Demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular Jupyter kernel\n",
    "\n",
    "This notebook uses the Singular kernel for Jupyter and gives a first example of its usage.\n",
    "\n",
    "Below you will find a first example how to use Singular. We use the standard ring in Singular to create an ideal and\n",
    "compute its standard basis.\n",
    "\n",
    "Then we create a 3D-version of the Singular logo, using a polynomial and then printing an image using surf and the jupyter_surf.lib in Singular."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ring r;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "//   characteristic : 32003\n",
       "//   number of vars : 3\n",
       "//        block   1 : ordering dp\n",
       "//                  : names    x y z\n",
       "//        block   2 : ordering C\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ideal I = (xy,x^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "_[1]=xy\n",
       "_[2]=x2\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std(I);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly logo = ((x+3)^3 + 2*(x+3)^2 - y^2)*(x^3 - y^2)*((x-3)^3-2*(x-3)^2-y^2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "// ** loaded /usr/local/bin/../share/singular/LIB/surf_jupyter.lib (0.0.0.1,Jan_2016)\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LIB \"surf_jupyter.lib\";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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     },
     "metadata": {
      "image/jpeg": {
       "height": 400,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_jupyter(logo);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Singular",
   "language": "singular",
   "name": "singular"
  },
  "language_info": {
   "codemirror_mode": "singular",
   "file_extension": ".singular",
   "mimetype": "text/x-singular",
   "name": "Singular"
  },
  "widgets": {
   "state": {},
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}