abhigyan/Jupyter/Session-21.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parametric plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "theta"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('theta', latex_name=\"\\\\theta\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polar_plot(2*cos(7*theta), (theta, 0, 2*pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polar_plot( exp(theta/10), (theta, -12*pi, 2*pi), plot_points=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sudoku using Sage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = matrix(9, 9, [5,0,0, 0,8,0, 0,4,9, 0,0,0, 5,0,0, 0,3,0, \n",
    "                  0,6,7, 3,0,0, 0,0,1, 1,5,0, 0,0,0, 0,0,0, 0,0,0, 2,0,8, \n",
    "                  0,0,0, 0,0,0, 0,0,0, 0,1,8, 7,0,0, 0,0,4, 1,5,0, 0,3,0,\n",
    "                  0,0,2, 0,0,0, 4,9,0, 0,5,0, 0,0,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 0 0 0 8 0 0 4 9]\n",
      "[0 0 0 5 0 0 0 3 0]\n",
      "[0 6 7 3 0 0 0 0 1]\n",
      "[1 5 0 0 0 0 0 0 0]\n",
      "[0 0 0 2 0 8 0 0 0]\n",
      "[0 0 0 0 0 0 0 1 8]\n",
      "[7 0 0 0 0 4 1 5 0]\n",
      "[0 3 0 0 0 2 0 0 0]\n",
      "[4 9 0 0 5 0 0 0 3]\n"
     ]
    }
   ],
   "source": [
    "print A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5 1 3 6 8 7 2 4 9]\n",
       "[8 4 9 5 2 1 6 3 7]\n",
       "[2 6 7 3 4 9 5 8 1]\n",
       "[1 5 8 4 6 3 9 7 2]\n",
       "[9 7 4 2 1 8 3 6 5]\n",
       "[3 2 6 7 9 5 4 1 8]\n",
       "[7 8 2 9 3 4 1 5 6]\n",
       "[6 3 5 1 7 2 8 9 4]\n",
       "[4 9 1 8 5 6 7 2 3]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sudoku(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Laplacian of a scalar field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(x, y, z)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var('x,y,z')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "g(x, y, z) = x^2 + y^3 + z^4 + x*y*z^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=diff(g,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output of the above call is Hessian of a scalar field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[             (x, y, z) |--> 2            (x, y, z) |--> z^2          (x, y, z) |--> 2*y*z]\n",
      "[           (x, y, z) |--> z^2            (x, y, z) |--> 6*y          (x, y, z) |--> 2*x*z]\n",
      "[         (x, y, z) |--> 2*y*z          (x, y, z) |--> 2*x*z (x, y, z) |--> 2*x*y + 12*z^2]\n"
     ]
    }
   ],
   "source": [
    "print a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Laplacian is the trace of Hessian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = diff(g,2).trace()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y, z \\right) \\ {\\mapsto} \\ 2 \\, x y + 12 \\, z^{2} + 6 \\, y + 2</script></html>"
      ],
      "text/plain": [
       "(x, y, z) |--> 2*x*y + 12*z^2 + 6*y + 2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Divergence of Vector Field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "f(x,y,z) = (x*y^2, y*z^2, z*x^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[  (x, y, z) |--> y^2 (x, y, z) |--> 2*x*y     (x, y, z) |--> 0]\n",
       "[    (x, y, z) |--> 0   (x, y, z) |--> z^2 (x, y, z) |--> 2*y*z]\n",
       "[(x, y, z) |--> 2*x*z     (x, y, z) |--> 0   (x, y, z) |--> x^2]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivative(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Divergence is the trace of above matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(x, y, z) |--> x^2 + y^2 + z^2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivative(f).trace()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arbitrary precision arithmetic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In sage you don't have to worry about the number of digits for precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorial(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sage knows about prime numbers quite well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1709, 1721, 1723, 1733, 1741, 1747]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prime_range(1700, 1750)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can do linear algebra using sage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "A=matrix(3,3,[1,2,3,4,5,6,7,8,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[4 5 6]\n",
      "[7 8 0]\n"
     ]
    }
   ],
   "source": [
    "print A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5.734509942225074?, -0.3883838424073199?, 12.12289378463240?]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.eigenvalues()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.trace()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[30 36 15]\n",
       "[66 81 42]\n",
       "[39 54 69]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[278 350 291]\n",
