{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Инфраструктура Python. CAS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Символьная (и точная) математика в Python делается через библиотеку `sympy` (входит в Anaconda). Она несколько уступает CAS с многолетней историей вроде Maple или Mathematica, зато тесно интегрирована с Python http://docs.sympy.org/latest/index.html\n",
    "\n",
    "Попробовать `sympy` можно онлайн http://gamma.sympy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import networkx, PIL\n",
    "from io import BytesIO\n",
    "import itertools\n",
    "import os\n",
    "\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "from sympy import *\n",
    "from sympy.solvers.diophantine import diophantine\n",
    "from sympy.ntheory.factor_ import digits\n",
    "\n",
    "from sympy.abc import h, k, n, t, x, y, z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.1.1'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Символьные вычисления"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Библиотека `sympy` предназначена для символьных вычислений. Она представляет математические выражения (переопределяя сотни имен `numpy`) в виде деревьев, над которыми может проводить различные операции, например, интегрирование."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x - log(tanh(x) + 1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr = integrate(tanh(x), x)\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x - log(tanh(x) + 1)\n",
      "Add(Symbol('x'), Mul(Integer(-1), log(Add(tanh(Symbol('x')), Integer(1)))))\n"
     ]
    }
   ],
   "source": [
    "print expr\n",
    "print srepr(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Add: x - log(tanh(x) + 1)\n",
      "commutative: True\n",
      "+-Symbol: x\n",
      "| commutative: True\n",
      "+-Mul: -log(tanh(x) + 1)\n",
      "  commutative: True\n",
      "  +-NegativeOne: -1\n",
      "  | algebraic: True\n",
      "  | commutative: True\n",
      "  | complex: True\n",
      "  | composite: False\n",
      "  | even: False\n",
      "  | finite: True\n",
      "  | hermitian: True\n",
      "  | imaginary: False\n",
      "  | infinite: False\n",
      "  | integer: True\n",
      "  | irrational: False\n",
      "  | negative: True\n",
      "  | noninteger: False\n",
      "  | nonnegative: False\n",
      "  | nonpositive: True\n",
      "  | nonzero: True\n",
      "  | odd: True\n",
      "  | positive: False\n",
      "  | prime: False\n",
      "  | rational: True\n",
      "  | real: True\n",
      "  | transcendental: False\n",
      "  | zero: False\n",
      "  +-log: log(tanh(x) + 1)\n",
      "    commutative: True\n",
      "    +-Add: tanh(x) + 1\n",
      "      commutative: True\n",
      "      +-One: 1\n",
      "      | algebraic: True\n",
      "      | commutative: True\n",
      "      | complex: True\n",
      "      | even: False\n",
      "      | finite: True\n",
      "      | hermitian: True\n",
      "      | imaginary: False\n",
      "      | infinite: False\n",
      "      | integer: True\n",
      "      | irrational: False\n",
      "      | negative: False\n",
      "      | noninteger: False\n",
      "      | nonnegative: True\n",
      "      | nonpositive: False\n",
      "      | nonzero: True\n",
      "      | odd: True\n",
      "      | positive: True\n",
      "      | rational: True\n",
      "      | real: True\n",
      "      | transcendental: False\n",
      "      | zero: False\n",
      "      +-tanh: tanh(x)\n",
      "        commutative: True\n",
      "        +-Symbol: x\n",
      "          commutative: True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sympy.printing.tree.print_tree(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x - log(tanh(x) + 1)\n",
      "\n",
      "Mul(NegativeOne(), log(Add(One(), tanh(Symbol(x)))))_(1,)\r\n",
      "Symbol(x)_(1, 1, 0, 1, 0)\r\n",
      "NegativeOne()_(1, 0)\r\n",
      "Add(Symbol(x), Mul(NegativeOne(), log(Add(One(), tanh(Symbol(x))))))_()\r\n",
      "log(Add(One(), tanh(Symbol(x))))_(1, 1)\r\n",
      "tanh(Symbol(x))_(1, 1, 0, 1)\r\n",
      "Symbol(x)_(0,)\r\n",
      "One()_(1, 1, 0, 0)\r\n",
      "Add(One(), tanh(Symbol(x)))_(1, 1, 0)\n"
     ]
    },
    {
     "data": {
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KAACwEiUFAABYiZICAACsREkBAABWoqQAAAArUVIAAICVKCkAAMBKlBQAAGAl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\nRK5CYII=\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGBA size=553x539 at 0x19F706A0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy.printing.dot\n",
    "dotstr = sympy.printing.dot.dotprint(expr)\n",
    "graph = networkx.nx_pydot.read_dot(BytesIO(dotstr))\n",
    "\n",
    "print expr\n",
    "print\n",
    "print '\\r\\n'.join(list(graph.nodes))\n",
    "\n",
    "A = networkx.nx_agraph.to_agraph(graph)\n",
    "for node in A.nodes():\n",
    "    if not node.attr['fontname']:\n",
    "        node.attr['fontsize'] = 8\n",
    "        node.attr['fontname'] = 'Verdana'\n",
    "        node.attr['shape'] = 'none'\n",
    "        node.attr['style'] = 'filled'\n",
    "        node.attr['color'] = '#F0F0F0'\n",
    "\n",
    "io = BytesIO()\n",
    "A.draw(io, format='png', prog='dot')\n",
