sagemath-numericalsgps.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using `numericalsgps` in `SageMath`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We show some examples of using `sagemath`with `numericalsgps`.\n",
    "After installing `numericalsgps`, we load it; beware that you need double quotes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gap.LoadPackage('\"num\"')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see how many factorizations have the first 100 elements in $\\langle 10,13,19,21 \\rangle$, and let us plot the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = gap.NumericalSemigroup(10,13,19,21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = gap.FirstElementsOfNumericalSemigroup(100,s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "nf = [len(gap.Factorizations(n,s)) for n in l]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "list_plot(nf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This semigroup has Frobenius number 37."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = gap.FrobeniusNumber(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can choose those elements with a unique expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0,\n",
       " 10,\n",
       " 13,\n",
       " 19,\n",
       " 20,\n",
       " 21,\n",
       " 23,\n",
       " 26,\n",
       " 29,\n",
       " 30,\n",
       " 31,\n",
       " 32,\n",
       " 33,\n",
       " 34,\n",
       " 36,\n",
       " 38,\n",
       " 41,\n",
       " 43,\n",
       " 44,\n",
       " 45,\n",
       " 46,\n",
       " 47,\n",
       " 48,\n",
       " 54,\n",
       " 56]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[n for n in l if len(gap.Factorizations(n,s))==1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also write some functions using `gap` functionalities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eliahou(n,s):\n",
    "    gens = gap.MinimalGenerators(s)\n",
    "    v = [g for g in gens if gap.BelongsToNumericalSemigroup(n-g,s)]\n",
    "    e = [(a,b) for a in gens for b in gens if a<b and gap.BelongsToNumericalSemigroup(n-a-b,s)]\n",
    "    g = graphs.EmptyGraph()\n",
    "    g.add_vertices(v)\n",
    "    g.add_edges(e)\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graph on 4 vertices"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eliahou(300,s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[ 39, 40, 42, 51, 57 ]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gap.BettiElements(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "g=eliahou(40,s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graph on 3 vertices"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can plot how many complete intersection numerical semigroups there are with Frobenius number ranging in an interval. Note that complete intersections are symmetric numerical semigroups, and thus we will not have any complete intersection numerical semigroup with an even Frobenius