Using SymPy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy / Havana\n",
    "\n",
    "In case I get to go to [SciPy / Havana](http://conf.scipyla.org/), I'm boning up on SymPy, an important component within the SciPy Ecosystem.\n",
    "\n",
    "Here's the kind of thing one might do with SymPy, a computer algebra system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy as sym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = sym.symbols('x')\n",
    "sym.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHAAAAApCAYAAADtYa10AAAABHNCSVQICAgIfAhkiAAABbNJREFU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\n",
      "text/latex": [
       "$$\\int_{0}^{\\pi} \\sin{\\left (x \\right )}\\, dx$$"
      ],
      "text/plain": [
       "π          \n",
       "⌠          \n",
       "⎮ sin(x) dx\n",
       "⌡          \n",
       "0          "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.Integral(sym.sin(x), (x, 0, sym.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAMJJREFU\nKJHF0j9LQlEYB+DH6BNYhJ/HxcmpD9CgQ0OImxAIbi5u7eLSJji5NzQGDRItDtHQ3J0aSnS4LxJy\ntBMN/eBw4XCe+77nD3/MCdqYYYkPFLhHC0cpdIk13nCLIcZ4j/kpKruojmbijzW8Bjz/TevXgW7s\n6zORz/h+5VY5xiIqNXLRKMA8F3QCPKOaA64CPClP8Md0AyxwlgN6AR5xmgP6AR4c2MP3Z3GBCVbK\nSywS619izTaDqHJo3OW0+8/ZALIVMPhgrAZWAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.Integral(sym.sin(x), (x, 0, sym.pi)).doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition, we have numpy, with its multi-dimensional array object.  Numpy comes with a host of numeric recipes, already built in..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[What are the ethics](http://ucsmp.uchicago.edu/resources/conferences/2012-03-01/) of using CAS in a poorly developing country, such as the United States, known for high infant mortality and poverty rates?  \n",
    "\n",
    "Not everyone can easily afford a TI N-spire, and schools tend to not provide adequate computer infrastructure, even for accessing free and open source tools.\n",
    "\n",
    "Fortunately, even without a TI, we have CAS in the form of the SciPy ecosystem.  Adapting a solution from a CAS blog post, [Quadratics and CAS](https://casmusings.wordpress.com/2017/06/30/quadratics-and-cas/), I was able to derive the same solution for the coefficients a, b and c. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.,   4., -30.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x=[10,5,-2],y=[210, 40, -30], deg=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But don't we want algebra students to be able to derive the solution manually?  Yes, we do. However, once this step becomes a means to an end, rather than an end in itself, a CAS will save time and facilitate deeper explorations.\n",
    "\n",
    "For further reading:\n",
    "* [Learning Math with Python: Youtube Lectures by Juan Klopper](https://youtu.be/P8DIM41B-mM?list=PLsu0TcgLDUiIqN76ZuRkhDUCd-c_EjIkN)\n",
    "* [Tutorial de SymPy: introducción y comandos básicos ... ](https://youtu.be/OGQRcYVys1Q)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}