{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Simple Registry for Managing and Auto-numbering _sympy_ Equations\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "bla bl\n",
    "\n",
    "<figure>\n",
    "    \n",
    "![Autocomplete](https://gist.github.com/WetHat/6a8e38fb92ab831d8cdb5d66f2d2e524/raw/ed180f06d6bfd29bd4557dbb1e66504c1e643273/Xautocomplete.png)\n",
    "\n",
    " **Fig 1. JupyterLab Autocompletion Dialog for Registered Equations**\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "\n",
    "\n",
    "class EquationRegistry():\n",
    "\n",
    "    def __init__(self):\n",
    "        # bypass self.__setattr__\n",
    "        self.__dict__['_indexmap'] ={}\n",
    "\n",
    "    def __setattr__(self, name, value):\n",
    "        index = self._indexmap.get(name,0)\n",
    "        if index == 0: # a new field is requested\n",
    "            self._indexmap[name] = len(self._indexmap) + 1\n",
    "        self.__dict__[name] = value\n",
    "\n",
    "    def __call__(self, name):\n",
    "        index = self._indexmap[name]\n",
    "        self._indexmap[name] = index # mark as published\n",
    "        return IPd.Math(r'\\begin{align}\\fbox{\\(' \\\n",
    "                       + sp.latex(self.__dict__[name]) \\\n",
    "                       + r'\\)} \\tag*{(' \\\n",
    "                       + str(index) \\\n",
    "                       + r')}\\end{align}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Sum, Eq, IndexedBase, diff, Function, factor_terms, expand\n",
    "from sympy.abc import *\n",
    "import IPython.display as IPd\n",
    "\n",
    "EQ = EquationRegistry()  # create the equation registry for this notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{align}\\fbox{\\({\\epsilon}_{i} = x - {p}_{i}\\)} \\tag*{(1)}\\end{align}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epsilon = IndexedBase('\\epsilon')\n",
    "p = IndexedBase('p')\n",
    "EQ.error = Eq(epsilon[i], x-p[i])\n",
    "EQ('error')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{align}\\fbox{\\(E{\\left(x \\right)} = \\sum_{i=0}^{n - 1} \\left(x - {p}_{i}\\right)^{2}\\)} \\tag*{(2)}\\end{align}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E=Function('E')\n",
    "EQ.energy=Eq(E(x),Sum(EQ.error.rhs**2,(i,0,n-1)))\n",
    "EQ('energy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{align}\\fbox{\\(\\frac{d}{d x} E{\\left(x \\right)} = \\sum_{i=0}^{n - 1} \\left(2 x - 2 {p}_{i}\\right)\\)} \\tag*{(3)}\\end{align}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "EQ.dE_dx = Eq(diff(EQ.energy.lhs,x),EQ.energy.rhs.diff(x))\n",
    "EQ('dE_dx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first derivative of the energy function $E(x)$ can be simplified like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\begin{align}\\fbox{\\(\\frac{d}{d x} E{\\left(x \\right)} = 2 n x - 2 \\sum_{i=0}^{n - 1} {p}_{i}\\)} \\tag*{(4)}\\end{align}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EQ.dE_dx_simple = Eq(EQ.dE_dx.lhs,factor_terms(expand(EQ.dE_dx.rhs)).doit())\n",
    "EQ('dE_dx_simple')                 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Appendix\n",
    "\n",
    "Packages used in this gist:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "**Python Packages used in This Notebook**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "| Component                         | Version                    | Description          |\n",
       "| --------------------------------- | -------------------------- | -------------------- |\n",
       "| [Python](https://www.python.org/) | 3.8.6   | Programming Language |\n",
       "| [jnbBuffs](https://github.com/WetHat/jupyter-notebooks) | 0.1.2 | Utilities for authoring JupyterLab Python notebooks. |\n",
       "| [jupyterlab](http://jupyter.org) | 3.0.12 | The JupyterLab server extension. |\n",
       "| [sympy](https://sympy.org) | 1.7.1 | Computer algebra system (CAS) in Python |"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from jnbBuffs.manifest import notebook_manifest\n",
    "import IPython.display as IPd\n",
    "\n",
    "display(IPd.Markdown('**Python Packages used in This Notebook**'))\n",
    "notebook_manifest('jupyterlab', 'sympy', 'jnbBuffs')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (JupyterLab)",
   "language": "python",
   "name": "jupyterlab"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}