number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EJgCAjtEEJr3kgHnT2w7YL73kgLkZW68pPcr2P86YahlqnDHVsshxxlTLkOPMQC85AIAhCEwAAB0CEwBAh8AEANBx0bILACYO0QJKgENnzzNMVfWaqvpUVX2rqlpV3bDjeFXV+6rqoar6XlXdXVUvG6xiAIAF289Hcs9L8mdJfv4Cx9+d5BeS/FySVyf5bpK7qurifVUIALBke/5IrrV2Z5I7k6R2zP3XZMcvJvn3rbVPTvf9qyQPJ7lhtlIBAJZj6EXfL0lyaZK7z+xorW0kuSfJtQO/FgDAQgy96PvS6c+Hd+x/eNuxc2xtbWVra+vs483NzYFLAgCYzdJvK3Dq1Kmsrq6e3dbW1pZdEgDAOYYOTN+e/jy+Y//xbcfOcdNNN2VjY+Ps9uCDDw5cEgDAbIYOTF/PJBhdf2ZHVR3L5Ntyp8/3CysrKzl27Ng5GwDAmOx5DVNVPT/JS7fteklVXZXksdbaA1V1a5JfqaqvZBKgfj3Jt5J8YuZqAQCWYD+Lvl+V5A+2Pb55+vMjSd6a5DczuVfTh5JckuSPkryhtfb9fVcJALBE1RbbI6H7Ypubm1ldXc3GxoaP5zhSDmNrlLG9p0WNM6ZahhpnTLUMNc6YalnkOGOqZchxZrCLCvSSAy5gBP8RAxiNpd9WAABg7AQmAIAOgQkAoENgAgDoEJgAADpGE5jW19dz4sSJnDx5ctmlcIRU9TcAcB8mjrQxfXV+bPc0cb+X/Y8zplqGGmdMtQw1zphqWeQ4Y6plyHFmsKv/NR7NDBMAwFgJTAAAHQITAECHwAQA0KGXHAfSCBYJAnCEmGECAOgQmAAAOgQmAIAOgQkAoENgAgDoGE1g0ksOABgrveQ4kA5RD6Ozxvae9Kza/zhjqmWoccZUy1DjjKmWRY4zplqGHGcGeskBAAxBYAIA6BCYAAA6tEZh10bwOfNoOTcAh5sZJgCADoEJAKBDYAIA6BCYAAA6BCYAgI7RBCatUeanqr8BABemNcoRcIhuX3/W2N6TdgXjr2WR44yplqHGGVMtQ40zploWOc6YahlynBlojQIAMASBCQCgQ2ACAOgQmAAAOvSSm5MRLGIbLecGgIPGDBMAQIfABADQITABAHQITAAAHQITAEDHaALTWHrJja3v2phqAYCjSi+5HcbWG0cvpPHXMtQ4Y6plqHHGVMsixxlTLUONM6ZahhpnTLUscpwx1TLkODPQSw4AYAgCEwBAh8AEANAhMAEAdIyil9z5Fnytrp77eFEL/AAAdjLDBADQITABAHQITAAAHQITAEDHwhZ9V1VtbGw8bf/W1laSrW17npj+3DzneZvnPtyXIcYY2zhjqmVs44yplqHGGVMtQ40zplqGGmdMtQw1zphqGWqcMdUytnHGVMuQ45zP6urqsSRPtE7rk4W1RqmqY0menpgAAJZrtbX2jLFskYGpkrzgPIeem2Rl2+PjSe5N8vIkD834sn+S5B/POMZQ44yplhck+WaSF+f/T+ktq5axjTOm8ztUPUONM6ZaXMPzHWNs1/CYzu8Q44zt/A41zphq2es57s4wLewjuWkh3Um1qjrzxh7qpb1djPWjWccYapyR1XLmj0/MMtaY3tNQ44zp/A5Vz1DjjKyWM390Dc9njDN/HMU1PKbzO8Q4Yzu/Q40zslrO/HHmc3zGYV/0vT6iccZUy1DG9p7G9M9pKIfx3IzpHI/tPY3pn9NQxvSexjbOEMb0nsZUy+AW9pHcbm1b69T9PJH9cY7ny/mdP+d4vpzf+XJ+528e53iMM0xbSX4t5351jmE5x/Pl/M6fczxfzu98Ob/zN/g5Ht0MEwDA2IxxhgkAYFQEJgCADoEJAKBDYAIA6BCYjoiqem9VtR3b/cuu6yCrqtdU1aeq6lvT83nDjuNVVe+rqoeq6ntVdXdVvWxJ5R44uzi/Hz7PNf3pJZV74FTVTVX1p1X1RFU9UlWfqKordzzn4qpar6pHq+rJqrq9qo4vq+aDZpfn+HPnuY7/87JqPkiq6h1VdV9VbU6301X1U9uOD3r9CkxHy18kedG27SeWW86B97wkf5bk5y9w/N1JfiHJzyV5dZLvJrmrqi5eTHkHXu/8Jsmnc+41/S8XUNdhcV0mNwi8Jsnrkjwnye9V1fO2PeeWJG9M8ubp8y9LcseC6zzIdnOOk+S/5Nzr+N2LLPIA+2aS9yS5Osmrknw2ySer6senxwe9ft1W4IioqvcmuaG1dtWSSzmUqqoleVNr7RPTx5XkW0n+Y2vt/dN9q0keTvLW1trvLKvWg2jn+Z3u+3CSS1prNyyprEOlqv5ekkeSXNda+/z0ev1Okhtbax+fPuflSb6U5NrW2heWV+3BtPMcT/d9Lsn/bq394hJLOzSq6rEkv5zk4xn4+jXDdLS8bPrxxteq6qNVdfmyCzrEXpLk0iR3n9nRWttIck+Sa5dV1CH02ulHHV+uqt+qqhcuu6ADbHX687Hpz6szmRHZfg3fn+SBuIb3a+c5PuNnq+pvq+qLVXWqqv7uogs76Krq2VX1lkxmpk9nDtfvwprvsnT3JHlrki9nMuX7q0n+sKpe0VqbtVs2T3fp9OfDO/Y/vO0Ys/l0JtPrX09yRZL/kOTOqrq2tfbDpVZ2wFTVs5LcmuSPW2tfnO6+NMlTrbXHdzzdNbwPFzjHSfLfknwjkxnpf5jkN5JcmeSfLbrGg6iqXplJQLo4yZOZzET/ZVVdlYGvX4HpiGit3bnt4X1VdU8m/5L+iyS3Lacq2L8dH2v+eVXdl+SrSV6b5DNLKergWk/yiljXOE/nPcettQ9te/jnVfVQks9U1RWtta8ussAD6stJrspk9u6fJ/lIVV03jxfykdwRNU3df5XkpUsu5bD69vTnzm9kHN92jAG11r6W5G/jmt6Tqvpgkp9O8k9ba9/cdujbSZ5bVZfs+BXX8B49wzk+n3umP13Hu9Bae6q19tettXtbazdl8kWRf5s5XL8C0xFVVc/P5GOMh5ZdyyH19Uz+pbz+zI5p9+xXZzJ9zMCq6sVJXhjX9K5Mb3vxwSRvSvKTrbWv73jKvUl+kHOv4SuTXB7X8K7s4hyfz1XTn67j/XlWkpXM4fr1kdwRUVXvT/KpTD6GuyyTLs4/TPKxZdZ1kE1D5/b/C3zJ9HPzx1prD1TVrUl+paq+kkmA+vVM1il8YsGlHkjPdH6n268muT2TYHpFkt9M8tdJ7lpspQfWepIbk/xMkieq6sy6jo3W2vdaaxtVdVuSm6ffPNpM8oEkp31Dbtee8RxX1RXT4/8zyaOZrGG6JcnnW2v3LaPgg6SqTiW5M5OF3C/I5Fy+Nsnr53L9ttZsR2BL8juZ/GW9lcm9K34nyRXLrusgb9N/Mdt5tg9Pj1eS92XyF/r3M/m2xj9Ydt0HZXum85vk72QSjB5J8lSSv0nyoSTHl133QdkucG5bJre9OPOcizP5S/+xTO4jdkeSS5dd+0HZeuc4yVqS/5VJWPp+kq9kEvyPLbv2g7Blsv72b6Z/rz0y/W/s67YdH/T6dR8mAIAOa5gAADoEJgCADoEJAKBDYAIA6BCYAAA6BCYAgA6BCQCgQ2ACAOgQmAAAOgQmAIAOgQkAoENgAgDo+H/DDQi+c6NDUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bar_chart([len(gap.CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber(n)) for n in range(1,60,2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.2",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}