{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e3aebf06",
   "metadata": {},
   "source": [
    "# Factorizing Polynomial with Sympy\n",
    "*~ example by [Rito Ghosh](https://www.linkedin.com/in/ritobrata-ghosh/)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "48541d8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing required functions from package\n",
    "from sympy import symbols, factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c67c56a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# declaring symbols\n",
    "a, b, c = symbols('a b c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2318e26f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'(a^2*c^9+14*a^2*c^8-2*a^2*c^7-528 *a^2*c^6-639*a ^2*c^5+3706*a^2*c^4+9608*a^2*c^3+8144*a^2*c^2+2640*a^2*c+288*a^2)/(2*(c^2+4*c+3)^2*(2*c^3+12*c^2-21*c-10)^2)'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the expression of polynomial to fatorize\n",
    "expr = '(a^2*c^9+14*a^2*c^8-2*a^2*c^7-528 *a^2*c^6-639*a ^2*c^5+3706*a^2*c^4+9608*a^2*c^3+8144*a^2*c^2+2640*a^2*c+288*a^2)/(2*(c^2+4*c+3)^2*(2*c^3+12*c^2-21*c-10)^2)'\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5df5f38f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a^{2} \\left(c + 2\\right) \\left(c^{4} + 6 c^{3} - 31 c^{2} - 52 c - 12\\right)^{2}}{2 \\left(c + 1\\right)^{2} \\left(c + 3\\right)^{2} \\left(2 c^{3} + 12 c^{2} - 21 c - 10\\right)^{2}}$"
      ],
      "text/plain": [
       "a**2*(c + 2)*(c**4 + 6*c**3 - 31*c**2 - 52*c - 12)**2/(2*(c + 1)**2*(c + 3)**2*(2*c**3 + 12*c**2 - 21*c - 10)**2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calling the `factor` function\n",
    "factor(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85aea0ce",
   "metadata": {},
   "source": [
    "### Requirements (including Jupyter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7eb60d9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name: sptest\n",
      "channels:\n",
      "  - defaults\n",
      "dependencies:\n",
      "  - _libgcc_mutex=0.1=main\n",
      "  - _openmp_mutex=5.1=1_gnu\n",
      "  - anyio=3.5.0=py310h06a4308_0\n",
      "  - argon2-cffi=21.3.0=pyhd3eb1b0_0\n",
      "  - argon2-cffi-bindings=21.2.0=py310h7f8727e_0\n",
      "  - asttokens=2.0.5=pyhd3eb1b0_0\n",
      "  - attrs=21.4.0=pyhd3eb1b0_0\n",
      "  - babel=2.9.1=pyhd3eb1b0_0\n",
      "  - backcall=0.2.0=pyhd3eb1b0_0\n",
      "  - beautifulsoup4=4.11.1=py310h06a4308_0\n",
      "  - bleach=4.1.0=pyhd3eb1b0_0\n",
      "  - brotlipy=0.7.0=py310h7f8727e_1002\n",
      "  - bzip2=1.0.8=h7b6447c_0\n",
      "  - ca-certificates=2022.07.19=h06a4308_0\n",
      "  - certifi=2022.6.15=py310h06a4308_0\n",
      "  - cffi=1.15.1=py310h74dc2b5_0\n",
      "  - charset-normalizer=2.0.4=pyhd3eb1b0_0\n",
      "  - cryptography=37.0.1=py310h9ce1e76_0\n",
      "  - dbus=1.13.18=hb2f20db_0\n",
      "  - debugpy=1.5.1=py310h295c915_0\n",
      "  - decorator=5.1.1=pyhd3eb1b0_0\n",
      "  - defusedxml=0.7.1=pyhd3eb1b0_0\n",
