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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an example of a Maxima-Jupyter notebook, showing text, formulas, and plots. To start with, I'll compute an integral."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{0}$}\\sqrt{\\pi}\\]"
      ],
      "text/plain": [
       "(%o0)                              sqrt(%pi)"
      ],
      "text/x-maxima": [
       "sqrt(%pi)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate (exp(-t^2), t, minf, inf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Terrific. How about an example that shows the nice $\\rm{\\LaTeX}$ integral sign."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{1}$}\\int_{a}^{b}{x\\,\\log x\\;dx}\\]"
      ],
      "text/plain": [
       "                                 b\n",
       "                                /\n",
       "                                [\n",
       "(%o1)                           I  x log(x) dx\n",
       "                                ]\n",
       "                                /\n",
       "                                 a"
      ],
      "text/x-maxima": [
       "'integrate(x*log(x),x,a,b)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'integrate (x*log(x), x, a, b);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Questions from Maxima to the user (via `asksign`) cause the notebook to open an input prompt and report the input back to the Maxima kernel. In the next example, let's try the same input twice and answer the question in different ways."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Is k equal to - 1?\n",
      " y;\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{2}$}\\log u\\]"
      ],
      "text/plain": [
       "(%o2)                               log(u)"
      ],
      "text/x-maxima": [
       "log(u)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate (u^k, u);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Is k equal to - 1?\n",
      " n;\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{3}$}\\frac{u^{k+1}}{k+1}\\]"
      ],
      "text/plain": [
       "                                     k + 1\n",
       "                                    u\n",
       "(%o3)                               ------\n",
       "                                    k + 1"
      ],
      "text/x-maxima": [
       "u^(k+1)/(k+1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate (u^k, u);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about finding the roots of a polynomial?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{4}$}\\left[ x=\\frac{2^{\\frac{1}{3}}\\,\\sqrt{3}\\,i-2^{\\frac{1}{3}}}{2} , x=-\\left(\\frac{2^{\\frac{1}{3}}\\,\\sqrt{3}\\,i+2^{\\frac{1}{3}}}{2}\\right) , x=2^{\\frac{1}{3}} \\right] \\]"
      ],
      "text/plain": [
       "            1/3               1/3         1/3               1/3\n",
       "           2    sqrt(3) %i - 2           2    sqrt(3) %i + 2          1/3\n",
       "(%o4) [x = ----------------------, x = - ----------------------, x = 2   ]\n",
       "                     2                             2"
      ],
      "text/x-maxima": [
       "[x = (2^(1/3)*sqrt(3)*%i-2^(1/3))/2,x = -((2^(1/3)*sqrt(3)*%i+2^(1/3))/2),\n",
       " x = 2^(1/3)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "foo : solve (x^3 - 2, x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's verify that the elements of `foo` are indeed the roots in question."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{5}$}\\left[ \\frac{\\left(2^{\\frac{1}{3}}\\,\\sqrt{3}\\,i-2^{\\frac{1}{3}}\\right)^3}{8} , -\\left(\\frac{\\left(2^{\\frac{1}{3}}\\,\\sqrt{3}\\,i+2^{\\frac{1}{3}}\\right)^3}{8}\\right) , 2 \\right] \\]"
      ],
      "text/plain": [
       "             1/3               1/3 3      1/3               1/3 3\n",
       "           (2    sqrt(3) %i - 2   )     (2    sqrt(3) %i + 2   )\n",
       "(%o5)     [-------------------------, - -------------------------, 2]\n",
       "                       8                            8"
      ],
      "text/x-maxima": [
       "[(2^(1/3)*sqrt(3)*%i-2^(1/3))^3/8,-((2^(1/3)*sqrt(3)*%i+2^(1/3))^3/8),2]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bar : map (lambda ([u], u^3), map (rhs, foo));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, it's still not obvious. Let's simplify a little."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{6}$}\\left[ 2 , 2 , 2 \\right] \\]"
      ],
      "text/plain": [
       "(%o6)                              [2, 2, 2]"
      ],
      "text/x-maxima": [
       "[2,2,2]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map (radcan, bar);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a different way to simplify."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{7}$}\\left[ 2 , 2 , 2 \\right] \\]"
      ],
      "text/plain": [
       "(%o7)                              [2, 2, 2]"
      ],
      "text/x-maxima": [
       "[2,2,2]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map (expand, bar);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's make a plot. Note that in order for the results from `plot2d` to be displayed in the notebook a file name needs to specified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "plot2d: some values will be clipped.\n"
     ]
    },
    {
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       "\t\tL332.28,203.33 L333.39,202.75 L334.51,202.19 L335.62,201.66 L336.73,201.16 L337.85,200.69 L338.96,200.25 L340.07,199.84\n",
       "\t\tL341.19,199.46 L342.30,199.11 L343.42,198.79 L344.53,198.51 L345.64,198.27 L346.76,198.06 L347.87,197.88 L348.98,197.74\n",
       "\t\tL350.10,197.63 L351.21,197.56 L352.33,197.53 L352.88,197.53 L353.44,197.53 L354.00,197.55 L354.55,197.57 L355.11,197.60\n",
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       "\t\tL360.12,198.29 L360.68,198.42 L361.24,198.54 L361.79,198.68 L362.35,198.83 L362.91,198.98 L363.46,199.15 L364.02,199.32\n",
