Quelle  test.ipynb   Sprache: unbekannt

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 1,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x := 5;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Group([ (1,2,3), (1,15) ])"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G := Group((1,2,3), (1,15));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Size(G);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Group(())"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "text/plain": ""
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Center(G);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.38.0 (20140413.2041)\n",
       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"62pt\" height=\"116pt\"\n",
       " viewBox=\"0.00 0.00 62.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-112 58,-112 58,4 -4,4\"/>\n",
       "<!-- x -->\n",
       "<g id=\"node1\" class=\"node\"><title>x</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">x</text>\n",
       "</g>\n",
       "<!-- y -->\n",
       "<g id=\"node2\" class=\"node\"><title>y</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">y</text>\n",
       "</g>\n",
       "<!-- x->y -->\n",
       "<g id=\"edge1\" class=\"edge\"><title>x->y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.6966C27,-63.9827 27,-54.7125 27,-46.1124\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5001,-46.1043 27,-36.1043 23.5001,-46.1044 30.5001,-46.1043\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/svg+xml": {
       "height": 500,
       "width": 500
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JupyterSplashDot(\"digraph { x -> y; }\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Syntax error: ; expected in stream:1\n",
      "^\n"
     ]
    }
   ],
   "source": [
    "x := 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error, Something went wrong?\n"
     ]
    }
   ],
   "source": [
    "Error(\"Something went wrong?\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "AutoDoc (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/AutoDoc-2017.09.08/doc/chap2.html#X86A674A5869BAEC2\">@Group</a><br/>loops (not loaded): group - no html help available. Please check other formats!<br/>polycyclic: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/polycyclic-2.11/doc/chap4.html#X7D7B075385435151\">Group</a><br/>RCWA (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rcwa-4.6.1/doc/chap3.html#X81242A6586A604A3\">Group</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8171DAF2833FF728\">Groups and Homomorphisms</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8131EE9182385680\">Group Homomorphisms by Images</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8131EE9182385680\">group general mapping</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8131EE9182385680\">GroupHomomorphismByImages vs. GroupGeneralMappingByImages</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8131EE9182385680\">group general mapping single-valued</a><br/>Tutorial: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/tut/chap5.html#X8131EE9182385680\">group general mapping total</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X8716635F7951801B\">Groups</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X822370B47DEA37B1\">Group Elements</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X7B75879B8085120A\">Group Properties</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X83702FC27B3C3098\">Group Homomorphisms</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7BC6C20E7CEDBFC5\">GroupHomomorphismByFunction</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X783030917CB43959\">Group Automorphisms</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X79640F3682BDBFC1\">Groups of Automorphisms</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap41.html#X87115591851FB7F4\">Group Actions</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap49.html#X7D5C75647DB168F1\">Group Products</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap50.html#X81B00B667D2BD022\">Group Libraries</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap71.html#X81EFD9FE804AC6EE\">Group Operations Applicable to Character Tables</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap77.html#X7AA51AC9870D2360\">Group Actions – Name Changes</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X7D8E473384DE9CD4\">Group for several generators</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X7D8E473384DE9CD4\">Group for a list of generators (and an identity element)</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X7F81960287F3E32A\">GroupByGenerators</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X7F81960287F3E32A\">GroupByGenerators