abhigyan/Jupyter/Random Integration, Differentiation, Area, and a little LaTeX.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LaTeX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We convert a normal text to a latex text using the command `latex_name`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DG"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('DG', latex_name='\\\\Delta G^\\\\alpha')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\Delta G^\\alpha}</script></html>"
      ],
      "text/plain": [
       "DG"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DG.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(x1, x2, eta1)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('x1,x2,eta1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sage automatically converts numbered variables to subscripted variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "expr = x1+x2+eta1^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta_{1}^{2} + x_{1} + x_{2}</script></html>"
      ],
      "text/plain": [
       "eta1^2 + x1 + x2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(a, b, c)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('a,b,c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x)=a*x^2+b*x+c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "[x1,x2]=f(x).solve(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = -\\frac{b + \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}</script></html>"
      ],
      "text/plain": [
       "x == -1/2*(b + sqrt(b^2 - 4*a*c))/a"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}x = -\\frac{b - \\sqrt{b^{2} - 4 \\, a c}}{2 \\, a}</script></html>"
      ],
      "text/plain": [
       "x == -1/2*(b - sqrt(b^2 - 4*a*c))/a"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\sqrt{\\pi} \\operatorname{erf}\\left(x\\right)</script></html>"
      ],
      "text/plain": [
       "1/2*sqrt(pi)*erf(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate(e^(-x^2),x).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(erf(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{2 \\, e^{\\left(-x^{2}\\right)}}{\\sqrt{\\pi}}</script></html>"
      ],
      "text/plain": [
       "2*e^(-x^2)/sqrt(pi)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "derivative(erf(x),x).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot(erf(x),(-10,10),frame=True,color='magenta',legend_label='erf(x)')\n",
    "p2 = plot(erf(x).derivative(x),(-10,10),frame=True,color='blue',legend_label='erfprime(x)')\n",
    "p3 = plot(erf(x).derivative(x).derivative(x),(-10,10),frame=True,color='green',legend_label='erfprime(x)')\n",
    "pnew = p1+p2+p3\n",
    "pnew.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1(x,y) = 2*x^3 + 3*y^2+3*x^2*y^4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y \\right) \\ {\\mapsto} \\ 3 \\, x^{2} y^{4} + 2 \\, x^{3} + 3 \\, y^{2}</script></html>"
      ],
      "text/plain": [
       "(x, y) |--> 3*x^2*y^4 + 2*x^3 + 3*y^2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "g(x,y)=f1.derivative(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "h(x,y) =f1.derivative(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y \\right) \\ {\\mapsto} \\ 6 \\, x y^{4} + 6 \\, x^{2}</script></html>"
      ],
      "text/plain": [
       "(x, y) |--> 6*x*y^4 + 6*x^2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y \\right) \\ {\\mapsto} \\ 12 \\, x^{2} y^{3} + 6 \\, y</script></html>"
      ],
      "text/plain": [
       "(x, y) |--> 12*x^2*y^3 + 6*y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g.show()\n",
    "h.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "d2fdx2 = derivative(f1,x,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y \\right) \\ {\\mapsto} \\ 6 \\, y^{4} + 12 \\, x</script></html>"
      ],
      "text/plain": [
       "(x, y) |--> 6*y^4 + 12*x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d2fdx2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "j(x) = function('j')(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "expr = 5*j^2 + sin(j) == x^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ 5 \\, j\\left(x\\right)^{2} + \\sin\\left(j\\left(x\\right)\\right) = x^{2}</script></html>"
      ],
      "text/plain": [
       "x |--> 5*j(x)^2 + sin(j(x)) == x^2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "dhdx = solve(diff(expr),diff(j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial x}j\\left(x\\right) = \\frac{2 \\, x}{\\cos\\left(j\\left(x\\right)\\right) + 10 \\, j\\left(x\\right)}</script></html>"
      ],
      "text/plain": [
       "diff(j(x), x) == 2*x/(cos(j(x)) + 10*j(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dhdx[0].show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{\\pi}</script></html>"
      ],
      "text/plain": [
       "sqrt(pi)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate(e^-(x^2),x,-oo,oo).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "expr2 = +1/x^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{x^{2}}</script></html>"
      ],
      "text/plain": [
       "x^(-2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Integral is divergent.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py\u001b[0m in \u001b[0;36msr_integral\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    790\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 791\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mmax_to_sr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmaxima_eval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmax_integrate\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msr_to_max\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    792\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mRuntimeError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0merror\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/libs/ecl.pyx\u001b[0m in \u001b[0;36msage.libs.ecl.EclObject.__call__ (build/cythonized/sage/libs/ecl.c:7796)\u001b[0;34m()\u001b[0m\n\u001b[1;32m    805\u001b[0m         \u001b[0mlispargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mEclObject\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 806\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mecl_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mecl_safe_apply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0mEclObject\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mlispargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    807\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/libs/ecl.pyx\u001b[0m in \u001b[0;36msage.libs.ecl.ecl_safe_apply (build/cythonized/sage/libs/ecl.c:5458)\u001b[0;34m()\u001b[0m\n\u001b[1;32m    377\u001b[0m         \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msi_coerce_to_base_string\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mecl_values\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 378\u001b[0;31m         raise RuntimeError(\"ECL says: {}\".format(\n\u001b[0m\u001b[1;32m    379\u001b[0m             char_to_str(ecl_base_string_pointer_safe(s))))\n",