       "\t\tL364.58,199.50 L365.13,199.69 L365.69,199.88 L366.25,200.08 L366.80,200.30 L367.36,200.51 L367.92,200.74 L368.47,200.98\n",
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       "\t\tL409.13,227.98 L409.68,228.32 L410.24,228.66 L410.80,228.99 L411.35,229.31 L411.91,229.63 L412.47,229.94 L413.02,230.25\n",
       "\t\tL413.58,230.55 L414.14,230.84 L414.70,231.13 L415.25,231.41 L415.81,231.68 L416.37,231.95 L416.92,232.21 L417.48,232.46\n",
       "\t\tL418.04,232.70 L418.59,232.94 L419.15,233.17 L419.71,233.40 L420.26,233.61 L420.82,233.82 L421.38,234.02 L421.93,234.21\n",
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       "\t</g>\n",
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       "\t\tL561.71,212.36 L562.27,211.92 L562.82,211.47 L563.38,211.02 L563.94,210.56 L564.49,210.09 L565.05,209.62 L565.61,209.14\n",
       "\t\tL566.17,208.65 L566.72,208.15 L567.28,207.64 L567.84,207.12 L568.39,206.59 L568.95,206.05 L569.51,205.50 L570.06,204.93\n",
       "\t\tL570.62,204.34  '/></g>\n",
       "\t</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,410.70 L64.34,410.70 M570.62,410.70 L560.12,410.70  '/>\t<g transform=\"translate(44.05,415.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"end\">\n",
       "\t\t<text>-10</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,313.80 L64.34,313.80 M570.62,313.80 L560.12,313.80  '/>\t<g transform=\"translate(44.05,318.35)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"end\">\n",
       "\t\t<text>-5</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,216.90 L64.34,216.90 M570.62,216.90 L560.12,216.90  '/>\t<g transform=\"translate(44.05,221.45)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"end\">\n",
       "\t\t<text> 0</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,120.01 L64.34,120.01 M570.62,120.01 L560.12,120.01  '/>\t<g transform=\"translate(44.05,124.56)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"end\">\n",
       "\t\t<text> 5</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,23.11 L64.34,23.11 M570.62,23.11 L560.12,23.11  '/>\t<g transform=\"translate(44.05,27.66)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"end\">\n",
       "\t\t<text> 10</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,410.70 L53.84,400.20 M53.84,23.11 L53.84,33.61  '/>\t<g transform=\"translate(53.84,436.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"middle\">\n",
       "\t\t<text>-10</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M183.04,410.70 L183.04,400.20 M183.04,23.11 L183.04,33.61  '/>\t<g transform=\"translate(183.04,436.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"middle\">\n",
       "\t\t<text>-5</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M312.23,410.70 L312.23,400.20 M312.23,23.11 L312.23,33.61  '/>\t<g transform=\"translate(312.23,436.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"middle\">\n",
       "\t\t<text> 0</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M441.43,410.70 L441.43,400.20 M441.43,23.11 L441.43,33.61  '/>\t<g transform=\"translate(441.43,436.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"middle\">\n",
       "\t\t<text> 5</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M570.62,410.70 L570.62,400.20 M570.62,23.11 L570.62,33.61  '/>\t<g transform=\"translate(570.62,436.25)\" stroke=\"none\" fill=\"black\" font-family=\"Arial\" font-size=\"14.00\"  text-anchor=\"middle\">\n",
       "\t\t<text> 10</text>\n",
       "\t</g>\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "</g>\n",
       "<g fill=\"none\" color=\"gray\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black' stroke-dasharray='2,4'  d='M53.84,216.90 L570.62,216.90  '/></g>\n",
       "<g fill=\"none\" color=\"gray\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black' stroke-dasharray='2,4'  d='M312.23,410.70 L312.23,23.11  '/></g>\n",
       "<g fill=\"none\" color=\"gray\" stroke=\"black\" stroke-width=\"2.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"2.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"black\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "</g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "\t<path stroke='black'  d='M53.84,23.11 L53.84,410.70 L570.62,410.70 L570.62,23.11 L53.84,23.11 Z  '/></g>\n",
       "<g fill=\"none\" color=\"black\" stroke=\"currentColor\" stroke-width=\"1.00\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\">\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n",
       "\n"
      ],
      "text/plain": [
       "/tmp/maxplot.svg"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot2d ([sin, cos, tan], [x, -10, 10], [y, -10, 10], [svg_file, \"maxplot.svg\"],[plot_format, gnuplot])$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By the way, output to standard output (e.g. the output of `print` or `describe`) is displayed in the notebook as plain text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "HELLO WORLD!"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{9}$}\\mbox{ HELLO WORLD! }\\]"
      ],
      "text/plain": [
       "(%o9)                            HELLO WORLD!"
      ],
      "text/x-maxima": [
       "\"HELLO WORLD!\""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print (\"HELLO WORLD!\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of `print`, the printed value is also returned, so it is typeset also."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, that's all for now!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Maxima",
   "language": "maxima",
   "name": "maxima"
  },
  "language_info": {
   "codemirror_mode": "maxima",
   "file_extension": ".mac",
   "mimetype": "text/x-maxima",
   "name": "maxima",
   "pygments_lexer": "maxima",
   "version": "5.47.0"
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 "nbformat": 4,
 "nbformat_minor": 4
}