipynb

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      "cell_type": "code",
      "source": "import sympy as sym\nfrom IPython.display import display, Math",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "def disp(expr):\n    display(Math(sym.latex(expr)))",
      "execution_count": 8,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "x = sym.symbols('x')\nexpr = 4 * x > 8\ndisp(sym.solve(expr))",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<IPython.core.display.Math object>",
            "text/latex": "$\\displaystyle 2 < x \\wedge x < \\infty$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "#infinity\nsym.oo > 99999999999999999999999",
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": "True",
            "text/latex": "$\\displaystyle \\text{True}$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "a,b,c = sym.symbols('a b c')\nex = a*x > b**2/c\ndisp(ex)\nsym.solve(ex)\n#not enough information to solve using only symbols need to replace those by numbers",
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<IPython.core.display.Math object>",
            "text/latex": "$\\displaystyle a x > \\frac{b^{2}}{c}$"
          },
          "metadata": {}
        },
        {
          "output_type": "error",
          "ename": "NotImplementedError",
          "evalue": "\ninequality has more than one symbol of interest.",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-12-7e62abfcae86>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mex\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mx\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mdisp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0msym\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[1;32mC:\\tools\\Anaconda3\\lib\\site-packages\\sympy\\solvers\\solvers.py\u001b[0m in \u001b[0;36msolve\u001b[1;34m(f, *symbols, **flags)\u001b[0m\n\u001b[0;32m    983\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    984\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mfi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Relational\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 985\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mreduce_inequalities\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    986\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    987\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mPoly\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;32mC:\\tools\\Anaconda3\\lib\\site-packages\\sympy\\solvers\\inequalities.py\u001b[0m in \u001b[0;36mreduce_inequalities\u001b[1;34m(inequalities, symbols)\u001b[0m\n\u001b[0;32m    985\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    986\u001b[0m     \u001b[1;31m# solve system\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 987\u001b[1;33m     \u001b[0mrv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_reduce_inequalities\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minequalities\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    988\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    989\u001b[0m     \u001b[1;31m# restore original symbols and return\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;32mC:\\tools\\Anaconda3\\lib\\site-packages\\sympy\\solvers\\inequalities.py\u001b[0m in \u001b[0;36m_reduce_inequalities\u001b[1;34m(inequalities, symbols)\u001b[0m\n\u001b[0;32m    905\u001b[0m                 raise NotImplementedError(filldedent('''\n\u001b[0;32m    906\u001b[0m                     \u001b[0minequality\u001b[0m \u001b[0mhas\u001b[0m \u001b[0mmore\u001b[0m \u001b[0mthan\u001b[0m \u001b[0mone\u001b[0m \u001b[0msymbol\u001b[0m \u001b[0mof\u001b[0m \u001b[0minterest\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 907\u001b[1;33m                     '''))\n\u001b[0m\u001b[0;32m    908\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    909\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mexpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_polynomial\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgen\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
            "\u001b[1;31mNotImplementedError\u001b[0m: \ninequality has more than one symbol of interest."
          ]
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "ex = 3*x/2 + (4-5*x)/3 <= 2 - 5*(2-x)/4\ndisp(ex)",
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<IPython.core.display.Math object>",
            "text/latex": "$\\displaystyle \\frac{4}{3} - \\frac{x}{6} \\leq \\frac{5 x}{4} - \\frac{1}{2}$"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "disp(sym.solve(ex))",
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<IPython.core.display.Math object>",
            "text/latex": "$\\displaystyle \\frac{22}{17} \\leq x \\wedge x < \\infty$"
          },
          "metadata": {}
        }
      ]
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