sympy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tool of the Week - Sympy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## import/initialize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "%matplotlib inline\n",
    "sp.init_printing() # print expressions nicely (math looking)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## create symbols "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( x, \\quad y, \\quad z\\right )$$"
      ],
      "text/plain": [
       "(x, y, z)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, z = sp.symbols('x y z')\n",
    "display((x,y,z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## create expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAUBAMAAAB/pwA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NuzJUme9mZ+xlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfElEQVQIHWNggIDctQJQFpsD8wQok8OB+wuMGcDyFcpkYOD5CGdyKMCZuXAW+wU4M4whGsrmnnNmIZTJ9///BwYGIWVXNQWwCGMCexMHxFI2AbaPrA4QUQauBWAGiOBXgDP3b4AyeQT0GZgEwJz4A+sZ3CHCwkpC1wvATAAiEBajWZbtCwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$x^{2}$$"
      ],
      "text/plain": [
       " 2\n",
       "x "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# one variable\n",
    "expr = x**2\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$y = x^{2}$$"
      ],
      "text/plain": [
       "     2\n",
       "y = x "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# two variable (non implicit form)\n",
    "expr2 = sp.Eq(y,x**2)\n",
    "expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEkAAAAYBAMAAABEj829AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM0ydqsiRIlm3btUme8mhfXmAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVQoFWNgQAEcty+i8LFz2hiCsEugiC5jsE9AEcDKWc6QX4BVAk3wvACaAFbuEqyiaIIcF9AEsHLnYhVFE2RvYDeACB1Bk0HmGp05DXU9PlXv//+HasKuitElrKQFyVioKkZfB4Y8ROBIMMxyWISpioP9AYM/QriRoV+gDMFlgJqVw6vAsJuBQUgJBJQZBEAcGGhSUlqnpKQK5ArwOTB8gQmDaBQOzCyGegHmz0iqUDgMcFWXGFgeIFQdZPnA4IjgwlVtZeAOgAuz/+H+wDYBzkWYdZWhHiHMGOLoOxNJEdwsUZf7CcjiqGxE2F9ClUDhCUJ4rAqM31HEsXK4JnA7YJVAEWR3uQzkAwA4PjfyDpCS0wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- x^{2} + y$$"
      ],
      "text/plain": [
       "   2    \n",
       "- x  + y"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# two variable (implicit form)\n",
    "expr3 = y - x**2\n",
    "expr3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## plot expressions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x20d0fab9da0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# regular expression\n",
    "sp.plot(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x20d10bb3ef0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# implicit equation\n",
    "sp.plot_implicit(expr3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x20d114e00b8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3d plot\n",
    "plot3d(expr3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## substitute for symbol in expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- x^{2} + y$$"
      ],
      "text/plain": [
       "   2    \n",
       "- x  + y"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- x^{2} + 2$$"
      ],
      "text/plain": [
       "   2    \n",
       "- x  + 2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr3.subs(y,2) # replace a symbol with an actual number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x^{3} - x^{2}$$"
      ],
      "text/plain": [
       " 3    2\n",
       "x  - x "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr3.subs(y,x**3) # replace a symbol with an entire expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## all sympy objects are immutable\n",
    "All sympy objects, except matrices, are immutable. Operations return a new object, they do not modify the original."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAOBAMAAAAyKEr9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E780QqzJwzRuQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAhklEQVQIHWNgEFIyYYACxgAG/wQom/0LA38DlM25koF/A5QNpOBqGBh4mhgYjtdKFhUwMDBqxDDwKLC1c4BVVk1gOsD0h1MApItrDQ8DswGQwSjAwPyFgYEfqJqB/w+Y/f4BSIEBA8cflgP1DOwHGNgSgObPd7BnEANKTA21ZDhbfjwsgQEAM70ceyGaTHkAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$3 x$$"
      ],
      "text/plain": [