      "\u001b[0;31mRuntimeError\u001b[0m: ECL says: Error executing code in Maxima: defint: integral is divergent.",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-77-dc321666f49b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mexpr2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0moo\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0moo\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/expression.pyx\u001b[0m in \u001b[0;36msage.symbolic.expression.Expression.integral (build/cythonized/sage/symbolic/expression.cpp:64072)\u001b[0;34m()\u001b[0m\n\u001b[1;32m  12404\u001b[0m                     \u001b[0mR\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mring\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSR\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  12405\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mintegral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m> 12406\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mintegral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m  12407\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m  12408\u001b[0m     \u001b[0mintegrate\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mintegral\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/integration/integral.py\u001b[0m in \u001b[0;36mintegrate\u001b[0;34m(expression, v, a, b, algorithm, hold)\u001b[0m\n\u001b[1;32m    826\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mindefinite_integral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    827\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 828\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mdefinite_integral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mhold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    829\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    830\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/function.pyx\u001b[0m in \u001b[0;36msage.symbolic.function.BuiltinFunction.__call__ (build/cythonized/sage/symbolic/function.cpp:11848)\u001b[0;34m()\u001b[0m\n\u001b[1;32m    996\u001b[0m             \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_evalf_try_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    997\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 998\u001b[0;31m                 res = super(BuiltinFunction, self).__call__(\n\u001b[0m\u001b[1;32m    999\u001b[0m                         *args, coerce=coerce, hold=hold)\n\u001b[1;32m   1000\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/function.pyx\u001b[0m in \u001b[0;36msage.symbolic.function.Function.__call__ (build/cythonized/sage/symbolic/function.cpp:6827)\u001b[0;34m()\u001b[0m\n\u001b[1;32m    485\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    486\u001b[0m                 \u001b[0mvec\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpush_back\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0mExpression\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_gobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 487\u001b[0;31m             \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_function_evalv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_serial\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    488\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_nargs\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    489\u001b[0m             res = g_function_eval1(self._serial,\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/function.pyx\u001b[0m in \u001b[0;36msage.symbolic.function.BuiltinFunction._evalf_or_eval_ (build/cythonized/sage/symbolic/function.cpp:12987)\u001b[0;34m()\u001b[0m\n\u001b[1;32m   1084\u001b[0m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_evalf_try_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1085\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1086\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_eval0_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1087\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1088\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/integration/integral.py\u001b[0m in \u001b[0;36m_eval_\u001b[0;34m(self, f, x, a, b)\u001b[0m\n\u001b[1;32m    181\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mintegrator\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrators\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    182\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 183\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mintegrator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    184\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    185\u001b[0m                 \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/symbolic/integration/external.py\u001b[0m in \u001b[0;36mmaxima_integrator\u001b[0;34m(expression, v, a, b)\u001b[0m\n\u001b[1;32m     32\u001b[0m         \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmaxima\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msr_integral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     33\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 34\u001b[0;31m         \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmaxima\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msr_integral\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     35\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_sage_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     36\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/abhigyan/anaconda3/envs/sage/lib/python3.7/site-packages/sage/interfaces/maxima_lib.py\u001b[0m in \u001b[0;36msr_integral\u001b[0;34m(self, *args)\u001b[0m\n\u001b[1;32m    795\u001b[0m \u001b[0;31m# in pexpect interface, one looks for this - e.g. integrate(1/x^3,x,-1,3) gives a principal value\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    796\u001b[0m \u001b[0;31m#            if \"divergent\" in s or 'Principal Value' in s:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 797\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Integral is divergent.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    798\u001b[0m             \u001b[0;32melif\u001b[0m \u001b[0;34m\"Is\"\u001b[0m \u001b[0;32min\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# Maxima asked for a condition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    799\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_missing_assumption\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Integral is divergent."
