SympyNumericalBinding.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prototyping\n",
    "create expression to test, using binomial coefficient because it's everywhere and simple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y, xprime, yprime=symbols('x, y, xp, yp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "xthing=x+y**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD8AAAAlCAYAAAD1EjEiAAAABHNCSVQICAgIfAhkiAAAA4BJREFU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\n",
      "text/latex": [
       "$${\\binom{x + y^{2}}{y}}$$"
      ],
      "text/plain": [
       "⎛     2⎞\n",
       "⎜x + y ⎟\n",
       "⎜      ⎟\n",
       "⎝  y   ⎠"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Test=binomial(xthing, y); Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## prototype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHUAAAAXCAYAAAA1OADtAAAABHNCSVQICAgIfAhkiAAABCVJREFU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\n",
      "text/latex": [
       "$$\\left ( \\left\\{x, y\\right\\}, \\quad y\\right )$$"
      ],
      "text/plain": [
       "({x, y}, y)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nSelf_arg, kSelf_arg=Test.args; nSelf_arg.free_symbols, kSelf_arg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['x', 'y']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nSelf_argN=lambdify(tuple(nSelf_arg.free_symbols), nSelf_arg, dummify=False)\n",
    "nSelf_argNargs=list(nSelf_argN.__code__.co_varnames)\n",
    "nSelf_argNargs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['y']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kSelf_argN=lambdify(tuple(kSelf_arg.free_symbols), kSelf_arg, dummify=False)\n",
    "kSelf_argNargs=list(kSelf_argN.__code__.co_varnames)\n",
    "kSelf_argNargs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['y', 'x']"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binomialN_args=list(set(nSelf_argNargs).union(set(kSelf_argNargs)))\n",
    "binomialN_args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import binom as binomalN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'lambda y,x: binomalN( nSelf_argN(x,y), kSelf_argN(y) )'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TestN=f\"lambda {','.join(binomialN_args)}: binomalN( nSelf_argN({','.join(nSelf_argNargs)}), kSelf_argN({','.join(kSelf_argNargs)}) )\"\n",
    "TestN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "TestNN=eval(TestN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prototype Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAASCAYAAAAkAezhAAAABHNCSVQICAgIfAhkiAAAAeRJREFU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\n0aiFb0mBbxFO4RW+44VUIFr9+hOYQIY/+ESDwLkMs9gAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$21.0$$"
      ],
      "text/plain": [
       "21.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TestNN(x=3,y=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAASCAYAAABFGc6jAAAABHNCSVQICAgIfAhkiAAAARBJREFU\nOI3t1L8rRWEcx/EX+QuQ/AM2f8RlMSnFzMCglAxKKWVjv7sMbMomNsWoKOku0s1gMrgMBsRwvkq3\n0znnOSWLTz2d03k+n+f9Pc8v/kADWMAhbvGKDs4xj96czAyaOMMzPrFXBloM4wP2sYUdPMX3A/R0\nZa6i7wWtqqBxTOZUPoz7GGS6q28MI1FAoyqoSOsxSLPAUwjKm/c8vcXzvWpldUB9mI33498EbWMU\nRzipCyrTsmzeW+gv8TbU3AxLEbyR7bwy1QKtROgaQxUzyaC1CFxiMKG4JNBGmC+Ur0kS6OeVModd\nfMgOZifH3w7Pt6aika3jBO5kdx88YrV7kM2oqKidJmbaeX/3ryR9AQwfU0sy3cQnAAAAAElFTkSu\nQmCC\n",
      "text/latex": [
       "$$21$$"
      ],
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Test.subs({x:3, y:2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result (Pass)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bind functional proto-code to class "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class binomial2(binomial):\n",
    "    def __NumericalMap_Defualt__(self):\n",
    "        #get the arguments of n, k of binomial(n,k)\n",
    "        nSelf_arg, kSelf_arg = self.args\n",
    "\n",
    "        #lambdify the n argument and collect terms, for moment using clean lambdify in testing\n",