       "[664 852 654]\n",
       "[703 860 445]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A^3-5*A+4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implicit plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "g(x,y)=x^4+y^4-16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "implicit_plot(g, (x,-3,3), (y,-4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x,y)=exp(-(x^2+y^2))\n",
    "contour_plot(f,(x,-1,1),(y,-1,1),fill=True,axes=True,labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vector algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = vector( [1, 2, 3] )\n",
    "v = vector( [2, 3, 4] )\n",
    "a = v.dot_product(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "w=v.cross_product(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, -2, 1)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.dot_product(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(6)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(14)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sqrt(29)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 5, 7)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u+v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, -1, -1)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u-v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Taylor series for approximation of a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/122880*sqrt(2)*(3*pi - 4*x)^5 - 1/384*sqrt(2)*(3*pi - 4*x)^3 + 1/4*sqrt(2)*(3*pi - 4*x)\n"
     ]
    }
   ],
   "source": [
    "f(x) = cos(x) + sin(x)\n",
    "p(x) = taylor(f(x), x, 3*pi/4, 5)\n",
    "print p(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( p(x), -3*pi, 3*pi, ymax=5, ymin=-5)\n",
    "p2 = plot( f(x), -3*pi, 3*pi, linestyle='--')\n",
    "(p1+p2).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1/3*(x - 1)^5*e^(-1)/sqrt(pi) + 1/3*(x - 1)^4*e^(-1)/sqrt(pi) + 2/3*(x - 1)^3*e^(-1)/sqrt(pi) - 2*(x - 1)^2*e^(-1)/sqrt(pi) + 2*(x - 1)*e^(-1)/sqrt(pi) + erf(1)\n"
     ]
    }
   ],
   "source": [
    "f2 = erf(x)\n",
    "p2(x) = taylor(f2(x), x, 1, 5)\n",
    "print p2(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p3a = plot( p2(x), 0, 4, ymax=2, ymin=-2)\n",
    "p3b = plot( f2(x), 0, 4, linestyle='--')\n",
    "(p3a+p3b).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fancy plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mandelbrot fractal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m(c):\n",
    "    z = complex(0,0)\n",
    "    c = complex(c)\n",
    "    for j in range(100):\n",
    "        if abs(z) > 2 :\n",
    "            break\n",
    "        z = z^2 + c\n",
    "    else:\n",
    "            return complex(0,0)\n",
    "    return complex(0, j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "complex_plot(m, (-2,1), (-1.5, 1.5), plot_points=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circling around"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = vector([1, 0])\n",
    "var('j')\n",
    "k = 20\n",
    "disp = sum(circle(matrix([[cos(j*2*pi/k),-sin(j*2*pi/k)], [sin(j*2*pi/k), cos(j*2*pi/k)]])*v, 1)\n",
    "                 for j in range(k))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 20 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "disp.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphical elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 4 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = []\n",
    "for i in range(15):\n",
    "    L.append([i/10, i/10])\n",
    "\n",
    "G = list_plot(L)\n",
    "G += line([[0,0], [2,1]])\n",
    "G += line([[0,0], [1,2]])\n",
    "G += circle((0,0), 1)\n",
    "G.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Platonic solids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe srcdoc=\"\n",
       "<html>\n",
       "<head>\n",
       "  <style>\n",
       "    * {\n",
       "      margin: 0;\n",
       "      padding: 0;\n",
       "      overflow: hidden;\n",
       "    }\n",
       "    body, html {      \n",
       "      height: 100%;\n",
       "      width: 100%;\n",
       "    }\n",
       "  </style>\n",
       "  <script type=&quot;text/javascript&quot; src=&quot;/nbextensions/jsmol/JSmol.min.js&quot;></script>\n",
       "</head>\n",
       "<body>\n",
       "  <script type=&quot;text/javascript&quot;>\n",
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       "  'draw line_8 diameter 1 curve {-2.618033988749895 2.8025170768881473 3.0}  {2.618033988749895 2.8025170768881473 3.0} ',\n",
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       "  'select atomno = 1',\n",
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       "  'select atomno = 2',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;0.00&quot;',\n",