with explicitly specified identity element</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap39.html#X8589EF9C7B658B94\">GroupWithGenerators</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7F348F497C813BE0\">GroupHomomorphismByImages</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7AB15AF5830F2A6B\">GroupHomomorphismByImagesNC</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7A59F2C47BD41DC8\">GroupGeneralMappingByImages</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7A59F2C47BD41DC8\">GroupGeneralMappingByImages from group to itself</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7A59F2C47BD41DC8\">GroupGeneralMappingByImagesNC</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7A59F2C47BD41DC8\">GroupGeneralMappingByImagesNC from group to itself</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7BC6C20E7CEDBFC5\">GroupHomomorphismByFunction by function (and inverse function) between two domains</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap40.html#X7BC6C20E7CEDBFC5\">GroupHomomorphismByFunction by function and function that computes one preimage</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap41.html#X87115591851FB7F4\">group actions</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap41.html#X83661AFD7B7BD1D9\">group actions operations syntax</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap41.html#X81B8F9CD868CD953\">group actions</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap41.html#X81B8F9CD868CD953\">group operations</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap43.html#X87F473777EFDE867\">GroupStabChain</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap45.html#X7903702E8194EF29\">GroupOfPcgs</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap46.html#X84F0521486672C3C\">GroupByRws</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap46.html#X84F0521486672C3C\">GroupByRwsNC</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap51.html#X7CB4A18685B850E2\">GroupHClassOfGreensDClass</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap65.html#X825897DC7A16E07D\">group algebra</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap65.html#X825897DC7A16E07D\">group ring</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap65.html#X86D2CA90847C091B\">GroupRing</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap72.html#X7C91D0D17850E564\">group characters</a><br/>Reference: <a target=\"_blank\" href=\"https://docs.gap-system.org/doc/ref/chap77.html#X7AA51AC9870D2360\">group operations</a><br/>AtlasRep: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/atlasrep/doc/chap2.html#X7E2FB5E5852AD970\">Groups, Generators, and Representations</a><br/>AtlasRep: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/atlasrep/doc/chap3.html#X87E64E2B7B8A8152\">Group Names Used in the AtlasRep Package</a><br/>AutoDoc (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/AutoDoc-2017.09.08/doc/chap2.html#X86A674A5869BAEC2\">@Group grpname</a><br/>AutoDoc (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/AutoDoc-2017.09.08/doc/chap2.html#X7D7A38F87BC40C48\">Grouping</a><br/>AutomGrp (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/automgrp/htm/CHAP002.htm#SECT005\">GroupNucleus</a><br/>CRISP: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/crisp-1.4.4/htm/CHAP003.htm#SECT001\">group classes!creation of</a><br/>CRISP: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/crisp-1.4.4/htm/CHAP003.htm#SECT002\">group classes!closure properties of</a><br/>CRISP: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/crisp-1.4.4/htm/CHAP003.htm#SECT003\">group classes!properties of</a><br/>CRISP: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/crisp-1.4.4/htm/CHAP003.htm#SECT004\">group classes!attributes for</a><br/>CRISP: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/crisp-1.4.4/htm/CHAP003.htm#SECT001\">GroupClass</a><br/>CTblLib: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/ctbllib/doc/chap3.html#X78DCD38B7D96D8A4\">GroupInfoForCharacterTable</a><br/>CTblLib: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/ctbllib/doc/chap3.html#X804D2AC37E0D4755\">GroupForGroupInfo</a><br/>CTblLib: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/ctbllib/doc/chap3.html#X83B9EFB47CE0A617\">GroupForTom</a><br/>Digraphs (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/digraphs/doc/chap5.html#X7A000B1D7CCF7093\">GroupOfCayleyDigraph</a><br/>fwtree (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/fwtree/htm/CHAP002.htm#SECT002\">GroupsByRankWidthObliquity</a><br/>genss (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/genss-1.6.5/doc/chap3.html#X837389DA857F0596\">GroupIteratorByStabilizerChain</a><br/>genss (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/genss-1.6.5/doc/chap3.html#X7DE1ACFA81002A5E\">GroupHomomorphismByImagesNCStabilizerChain</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap4.html#X82F6A1AB798648F4\">Groupoids</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap4.html#X7AC321DC7E3C6167\">Groupoids: their properties and attributes</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap4.html#X7F23BE3F85C9BA06\">Groupoid elements; stars; costars; homsets</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap4.html#X8406913B7ED86CFE\">Groupoid</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap4.html#X7D028B3B8385ED07\">GroupoidElement</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X870288C6803D9005\">GroupoidHomomorphismFromSinglePiece</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X870288C6803D9005\">GroupoidHomomorphism</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X87225D86785DEBC2\">GroupoidHomomorphismFromHomogeneousDiscrete</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X79DA704A8051CB72\">GroupoidAutomorphismByObjectPerm</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X79DA704A8051CB72\">GroupoidAutomorphismByGroupAuto</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X79DA704A8051CB72\">GroupoidAutomorphismByRayShifts</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X79DA704A8051CB72\">GroupoidInnerAutomorphism</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap5.html#X80F9594481CA9FDE\">GroupoidAutomorphismByGroupAutos</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap6.html#X8130246E854BC5D9\">GroupsOfGraphOfGroups</a><br/>groupoids (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/groupoids-1.54/doc/chap6.html#X8739267678808E85\">GroupoidsOfGraphOfGroupoids</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap2.html#X7C391012839DB4C5\">GroupCohomology</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap2.html#X7C391012839DB4C5\">GroupHomology</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap2.html#X7C391012839DB4C5\">GroupAlgebraAsFpGModule</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap11.html#X782177107A5D6D19\">GroupCohomology</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap11.html#X782177107A5D6D19\">GroupHomology</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap21.html#X7A7916087F55765C\">GroupAlgebraAsFpGModule</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap34.html#X83AAC8367CC7686F\">GroupHomologyOfCommutativeDiagram</a><br/>HAP (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/Hap1.12/doc/chap38.html#X7AE3B902812A10B0\">GroupOfResolution</a><br/>HAPprime Datatypes (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/happrime/doc/datatypes/chap5.html#X8716635F7951801B\">Groups</a><br/>HAPprog (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/HAPcryst/lib/datatypes/doc/chap2.html#X822604B67B2A9133\">GroupElementFromPosition</a><br/>HAPprog (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/HAPcryst/lib/datatypes/doc/chap2.html#X861BE6C787FA8032\">GroupRingOfResolution</a><br/>IdRel (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/idrel-2.38/doc/chap2.html#X7CBE13927DFF4446\">GroupRelatorsOfPresentation</a><br/>irredsol: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/irredsol-1.4/htm/CHAP005.htm\">group!primitive soluble</a><br/>LAGUNA: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/laguna-3.8.0/doc/chap3.html#X85C2DE1486FB45FD\">group algebra</a><br/>LAGUNA: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/laguna-3.8.0/doc/chap4.html#X7A39E44D87CDF7B0\">GroupBases</a><br/>loops (not loaded): groupoid - no html help available. Please check other formats!<br/>loops (not loaded): group with triality - no html help available. Please check other formats!<br/>PERMUT (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/permut/doc/chap4.html#X7B13DA0A800D8635\">Group properties related to permutability</a><br/>polycyclic: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/polycyclic-2.11/doc/chap5.html#X80BCCF0B81344933\">GroupOfPcp</a><br/>polycyclic: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/polycyclic-2.11/doc/chap5.html#X7F348F497C813BE0\">GroupHomomorphismByImages</a><br/>RCWA (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rcwa-4.6.1/doc/chap3.html#X81242A6586A604A3\">GroupByGenerators</a><br/>RCWA (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rcwa-4.6.1/doc/chap3.html#X81242A6586A604A3\">GroupWithGenerators</a><br/>RCWA (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rcwa-4.6.1/doc/chap3.html#X8143AB647801F438\">GroupByResidueClasses the group `permuting a given list of residue classes'</a><br/>RDS (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rds/htm/CHAP009.htm#SECT001\">Groups and actions</a><br/>RDS (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rds/htm/CHAP004.htm#SECT003\">GroupList2PermList</a><br/>RDS (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/rds/htm/CHAP008.htm#SECT002\">GroupOfHomologies</a><br/>recogbase (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/recogbase-1.2.5/doc/chap4.html#X7F73983582251807\">Group Recognition</a><br/>SONATA (not loaded): Group endomorphisms - no html help available. Please check other formats!