       "3⋅x"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = 3*x\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAAUBAMAAABohZD3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E780QqzJwzRuQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVQYGWNgQAKqpgeQeAxMArwbkPkcAnwfUfgTGH8i8xkYWP6g8jkKGBiElEzggqoMDIwBDP4JUAG2AAYG9i8M/A1Q/iSGeQycKxn4obbybXGxAcnA1HP9//8ByOVpYmA4XitZBDQbBBg1Yhh4FNjaOaC6GBiqJjAdYPrDKQCRZ2DgWsPDwGwA5TEKMDB/YWDgh+pm4P8D5r9/AJXnMmDg+MNyoJ6B/QBYhC0BaP98B3sGMaiCqaGWDGfLj4clgPkA2OMoahLiQs8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$3 x^{2}$$"
      ],
      "text/plain": [
       "   2\n",
       "3⋅x "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newExpr = expr.subs(x,x**2)\n",
    "newExpr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAOBAMAAAAyKEr9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E780QqzJwzRuQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAhklEQVQIHWNgEFIyYYACxgAG/wQom/0LA38DlM25koF/A5QNpOBqGBh4mhgYjtdKFhUwMDBqxDDwKLC1c4BVVk1gOsD0h1MApItrDQ8DswGQwSjAwPyFgYEfqJqB/w+Y/f4BSIEBA8cflgP1DOwHGNgSgObPd7BnEANKTA21ZDhbfjwsgQEAM70ceyGaTHkAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$3 x$$"
      ],
      "text/plain": [
       "3⋅x"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr # original expression unchanged"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solve equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$3 x + 6$$"
      ],
      "text/plain": [
       "3⋅x + 6"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = 3*x + 6\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACwAAAAVBAMAAADP3xFXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZpkQzYndq1TvMrsiRHaZuvfyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVQYGWNgYGBUZEABix6DuMyuKIJAzs0FQILxA0KYWWk3UIjJgYGBgTUBSECBOQPrX6gIsrAyA8NMLMLTGBjqD0D0I6v2N2CoX4ApDLQi34CBdQKQZneA2gemeL9C3da5AFmYrQDIc2JgWJ0DpE1cQMALyFICqWHPg/oJxAEBPgUQ6Q7E7BtALChoYuA5APE3sgO5Ahj4gO4GuQRZ+FhoUBlUBFnY////b1iEITaAFYJNglkJpsHCyOENkWVyANGYsXMBJMyBJS4BP/UsM/JFYAYAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left\\{-2\\right\\}$$"
      ],
      "text/plain": [
       "{-2}"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.solveset(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solve linear system of equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left\\{\\left ( \\frac{10}{11}, \\quad \\frac{9}{11}\\right )\\right\\}$$"
      ],
      "text/plain": [
       "⎧⎛10      ⎞⎫\n",
       "⎨⎜──, 9/11⎟⎬\n",
       "⎩⎝11      ⎠⎭"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use solveset for univariate equations and solveset for system of linear equations\n",
    "from sympy.solvers.solveset import linsolve\n",
    "\n",
    "# create the equations\n",
    "eq1 = sp.Eq(3*x + 4*y, 6) # 3x + 4y = 6\n",
    "eq2 = sp.Eq(5*x + 3*y, 7) # 5x + 3y = 7\n",
    "\n",
    "# put em in a list\n",
    "eqs = [eq1,eq2]\n",
    "\n",
    "# pass list to linsolve\n",
    "linsolve(eqs,(x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## differentiate/integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAAUBAMAAABohZD3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E780QqzJwzRuQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVQYGWNgQAKqpgeQeAxMArwbkPkcAnwfUfgTGH8i8xkYWP6g8jkKGBiElEzggqoMDIwBDP4JUAG2AAYG9i8M/A1Q/iSGeQycKxn4obbybXGxAcnA1HP9//8ByOVpYmA4XitZBDQbBBg1Yhh4FNjaOaC6GBiqJjAdYPrDKQCRZ2DgWsPDwGwA5TEKMDB/YWDgh+pm4P8D5r9/AJXnMmDg+MNyoJ6B/QBYhC0BaP98B3sGMaiCqaGWDGfLj4clgPkA2OMoahLiQs8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$3 x^{2}$$"
      ],
      "text/plain": [
       "   2\n",
       "3⋅x "
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create an expression\n",
    "expr = 3*x**2\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAOBAMAAAAyKEr9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiXYyEM1Embsi72bdVKu+2mc6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAiUlEQVQIHWNgYBBSNGCAAtcE9gAYu52BowHKZvsJE2Rg4FiAYPMHC5UxMDjpTVNUYPCPZuC5wCLAfYgngMH/AwP7EkYHxi9sExj4DzBwf2OBmAWU4v7NwMCvADSCbwFQnIHBHmQ38xcG9gW8DvoMTA4MDA8ZvC7kX+hnmA2UYCx8zOCn5FS9gQEALgkcvah2rdAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$6 x$$"
      ],
      "text/plain": [
       "6⋅x"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# differentiate w respect to x\n",