     ]
    }
   ],
   "source": [
    "expr2.integrate(x,-oo,oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "+Infinity"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr2.limit(x=0,dir='plus')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "+Infinity"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr2.limit(x=0,dir='minus')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_new(x) = x*log(x)+(1-x)*log(1-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_new.plot(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x |--> 0"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(g_new,x=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x |--> Infinity"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(g_new).limit(x=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(g_new).plot(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "s(x) = sin(x)/x^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1(x) = s.series(x==1, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{6} \\, {\\left(x - 1\\right)}^{3} {\\left(17 \\, \\cos\\left(1\\right) - 18 \\, \\sin\\left(1\\right)\\right)} - \\frac{1}{2} \\, {\\left(x - 1\\right)}^{2} {\\left(4 \\, \\cos\\left(1\\right) - 5 \\, \\sin\\left(1\\right)\\right)} + {\\left(x - 1\\right)} {\\left(\\cos\\left(1\\right) - 2 \\, \\sin\\left(1\\right)\\right)} + \\sin\\left(1\\right)</script></html>"
      ],
      "text/plain": [
       "1/6*(x - 1)^3*(17*cos(1) - 18*sin(1)) - 1/2*(x - 1)^2*(4*cos(1) - 5*sin(1)) + (x - 1)*(cos(1) - 2*sin(1)) + sin(1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s1(x).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "s2(x) = s.taylor(x,1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -\\frac{1}{3628800} \\, {\\left(x - 1\\right)}^{10} {\\left(31628180 \\, \\cos\\left(1\\right) - 24620669 \\, \\sin\\left(1\\right)\\right)} + \\frac{1}{362880} \\, {\\left(x - 1\\right)}^{9} {\\left(2857465 \\, \\cos\\left(1\\right) - 2266002 \\, \\sin\\left(1\\right)\\right)} - \\frac{1}{40320} \\, {\\left(x - 1\\right)}^{8} {\\left(283568 \\, \\cos\\left(1\\right) - 229993 \\, \\sin\\left(1\\right)\\right)} + \\frac{1}{5040} \\, {\\left(x - 1\\right)}^{7} {\\left(31205 \\, \\cos\\left(1\\right) - 26026 \\, \\sin\\left(1\\right)\\right)} - \\frac{1}{720} \\, {\\left(x - 1\\right)}^{6} {\\left(3852 \\, \\cos\\left(1\\right) - 3329 \\, \\sin\\left(1\\right)\\right)} + \\frac{1}{120} \\, {\\left(x - 1\\right)}^{5} {\\left(541 \\, \\cos\\left(1\\right) - 490 \\, \\sin\\left(1\\right)\\right)} - \\frac{1}{24} \\, {\\left(x - 1\\right)}^{4} {\\left(88 \\, \\cos\\left(1\\right) - 85 \\, \\sin\\left(1\\right)\\right)} + \\frac{1}{6} \\, {\\left(x - 1\\right)}^{3} {\\left(17 \\, \\cos\\left(1\\right) - 18 \\, \\sin\\left(1\\right)\\right)} - \\frac{1}{2} \\, {\\left(x - 1\\right)}^{2} {\\left(4 \\, \\cos\\left(1\\right) - 5 \\, \\sin\\left(1\\right)\\right)} + {\\left(x - 1\\right)} {\\left(\\cos\\left(1\\right) - 2 \\, \\sin\\left(1\\right)\\right)} + \\sin\\left(1\\right)</script></html>"
      ],
      "text/plain": [
       "x |--> -1/3628800*(x - 1)^10*(31628180*cos(1) - 24620669*sin(1)) + 1/362880*(x - 1)^9*(2857465*cos(1) - 2266002*sin(1)) - 1/40320*(x - 1)^8*(283568*cos(1) - 229993*sin(1)) + 1/5040*(x - 1)^7*(31205*cos(1) - 26026*sin(1)) - 1/720*(x - 1)^6*(3852*cos(1) - 3329*sin(1)) + 1/120*(x - 1)^5*(541*cos(1) - 490*sin(1)) - 1/24*(x - 1)^4*(88*cos(1) - 85*sin(1)) + 1/6*(x - 1)^3*(17*cos(1) - 18*sin(1)) - 1/2*(x - 1)^2*(4*cos(1) - 5*sin(1)) + (x - 1)*(cos(1) - 2*sin(1)) + sin(1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = piecewise([((0,pi/2),-1),((pi/2,pi),1)])\n",
    "f.fourier_series_cosine_coefficient(10)\n",
    "f.fourier_series_sine_coefficient(10)\n",
    "s3 = f.fourier_series_partial_sum(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = f.plot(x,0,pi)\n",
    "p2 = s3.plot(x,0,pi)\n",
    "pnew = p1+p2\n",
    "pnew.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 8.8",
   "language": "sage",
   "name": "sagemath"
  },
  "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
}