{
  "cells": [
    {
      "cell_type": "markdown",
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      "source": [
        " # Interacting with `sympy`\n",
        " \n",
        "`pymbolic` can help take care of many *structural* transformations on your expression trees with great ease. Its main purpose is to help with program transformation after all, not to be a full computer algebra system. That said, if you need a full computer algebra system for things like calculus and simplification, it's easy to get your expressions converted between `pymbolic` and `sympy`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/lib/python3/dist-packages/sympy/core/function.py:105: DeprecationWarning: inspect.getargspec() is deprecated, use inspect.signature() instead\n",
            "  evalargspec = inspect.getargspec(cls.eval)\n"
          ]
        }
      ],
      "source": [
        "import sympy as sp\n",
        "from pymbolic import var\n",
        "\n",
        "x = var(\"x\")\n",
        "y = var(\"y\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(x**2 + 2*x + 1) / (x**2 + x)\n"
          ]
        }
      ],
      "source": [
        "expr = (x**2 + 2*x + 1)/(x**2 + x)\n",
        "print(expr)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's import pymbolic's sympy interoperability code."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "# pymbolic.interop.sympy in newer versions of pymbolic\n",
        "from pymbolic.sympy_interface import (\n",
        "    PymbolicToSympyMapper, SympyToPymbolicMapper)\n",
        "\n",
        "p2s = PymbolicToSympyMapper()\n",
        "s2p = SympyToPymbolicMapper()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(x**2 + 2*x + 1)/(x**2 + x)\n"
          ]
        }
      ],
      "source": [
        "sympy_expr = p2s(expr)\n",
        "print(sympy_expr)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(x + 1)/x\n"
          ]
        }
      ],
      "source": [
        "sympy_result = sp.cancel(sympy_expr)\n",
        "print(sympy_result)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "x**(-1)*(1 + x)\n"
          ]
        }
      ],
      "source": [
        "result = s2p(sympy_result)\n",
        "print(result)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "One thing to note is that `PymbolicToSympyMapper` is a regular `pymbolic` mapper, and its behavior can be overridden in case something about the translation to sympy is not quite what you want.\n",
        "\n",
        "`SympyToPymbolicMapper` also behaves very similarly (and can be overridden similarly) although it is not entirely the same kind of mapper."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": []
    }
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