       "  'select atomno = 3',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;0.87&quot;',\n",
       "  'select atomno = 4',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-0.93&quot;',\n",
       "  'select atomno = 5',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;0.00&quot;',\n",
       "  'select atomno = 6',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;0.93&quot;',\n",
       "  'select atomno = 7',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;-1.0&quot;',\n",
       "  'select atomno = 8',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;0.0&quot;',\n",
       "  'select atomno = 9',\n",
       "  'color atom  [76,76,76]',\n",
       "  'label &quot;1.0&quot;',\n",
       "  'isosurface fullylit; pmesh o* fullylit; set antialiasdisplay on;',\n",
       "].join('\\n');;\n",
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       "      height: '500',\n",
       "      debug: false,\n",
       "      disableInitialConsole: true,   // very slow when used with inline mesh\n",
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       "      use: 'HTML5',\n",
       "      j2sPath: '/nbextensions/jsmol/j2s',\n",
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       "    var jmolApplet0 = Jmol.getApplet('jmolApplet0', Info);\n",
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       "</body>\n",
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       "\" \n",
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       "        height=\"500\"\n",
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       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G=icosahedron((0, -2, 0), size=0.8, color='red', opacity=0.5)\n",
    "G.show()\n",
    "H = dodecahedron((0,0,0), size = 1, color = 'blue', opacity = 1)\n",
    "H.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D parametric plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  '-0.556776 0.0602557 2.82649',\n",
       "  '-0.521509 -0.0482853 2.82649',\n",
       "  '-0.592043 -0.0482853 2.82649',\n",
       "  '-0.613839 0.0187968 2.82649',\n",
       "  '-0.556776 0.000255746 3.00649',\n",
       "  '-0.499713 0.0187968 2.82649',\n",
       "  '-0.556776 0.0602557 2.82649',\n",
       "  '-0.521509 -0.0482853 2.82649',\n",
       "  '-0.592043 -0.0482853 2.82649',\n",
       "  '-0.613839 0.0187968 2.82649',\n",
       "  '-0.556776 0.000255746 3.00649',\n",
       "  '-0.556776 0.000255746 3.00649',\n",
       "  '10',\n",
       "  '4',\n",
       "  '0',\n",
       "  '1',\n",
       "  '2',\n",
       "  '0',\n",
       "  '4',\n",
       "  '7',\n",
       "  '3',\n",
       "  '8',\n",
       "  '7',\n",
       "  '4',\n",
       "  '13',\n",
       "  '4',\n",
       "  '10',\n",
       "  '13',\n",
       "  '4',\n",
       "  '19',\n",
       "  '5',\n",
       "  '11',\n",
       "  '19',\n",
       "  '4',\n",
       "  '20',\n",
       "  '9',\n",
       "  '12',\n",
       "  '20',\n",
       "  '4',\n",
       "  '15',\n",
       "  '14',\n",
       "  '6',\n",
       "  '15',\n",
       "  '4',\n",
       "  '14',\n",
       "  '16',\n",
       "  '6',\n",
       "  '14',\n",
       "  '4',\n",
       "  '16',\n",
       "  '17',\n",
       "  '6',\n",
       "  '16',\n",
       "  '4',\n",
       "  '17',\n",
       "  '18',\n",
       "  '6',\n",
       "  '17',\n",
       "  '4',\n",
       "  '18',\n",
       "  '15',\n",
       "  '6',\n",
       "  '18&quot;',\n",
       "  'color pmesh  [0,0,255]',\n",
       "  'isosurface fullylit; pmesh o* fullylit; set antialiasdisplay on;',\n",
       "].join('\\n');;\n",
       "    var Info = {\n",
       "      width: '100%',\n",
       "      height: '500',\n",
       "      debug: false,\n",
       "      disableInitialConsole: true,   // very slow when used with inline mesh\n",
       "      color: '#3131ff',\n",
       "      addSelectionOptions: false,\n",
       "      use: 'HTML5',\n",
       "      j2sPath: '/nbextensions/jsmol/j2s',\n",
       "      script: script,\n",
       "    };\n",
       "    var jmolApplet0 = Jmol.getApplet('jmolApplet0', Info);\n",
       "  </script>\n",
       "</body>\n",
       "</html>\n",
       "\" \n",
       "        width=\"100%\"\n",
       "        height=\"500\"\n",
       "        style=\"border: 0;\">\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "Graphics3d Object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var('s,t')\n",
    "fx = (3*sin(t) + cos(s) + 5)* cos(2*t)\n",
    "fy = (3*sin(t) + cos(s) + 5)* sin(2*t)\n",
    "fz = sin(s) + 2*cos(t)\n",
    "G = parametric_plot3d([fx, fy, fz], (s, 0, 2*pi), (t, 0, 2*pi), color='green', axes=True)\n",
    "G.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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