    "expr2 = expr.diff(x)\n",
    "expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAAUBAMAAABohZD3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E780QqzJwzRuQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVQYGWNgQAKqpgeQeAxMArwbkPkcAnwfUfgTGH8i8xkYWP6g8jkKGBiElEzggqoMDIwBDP4JUAG2AAYG9i8M/A1Q/iSGeQycKxn4obbybXGxAcnA1HP9//8ByOVpYmA4XitZBDQbBBg1Yhh4FNjaOaC6GBiqJjAdYPrDKQCRZ2DgWsPDwGwA5TEKMDB/YWDgh+pm4P8D5r9/AJXnMmDg+MNyoJ6B/QBYhC0BaP98B3sGMaiCqaGWDGfLj4clgPkA2OMoahLiQs8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$3 x^{2}$$"
      ],
      "text/plain": [
       "   2\n",
       "3⋅x "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# integrate it back\n",
    "expr2.integrate(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## simplify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$7 x + 5$$"
      ],
      "text/plain": [
       "7⋅x + 5"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# some simplifications (obvious ones) are done automatically\n",
    "expr = 3*x + 4*x + 5 # the x terms can be combined, this is done automatically\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\sin^{2}{\\left (x \\right )} + \\cos^{2}{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "   2         2   \n",
       "sin (x) + cos (x)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to let sympy decide how to simplify - use simplify(expr)\n",
    "expr = sp.sin(x)**2 + sp.cos(x)**2\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAIVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADdcGRXAAAACnRSTlMAVO8Qq4lmdpnNpXqjvAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAACBJREFUCB1jYAADRmUGBpOQxUA2GykEO1Axh9PKNrAZAEESCWTnoGnkAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAUBAMAAADVZMaCAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARN3vMmYQu3aZIqtUic3QRwAsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABZElEQVQoFXWSP0jDQBTGv5Q2bUKKRRfBQUEKDg66iJN0cW7BxalkS0BQF0V0sOBiEP8sgg5KKohrR3GQ4ubWxcGtipNDcLGDk99LSe9S6IPcfd97v7zc5Q5Iwq4lanh2Qi3jaXpIPmn+W9NDclP53IXSgNPQXVG5TKgX0pi5MKjdDZSINIYPwJgtrbIQ8PFPmqcNzgrzr2AvAe+At369zcIOYHZyc5muUINunQkUfoA64OJBCvNA0S32jFBMgtntW+TZ5IWp7K4UFtktThGPos+VKGpJZhljDaBKYEoowRCnZE66weihWokxh28x+FHaioyMZKdWF0e048ArICC34LjnKLjUCsu3cEBbR7b8dlai4p6n24e4F0hhVsv4pb2BhTX+vLjvxrF/WROtMPMx+KP9ipMyjDosrg7mjBBxpI/edPvZZ2xxRdrRY79fSI9l7DGhXSR4aaDvJoMKhd5h9CXPhfgH6XBIHDXRH8MAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$z \\left(x + y\\right)$$"
      ],
      "text/plain": [
       "z⋅(x + y)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# expand(expr)\n",
    "expr = z*(x + y)\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$x z + y z$$"
      ],
      "text/plain": [
       "x⋅z + y⋅z"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr2 = sp.expand(expr)\n",
    "expr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$z \\left(x + y\\right)$$"
      ],
      "text/plain": [
       "z⋅(x + y)"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# factor(expr)\n",
    "sp.factor(expr2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### create matrix manually"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAyBAMAAAAOzY77AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUIhAyq2Z2mc3du0T2XE1VAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABKElEQVQ4EWOQ//+JAQtg+v9fgEHYxRWLFAOri7MAgxg2GZAYG3Y5zaYEhJxhALJubgPWIzA51qJ6FLlGBgZtmBwDQz+K3HUGBvsAuH2oct8ZGN4bYJdj/QWUm4BdjgUYGPm45ID68hWw68NnJgPQLfY43MJwF+wpWJih+gHV7/NR/M5jwAqMAai+5fK7GpAClFVzOlJYI0nAmTD74AJIjFE5BqYZakgBAmVCw2UzQ4wDsiSzKJAHkeMQYGDagCQXrv4VLsdbwMAM4sEBB0KOv4CB7zNcAshAkotfwMD3E4ecPzAx4pRbwMCGkrGJNBPoFmZcbuG9AHEZ3DlIZqL7HdkPDIcZAhPgmoAMToTfGYJmliFLcRX+XgELT2RxBHuQpU98ZSSeshUA5OhUzjX/9yIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  1⎦"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = sp.Matrix([[1,0],\n",
    "               [0,1]])\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### create standard matrices automatically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  1⎦"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# identity matrix\n",
    "M = sp.eye(2)\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 0\\\\0 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  0⎦"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# zero matrix\n",