<br/>SONATA (not loaded): Group automorphisms - no html help available. Please check other formats!<br/>SONATA (not loaded): Group reducts of ideals - no html help available. Please check other formats!<br/>SONATA (not loaded): GroupReduct - no html help available. Please check other formats!<br/>SONATA (not loaded): GroupReduct!near ring ideals - no html help available. Please check other formats!<br/>SONATA Tutorial (not loaded): Group endomorphisms - no html help available. Please check other formats!<br/>SONATA Tutorial (not loaded): Groups - no html help available. Please check other formats!<br/>Utils: <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/utils-0.49/doc/chap4.html#X8171DAF2833FF728\">Groups and homomorphisms</a><br/>Wedderga (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/wedderga-4.9.1/doc/chap9.html#X815ECCD97B18314B\">Group rings and group algebras</a><br/>Wedderga (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/wedderga-4.9.1/doc/chap9.html#X815ECCD97B18314B\">group ring</a><br/>Wedderga (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/wedderga-4.9.1/doc/chap9.html#X815ECCD97B18314B\">group algebra</a><br/>Wedderga (not loaded): <a target=\"_blank\" href=\"https://docs.gap-system.org/pkg/wedderga-4.9.1/doc/chap9.html#X856D7975810BF987\">group code</a><br/>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HELP(\"Group\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "rec( cursor_end := 3, cursor_start := 0, matches := [ \"Group\", \"GroupRing\", \"GroupBases\", \"GroupClass\", \"GroupByRws\", \"GroupOfPcp\", \"GroupString\", \"GroupForTom\", \"GroupByPcgs\", \"GroupOfPcgs\", \"GroupByRwsNC\", \"GrobnerBasis\", \"GroebnerBasis\", \"GroupStabChain\", \"GroebnerBasisNC\", \"GroupWithMemory\", \"GroupByGenerators\", \"GroupForGroupInfo\", \"GroupExtEquations\", \"Group_PseudoRandom\", \"GroupwordToMonword\", \"GroupWithGenerators\", \"GroupByPrimeResidues\", \"GroupByQuotientSystem\", \"GrowthFunctionOfGroup\", \"GroupOnSubgroupsOrbit\", \"Group_InitPseudoRandom\", \"GroupByNiceMonomorphism\", \"GroupEnumeratorByClosure\", \"GroupHomomorphismByImages\", \"GroupHClassOfGreensDClass\", \"GroupInfoForCharacterTable\", \"GroupByMultiplicationTable\", \"GroupHomomorphismByFunction\", \"GroupGeneralMappingByImages\", \"GroupHomomorphismByImagesNC\", \"GroupMethodByNiceMonomorphism\", \"GroupGeneralMappingByImagesNC\", \"GroupGeneralMappingByImages_for_pcp\", \"GroupSeriesMethodByNiceMonomorphism\", \"GroupMethodByNiceMonomorphismCollElm\", \"GroupMethodByNiceMonomorphismCollColl\", \"GroupMethodByNiceMonomorphismCollOther\", \"GroupSeriesMethodByNiceMonomorphismCollElm\", \"GroupToAdditiveGroupHomomorphismByFunction\", \"GroupSeriesMethodByNiceMonomorphismCollColl\", \"GroupSeriesMethodByNiceMonomorphismCollOther\" ], metadata := rec(  ), status := \"ok\" )"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JUPYTER_Complete(\"Gro\", 3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "rec( data := rec( metadata := rec( text/html := \"\", text/plain := \"\" ), text/html := \"\", text/plain := \"  \n",
       "  \u001b[22m\u001b[4m5 Groups and Homomorphisms\u001b[0m\n",
       "  \n",
       "  In  this  chapter  we  will show some computations with groups. The examples\n",
       "  deal  mostly with permutation groups, because they are the easiest to input.\n",
       "  The   functions   mentioned  here,  like  \u001b[22m\u001b[34mGroup\u001b[0m  (\u001b[36mReference:  Groups\u001b[0m),  \u001b[22m\u001b[34mSize\u001b[0m\n",
       "  (\u001b[36mReference:  Size\u001b[0m) or \u001b[22m\u001b[34mSylowSubgroup\u001b[0m (\u001b[36mReference: SylowSubgroup\u001b[0m), however, are\n",
       "  the  same for all kinds of groups, although the algorithms which compute the\n",
       "  information of course will be different in most cases.\n",
       "  \" ), found := true, status := \"ok\" )"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JUPYTER_Inspect(\"Group(\", 6);"
   ]
  }
 ],
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  "language_info": {
   "codemirror_mode": "gap",
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