{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Factoring Polynomials with SymPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example that uses [SymPy](http://sympy.org/en/index.html) to factor polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.html.widgets import interact\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import Symbol, Eq, factor, init_printing\n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def factorit(n):\n",
    "    display(Eq(x**n-1, factor(x**n-1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the output of the `factorit` function is properly formatted LaTeX."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{12} - 1 = \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{2} + 1\\right) \\left(x^{2} - x + 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{4} - x^{2} + 1\\right)$$"
      ],
      "text/plain": [
       " 12                       ⎛ 2    ⎞ ⎛ 2        ⎞ ⎛ 2        ⎞ ⎛ 4    2    ⎞\n",
       "x   - 1 = (x - 1)⋅(x + 1)⋅⎝x  + 1⎠⋅⎝x  - x + 1⎠⋅⎝x  + x + 1⎠⋅⎝x  - x  + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "factorit(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{21} - 1 = \\left(x - 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\\right) \\left(x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1\\right)$$"
      ],
      "text/plain": [
       " 21               ⎛ 2        ⎞ ⎛ 6    5    4    3    2        ⎞ ⎛ 12    11    \n",
       "x   - 1 = (x - 1)⋅⎝x  + x + 1⎠⋅⎝x  + x  + x  + x  + x  + x + 1⎠⋅⎝x   - x   + x\n",
       "\n",
       "9    8    6    4    3        ⎞\n",
       "  - x  + x  - x  + x  - x + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(factorit, n=(2,40));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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