{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random IVM Tetrahedron Volumes (with gmpy2)\n",
    "\n",
    "![quadrays](https://upload.wikimedia.org/wikipedia/commons/9/99/Quadray.gif)\n",
    "\n",
    "According to a proof by Dr. Robert Gray, at one time archived on a Synergetics listserv, any tetrahedron of IVM vertexes (assuming non-coplanar) will have a whole number volume.  \n",
    "\n",
    "In this Notebook, we randomly generate IVM tetrahedrons and compute their volumes.  Within the error of floating point, we demonstrate this result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tetravolume import Qvector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpfr('0.0',200)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import gmpy2\n",
    "from gmpy2 import mpfr\n",
    "gmpy2.get_context().precision=200\n",
    "mpfr(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import permutations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 1, 1, 2),\n",
       " (1, 2, 0, 1),\n",
       " (0, 2, 1, 1),\n",
       " (0, 1, 2, 1),\n",
       " (2, 1, 0, 1),\n",
       " (1, 1, 2, 0),\n",
       " (1, 2, 1, 0),\n",
       " (2, 1, 1, 0),\n",
       " (1, 0, 2, 1),\n",
       " (2, 0, 1, 1),\n",
       " (1, 0, 1, 2),\n",
       " (1, 1, 0, 2)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combos = set()\n",
    "for combo in permutations((0,1,1,2)):\n",
    "    combos.add(combo)\n",
    "combos = list(combos)\n",
    "combos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One frequency:\n",
    "\n",
    "![\"freq1\"](freq1.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ivm_vector(a=mpfr('0.0',200), b=mpfr('392.0',200), c=mpfr('222.0',200), d=mpfr('642.0',200))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "def any_ball():\n",
    "    # random coefficients for arbitrary choice of vectors...\n",
    "    coeffs = [random.randint(0, 300) for _ in range(12)]\n",
    "    vectors = ([coeffs[i] * Qvector(combos[i]) for i in range(12)])\n",
    "    vector_sum = Qvector((mpfr(0),mpfr(0),mpfr(0),mpfr(0)))\n",
    "    for v in vectors:\n",
    "        vector_sum = vector_sum + v\n",
    "    return vector_sum\n",
    "\n",
    "any_ball()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ivm_vector(a=mpfr('492.0',200), b=mpfr('329.0',200), c=mpfr('0.0',200), d=mpfr('267.0',200))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A,B,C,D = any_ball(), any_ball(), any_ball(), any_ball()\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ivm_vector(a=mpfr('248.0',200), b=mpfr('263.0',200), c=mpfr('0.0',200), d=mpfr('345.0',200))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A-B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpfr('182.36501857538358499472121928182087681992193154377123883742419',200)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A-B).length()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "lengths = [(\"AB\", (A-B).length()),\n",
    "           (\"AC\", (A-C).length()),\n",
    "           (\"AD\", (A-D).length()),\n",
    "           (\"BC\", (B-C).length()),\n",
    "           (\"CD\", (C-D).length()),\n",
    "           (\"DB\", (D-B).length())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('AB',\n",
       "  mpfr('182.36501857538358499472121928182087681992193154377123883742419',200)),\n",
       " ('AC',\n",
       "  mpfr('600.15164750252914722690451617422631602104978692970170354841761',200)),\n",
       " ('AD',\n",
       "  mpfr('551.34199912576948539719539536015344824528780410498293183661653',200)),\n",
       " ('BC',\n",
       "  mpfr('511.7528700456891428844478216824504677275886445592614561129447',200)),\n",
       " ('CD',\n",
       "  mpfr('598.36109499197890280611882194630845066148913520677993892985788',200)),\n",
       " ('DB',\n",
       "  mpfr('383.2270867253513957959972492873305724441048590574352961993633',200))]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tetravolume import Tetrahedron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = Tetrahedron(*[lengths[i][1] for i in range(6)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpfr('20009460.0',200)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.ivm_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpfr('16319836.0',200)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def demo():\n",
    "    A,B,C,D = any_ball(), any_ball(), any_ball(), any_ball()\n",
    "    lengths = [(\"AB\", (A-B).length()),\n",
    "           (\"AC\", (A-C).length()),\n",
    "           (\"AD\", (A-D).length()),\n",
    "           (\"BC\", (B-C).length()),\n",
    "           (\"CD\", (C-D).length()),\n",
    "           (\"DB\", (D-B).length())]\n",
    "    t = Tetrahedron(*[lengths[i][1] for i in range(6)])\n",
    "    return t.ivm_volume()\n",
    "\n",
    "demo()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpfr('18865099.805174635666877858142242985195480287075042724609375',200)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.xyz_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/wLHescQT2ZI\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x10d89ec50>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"wLHescQT2ZI\") # https://youtu.be/wLHescQT2ZI"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}