      "  - entrypoints=0.4=py310h06a4308_0\n",
      "  - executing=0.8.3=pyhd3eb1b0_0\n",
      "  - expat=2.4.4=h295c915_0\n",
      "  - fontconfig=2.13.1=h6c09931_0\n",
      "  - freetype=2.11.0=h70c0345_0\n",
      "  - giflib=5.2.1=h7b6447c_0\n",
      "  - glib=2.69.1=h4ff587b_1\n",
      "  - gmp=6.2.1=h295c915_3\n",
      "  - gmpy2=2.1.2=py310heeb90bb_0\n",
      "  - gst-plugins-base=1.14.0=h8213a91_2\n",
      "  - gstreamer=1.14.0=h28cd5cc_2\n",
      "  - icu=58.2=he6710b0_3\n",
      "  - idna=3.3=pyhd3eb1b0_0\n",
      "  - ipykernel=6.9.1=py310h06a4308_0\n",
      "  - ipython=8.4.0=py310h06a4308_0\n",
      "  - ipython_genutils=0.2.0=pyhd3eb1b0_1\n",
      "  - ipywidgets=7.6.5=pyhd3eb1b0_1\n",
      "  - jedi=0.18.1=py310h06a4308_1\n",
      "  - jinja2=3.0.3=pyhd3eb1b0_0\n",
      "  - jpeg=9e=h7f8727e_0\n",
      "  - json5=0.9.6=pyhd3eb1b0_0\n",
      "  - jsonschema=4.4.0=py310h06a4308_0\n",
      "  - jupyter=1.0.0=py310h06a4308_8\n",
      "  - jupyter_client=7.2.2=py310h06a4308_0\n",
      "  - jupyter_console=6.4.3=pyhd3eb1b0_0\n",
      "  - jupyter_core=4.10.0=py310h06a4308_0\n",
      "  - jupyter_server=1.18.1=py310h06a4308_0\n",
      "  - jupyterlab=3.4.4=py310h06a4308_0\n",
      "  - jupyterlab_pygments=0.1.2=py_0\n",
      "  - jupyterlab_server=2.12.0=py310h06a4308_0\n",
      "  - jupyterlab_widgets=1.0.0=pyhd3eb1b0_1\n",
      "  - krb5=1.19.2=hac12032_0\n",
      "  - ld_impl_linux-64=2.38=h1181459_1\n",
      "  - lerc=3.0=h295c915_0\n",
      "  - libclang=10.0.1=default_hb85057a_2\n",
      "  - libdeflate=1.8=h7f8727e_5\n",
      "  - libedit=3.1.20210910=h7f8727e_0\n",
      "  - libevent=2.1.12=h8f2d780_0\n",
      "  - libffi=3.3=he6710b0_2\n",
      "  - libgcc-ng=11.2.0=h1234567_1\n",
      "  - libgomp=11.2.0=h1234567_1\n",
      "  - libllvm10=10.0.1=hbcb73fb_5\n",
      "  - libpng=1.6.37=hbc83047_0\n",
      "  - libpq=12.9=h16c4e8d_3\n",
      "  - libsodium=1.0.18=h7b6447c_0\n",
      "  - libstdcxx-ng=11.2.0=h1234567_1\n",
      "  - libtiff=4.4.0=hecacb30_0\n",
      "  - libuuid=1.0.3=h7f8727e_2\n",
      "  - libwebp=1.2.2=h55f646e_0\n",
      "  - libwebp-base=1.2.2=h7f8727e_0\n",
      "  - libxcb=1.15=h7f8727e_0\n",
      "  - libxkbcommon=1.0.1=hfa300c1_0\n",
      "  - libxml2=2.9.14=h74e7548_0\n",
      "  - libxslt=1.1.35=h4e12654_0\n",
      "  - lz4-c=1.9.3=h295c915_1\n",
      "  - markupsafe=2.1.1=py310h7f8727e_0\n",
      "  - matplotlib-inline=0.1.2=pyhd3eb1b0_2\n",
      "  - mistune=0.8.4=py310h7f8727e_1000\n",
      "  - mpc=1.1.0=h10f8cd9_1\n",
      "  - mpfr=4.0.2=hb69a4c5_1\n",
      "  - nbclassic=0.3.5=pyhd3eb1b0_0\n",
      "  - nbclient=0.5.13=py310h06a4308_0\n",
      "  - nbconvert=6.4.4=py310h06a4308_0\n",
      "  - nbformat=5.3.0=py310h06a4308_0\n",
      "  - ncurses=6.3=h5eee18b_3\n",
      "  - nest-asyncio=1.5.5=py310h06a4308_0\n",
      "  - notebook=6.4.12=py310h06a4308_0\n",
      "  - nspr=4.33=h295c915_0\n",
      "  - nss=3.74=h0370c37_0\n",