    "M = sp.zeros(2,2)\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### scale matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  1⎦"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = sp.eye(2)\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAyBAMAAAAOzY77AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUIhAymburRN3NdmbDbtPBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABhUlEQVQ4Ee3UvUrDUBQH8H/TJP2uEcHFwdBBF4vdHFuwTg6NLiIOBl+gWaS6OUndMrk41DdoqS5OCj5AHQRxUNAXENQqKnK9JTnJaS2dHcySy/3lnJx770kwLZ4x5FKEMDBRXhpC0MqLBiaHSW9O92xtZ7/vifyjTaa5mD9mmC5op2QxCxGD2QMwRxZpIfHK7AAoWv770l0k3ph9AM0C1QKkuqFp79KuQmuaoalyM6rMzkKCKuOqZhAXc5gN5LxhBMhaikEtUQdlpnXgyaKcW8A1M752tZ3bbTFLFTR5At5ep4UQ3LT8rU3GQtjQPyM2Ew7/Dcr9TLgfgFar28F+XmKjxHAdyidZ1oBywWwbGCeLu4iyHsQU0Cj55zfmIvnC4joWGrZvmw6S38zk8Jz6pWJC77ekbF/v/CoO9P4PO+WS/c5Zk2m9OFlLlNeCTK/NPYvvIcvXgAWoJd8G166byJDhBCu2zELXcm72iHJi9e6Q5nv3jhBfgXEIxn+sP0f9I0f8W38A4yNePIsZA+oAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2 & 0\\\\0 & 2\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  2⎦"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### invert matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2 & 0\\\\0 & 2\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  2⎦"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = sp.eye(2) * 2\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{2} & 0\\\\0 & \\frac{1}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1/2   0 ⎤\n",
       "⎢        ⎥\n",
       "⎣ 0   1/2⎦"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Minv = M**-1\n",
    "Minv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### create column vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAyBAMAAACqpzYoAAAAJ1BMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAilU6eAAAADHRSTlMA74lUIhAyq2Z2mc3nXb/RAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAASklEQVQoFWOQOXOIAQR0zhxkEHZxBbNDXAwZxMAsEJGIyTYMgImzFtXA2QwMPXRkz0HYtVxmVwNWd4Kcj8399BQf5mGFnGaQ0hIAtho3xcYc7GMAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}1\\\\1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1⎤\n",
       "⎢ ⎥\n",
       "⎣1⎦"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = sp.Matrix([1,1])\n",
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### transform vector (i.e. matrix vector multiplication)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAyBAMAAACqpzYoAAAALVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMA74lUIhAymburRN3Ndm03EL0AAAAJcEhZcwAADsQAAA7EAZUrDhsAAACESURBVCgVY5B794gBBPTePWQQdnEFs0NcDBnEwCwQkQhmh1e0wdisExj0FkDF2QMYGAWgbMYNDJxPoGyepwycz2B6GRi4nyLY6xQQ7J0wMxkY2AsQ7OtAJtRe5gIGFxg7iYHhCpTNskmpcgOUzfPu3TsYG6QRCCBuHij2SAor5DSDlJYAx2NDseS6v+wAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2\\\\2\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⎤\n",
       "⎢ ⎥\n",
       "⎣2⎦"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M * v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### can use symbols in matrices as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}a & 0\\\\0 & b\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡a  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  b⎦"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a,b = sp.symbols('a b')\n",
    "\n",
    "M = sp.Matrix([[a,0],\n",
    "               [0,b]])\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAyBAMAAAC0bgabAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUIhAydqtEZt3Nu5nxBet/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVQoFWOQ//+JAQz0/39kEHZxhXBCXAwZxCBMEJlIHU54hWdRAdQ0VgWu7dwHoBymAKavnA4wGQbeC0iW8gN1wF2QnwDnMAfUM7AHQGXmG9xn8IIpiygPf7UAxgGpBwEqeQFi2ACaxlpXwOAI8zYTpwBDPcxzznwHGO7COAGMBQzfYRyG+QFs3+CcNwzsAnDODQbeBjjnBcP8BXBORPl7BziHgeENkA3xNscB1p9wDvcCXkT8cJY/A0ngDR2UJIac+AB5UUFFldUqngAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}x\\\\y\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡x⎤\n",
       "⎢ ⎥\n",
       "⎣y⎦"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = sp.Matrix([x,y])\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}a x\\\\b y\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡a⋅x⎤\n",
       "⎢   ⎥\n",
       "⎣b⋅y⎦"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M*v"
   ]
  }
 ],
 "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}