    "        nSelf_argN = lambdify(tuple(nSelf_arg.free_symbols), nSelf_arg, dummify=False)\n",
    "        nSelf_argNargs = list(nSelf_argN.__code__.co_varnames)\n",
    "\n",
    "\n",
    "        #repeat for the k argument\n",
    "        kSelf_argN = lambdify(tuple(kSelf_arg.free_symbols), kSelf_arg, dummify=False)\n",
    "        kSelf_argNargs = list(kSelf_argN.__code__.co_varnames)\n",
    "\n",
    "        #get concise argument list for final generated expression\n",
    "        binomialN_args = list(set(nSelf_argNargs).union(set(kSelf_argNargs)))\n",
    "\n",
    "        #import the mapping from sympy binomial to scipy.special.binom\n",
    "\n",
    "        from scipy.special import binom as binomalN\n",
    "        Numerclized=f\"lambda {','.join(binomialN_args)}: binomalN( nSelf_argN({','.join(nSelf_argNargs)}), kSelf_argN({','.join(kSelf_argNargs)}) )\"\n",
    "\n",
    "        return eval(Numerclized)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## create mark2 instance of binomial coefficient \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD8AAAAlCAYAAAD1EjEiAAAABHNCSVQICAgIfAhkiAAAA4BJREFU\naIHt2UmIHVUUgOGvOzYd245DxxljkBiEqEloFCEOiIvoQhFtdKPSi9CIgiAhgkQcNuJCxHmVzQNF\nwQFcKCpOwYVRcBETHIL2SqMGxGhMYpuocXGqsVJd7737hmtU+ofivTp16p5z7nxu8d9jCTbjM3yC\n63MbXJDbQAechlXF/5PxNUZq9AZ7NTSAu3FsrwVlZBvOrJGfjqlWL7arnftEF9vTlVv5uQBDovWr\nfCvi62pYXIVHuvcrO4vFuF/TQmcAr+GsTgpeKLrTiV27NpcGHuhTWcN4H7ck6F4kKmAOzbr97aK7\n/1CR34DfsLQkexxf4qQER1L4BusrstWF3RWiNRt4F88klPcRRnFlivGhwoHVNc8G8DE2FfcbsAvL\nEsptSGv5F/F8RfYenir+X4I/sbV0nd+mzJtFT2nLdfiqxfO1OChWgT1i0kmhIS349RX7E/hRjPFu\nGcV+9Q16GC/4u5ab8QF+F5NiMzZib+k6iAMV2aU1763BIYyJsT2NO9s5ncDbeLiVwgL8jJta6FyB\nfaLrjbfQG8PZpetlPFGRHV3z3rAY32tF7/pCDMVeuVfMTU0ZF7V+XpPnq/ATJvEKXu/AeEP6bP8h\nnhTD6uoObLTiWhHbqc0UpgqFuhZZip24p7hfKVq/ruvW0ZAe/KNF2W8m6qewXMR2zaygutQtw278\nWpGP4Q28igcL2Ta8hIf66OAsW0Xw1SWvF3YWv01Xpuewo48Gu+UtPJ2h3L1Ku9ajKg8XYSaD0RQG\nxUZpnZhzbsxgY7+IEXODHxEz7ZHgMrFr2yHW9t0ZbMwopb/V4A/UyP4pNutDDt6GIREjNcb2iaTm\n/8pCESPmBr9Lb9vIfzODYpv7fVlQZlpMOkeq6+fkFBHX9KygGvx2kbmlZGnd0C5dzcmS4vfTZgqL\nRMIykcmBdulqTqbECjIwK6i2/C/YgoszObAFF5buJ0S+cH8me2XGRUUfaqV0mzgPz0GudDWFaQkb\np+NFNnVOBgdypavtWCEORA4736/7GDEjKmAl3umzE3+IFHUUd+BWUQG5uUukyUlZ4pjYZh6TwZEc\n6WorRkQsHR2wTsozEU2KFeXcDGXXsUGcRnfMJnHc1E9ypat1nIFnlZa3ThgR5/K9TkqDYoe1Ed/h\nhB7LS2EYj+nxO+NxSjlwl1wuxvnnWn9e6ieLxcQ6zzzzzDPPXxuYrNm5CoskAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$${\\binom{x + y^{2}}{y}}$$"
      ],
      "text/plain": [
       "⎛     2⎞\n",
       "⎜x + y ⎟\n",
       "⎜      ⎟\n",
       "⎝  y   ⎠"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Test3=binomial2(xthing, y); Test3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test mark2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAASCAYAAAAkAezhAAAABHNCSVQICAgIfAhkiAAAAeRJREFU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\n0aiFb0mBbxFO4RW+44VUIFr9+hOYQIY/+ESDwLkMs9gAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$21.0$$"
      ],
      "text/plain": [
       "21.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Test3N=Test3.__NumericalMap_Defualt__()\n",
    "Test3N(x=3,y=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result (Pass)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# To Do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$y + {\\binom{x + y^{2}}{y}}$$"
      ],
      "text/plain": [
       "    ⎛     2⎞\n",
       "    ⎜x + y ⎟\n",
       "y + ⎜      ⎟\n",
       "    ⎝  y   ⎠"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Test4=y+binomial2(xthing, y); Test4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And I have no idea how to make `. __NumericalMap_Defualt__(self)` be called when `lambdify` acts on it and bind to to the rest of the expression"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Test4N=lambdify(tuple(Test4.free_symbols), Test4, dummify=False)\n",
    "Test4N(x=3, y=2)"
   ]
  }
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