      "  - openssl=1.1.1q=h7f8727e_0\n",
      "  - packaging=21.3=pyhd3eb1b0_0\n",
      "  - pandocfilters=1.5.0=pyhd3eb1b0_0\n",
      "  - parso=0.8.3=pyhd3eb1b0_0\n",
      "  - pcre=8.45=h295c915_0\n",
      "  - pexpect=4.8.0=pyhd3eb1b0_3\n",
      "  - pickleshare=0.7.5=pyhd3eb1b0_1003\n",
      "  - pip=22.1.2=py310h06a4308_0\n",
      "  - ply=3.11=py310h06a4308_0\n",
      "  - prometheus_client=0.14.1=py310h06a4308_0\n",
      "  - prompt-toolkit=3.0.20=pyhd3eb1b0_0\n",
      "  - prompt_toolkit=3.0.20=hd3eb1b0_0\n",
      "  - ptyprocess=0.7.0=pyhd3eb1b0_2\n",
      "  - pure_eval=0.2.2=pyhd3eb1b0_0\n",
      "  - pycparser=2.21=pyhd3eb1b0_0\n",
      "  - pygments=2.11.2=pyhd3eb1b0_0\n",
      "  - pyopenssl=22.0.0=pyhd3eb1b0_0\n",
      "  - pyparsing=3.0.4=pyhd3eb1b0_0\n",
      "  - pyqt=5.15.7=py310h6a678d5_1\n",
      "  - pyrsistent=0.18.0=py310h7f8727e_0\n",
      "  - pysocks=1.7.1=py310h06a4308_0\n",
      "  - python=3.10.4=h12debd9_0\n",
      "  - python-dateutil=2.8.2=pyhd3eb1b0_0\n",
      "  - python-fastjsonschema=2.15.1=pyhd3eb1b0_0\n",
      "  - pytz=2022.1=py310h06a4308_0\n",
      "  - pyzmq=23.2.0=py310h6a678d5_0\n",
      "  - qt-main=5.15.2=h327a75a_7\n",
      "  - qt-webengine=5.15.9=hd2b0992_4\n",
      "  - qtconsole=5.3.1=py310h06a4308_1\n",
      "  - qtpy=2.0.1=pyhd3eb1b0_0\n",
      "  - qtwebkit=5.212=h4eab89a_4\n",
      "  - readline=8.1.2=h7f8727e_1\n",
      "  - requests=2.28.1=py310h06a4308_0\n",
      "  - send2trash=1.8.0=pyhd3eb1b0_1\n",
      "  - setuptools=63.4.1=py310h06a4308_0\n",
      "  - sip=6.6.2=py310h6a678d5_0\n",
      "  - six=1.16.0=pyhd3eb1b0_1\n",
      "  - sniffio=1.2.0=py310h06a4308_1\n",
      "  - soupsieve=2.3.1=pyhd3eb1b0_0\n",
      "  - sqlite=3.39.2=h5082296_0\n",
      "  - stack_data=0.2.0=pyhd3eb1b0_0\n",
      "  - sympy=1.10.1=py310h06a4308_0\n",
      "  - terminado=0.13.1=py310h06a4308_0\n",
      "  - testpath=0.6.0=py310h06a4308_0\n",
      "  - tk=8.6.12=h1ccaba5_0\n",
      "  - toml=0.10.2=pyhd3eb1b0_0\n",
      "  - tornado=6.1=py310h7f8727e_0\n",
      "  - traitlets=5.1.1=pyhd3eb1b0_0\n",
      "  - typing-extensions=4.3.0=py310h06a4308_0\n",
      "  - typing_extensions=4.3.0=py310h06a4308_0\n",
      "  - tzdata=2022a=hda174b7_0\n",
      "  - urllib3=1.26.11=py310h06a4308_0\n",
      "  - wcwidth=0.2.5=pyhd3eb1b0_0\n",
      "  - webencodings=0.5.1=py310h06a4308_1\n",
      "  - websocket-client=0.58.0=py310h06a4308_4\n",
      "  - wheel=0.37.1=pyhd3eb1b0_0\n",
      "  - widgetsnbextension=3.5.2=py310h06a4308_0\n",
      "  - xz=5.2.5=h7f8727e_1\n",
      "  - zeromq=4.3.4=h2531618_0\n",
      "  - zlib=1.2.12=h7f8727e_2\n",
      "  - zstd=1.5.2=ha4553b6_0\n",
      "  - pip:\n",
      "    - mpmath==1.2.1\n",
      "    - pyqt5-sip==12.11.0\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "\n",
    "conda env export -n sptest > environment.yml\n",
    "head -n -1 environment.yml"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}