Added demos for the GAP, Pari, and Singular kernels

Author: nthiery

demo-gap.ipynb

@@ -0,0 +1,196 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Alt( [ 1 .. 6 ] )"
+     ]
+    }
+   ],
+   "source": [
+    "G := AlternatingGroup(6);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "Reference: <a target=\"_blank\" href=\"https://cloud.gap-system.org/doc/ref/chap40.html#X87677B0787B4461A\">AutomorphismGroup</a><br/>Reference: <a target=\"_blank\" href=\"https://cloud.gap-system.org/doc/ref/chap45.html#X7A19DF1E7E841074\">AutomorphismGroup for groups with pcgs</a><br/>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": []
+    }
+   ],
+   "source": [
+    "?AutomorphismGroup"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<group with 4 generators>"
+     ]
+    }
+   ],
+   "source": [
+    "a := AutomorphismGroup(G);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<group>"
+     ]
+    }
+   ],
+   "source": [
+    "SylowSubgroup(a,2);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<group>"
+     ]
+    }
+   ],
+   "source": [
+    "s := SylowSubgroup(a,2);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "32"
+     ]
+    }
+   ],
+   "source": [
+    "Order(s);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ 32, 43 ]"
+     ]
+    }
+   ],
+   "source": [
+    "IdGroup(s);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[ 32, 4, 2, 1 ]"
+     ]
+    }
+   ],
+   "source": [
+    "List(LowerCentralSeries(s), Order);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "GAP",
+   "language": "gap",
+   "name": "gap"
+  },
+  "language_info": {
+   "codemirror_mode": "gap",
+   "file_extension": ".g",
+   "mimetype": "text/x-gap",
+   "name": "gap"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}