    "PIL.Image.open(io)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ввести собственные символы (или распарсить выражение) можно, используя `Symbol`, `var` (`symbols`), `S` (`sympify`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x**2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Symbol('x') ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a + b + c"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(var('a b c'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x_1: -sqrt(-x_2**2 + 1)}, {x_1: sqrt(-x_2**2 + 1)}]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1, x2 = symbols('x_1 x_2')\n",
    "solve(x1 ** 2 + x2 ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1/2, 1/4, 1/8, 1/16]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[S('1/2') ** i for i in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x1: -sqrt(-x2**2 + 1)}, {x1: sqrt(-x2**2 + 1)}]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(S('x1 ** 2 + x2 ** 2 - 1'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Отображение выражений"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Выражения `sympy` можно просматривать в различных формах, конвертировать в код на разных языках программирования, впрочем, не всегда успешно."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\frac{1}{x} \\left(\\sin^{2}{\\left (\\alpha \\right )} + 2 \\cos{\\left (\\beta \\right )}\\right)\n",
      "(pow(sin(alpha), 2) + 2*cos(beta))/x\n",
      "(Math.pow(Math.sin(alpha), 2) + 2*Math.cos(beta))/x\n",
      "(Sin[alpha]^2 + 2*Cos[beta])/x\n"
     ]
    }
   ],
   "source": [
    "alpha, beta, x = var('alpha beta x')\n",
    "expr = (sin(alpha)**2 + 2*cos(beta)) / x\n",
    "print latex(expr)\n",
    "print ccode(expr)\n",
    "print jscode(expr)\n",
    "print mathematica_code(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\sigma\\left(n\\right)\n",
      "\n",
      "// Not supported in C:\n",
      "// divisor_sigma\n",
      "divisor_sigma(n)\n",
      "\n",
      "// Not supported in Javascript:\n",
      "// divisor_sigma\n",
      "n = divisor_sigma(n);\n",
      "\n",
      "divisor_sigma[n]\n"
     ]
    }
   ],
   "source": [
    "print latex(divisor_sigma(n))\n",
    "print\n",
    "print ccode(divisor_sigma(n))\n",
    "print\n",
    "print jscode(divisor_sigma(n), n)\n",
    "print\n",
    "print mathematica_code(divisor_sigma(n)) # должно быть DivisorSigma[1,n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(sin(alpha)**2 + 2*cos(beta))/x\n"
     ]
    }
   ],
   "source": [
    "print expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2              \n",
      "sin (α) + 2⋅cos(β)\n",
      "──────────────────\n",
      "        x         \n"
     ]
    }
   ],
   "source": [
    "pprint(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\frac{1}{x} \\left(\\sin^{2}{\\left (\\alpha \\right )} + 2 \\cos{\\left (\\beta \\right )}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import IPython\n",
    "display(IPython.display.Latex('$%s$' % latex(expr)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Оставить один из этих форматов вывода в качестве дефолтного в IPython можно одним из трех вызовов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(sin(alpha)**2 + 2*cos(beta))/x"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_printing(use_latex=False, pretty_print=False)\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   2              \n",
       "sin (α) + 2⋅cos(β)\n",
       "──────────────────\n",
       "        x         "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_printing(use_latex=False, pretty_print=True)\n",
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{x} \\left(\\sin^{2}{\\left (\\alpha \\right )} + 2 \\cos{\\left (\\beta \\right )}\\right)$$"
      ],
      "text/plain": [
       "   2              \n",
       "sin (α) + 2⋅cos(β)\n",
       "──────────────────\n",
       "        x         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\left [ 1, \\quad 2, \\quad 3\\right ]$$"
      ],
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_printing(use_latex='mathjax')\n",
    "display(expr)\n",
    "display([1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Просматривать встроенные типы в виде $\\LaTeX$ может быть неудобно, так что стоит использовать"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{x} \\left(\\sin^{2}{\\left (\\alpha \\right )} + 2 \\cos{\\left (\\beta \\right )}\\right)$$"
      ],
      "text/plain": [
       "   2              \n",
       "sin (α) + 2⋅cos(β)\n",
       "──────────────────\n",
       "        x         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_printing(use_latex='mathjax', print_builtin=False)\n",
    "display(expr)\n",
    "display([1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Стандартные операции над выражениями"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068\n",
      "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068\n"
     ]
    }
   ],
   "source": [
    "print N(pi, 100)\n",
    "print pi.evalf(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'sympy.core.numbers.Float'>\n",
      "<type 'float'>\n"
     ]
    }
   ],
   "source": [
    "print type(N(pi))\n",
    "print type(float(pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.207879576350762\n"
     ]
    }
   ],
   "source": [
    "print N(I ** I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{x + 2}{x + 3}$$"
      ],
      "text/plain": [
       "x + 2\n",
       "─────\n",
       "x + 3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify((x**2 - 4)/((x+3)*(x-2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( x + 3, \\quad 2\\right )$$"
      ],
      "text/plain": [
       "(x + 3, 2)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div(x**2 - 4 + x, x-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{x^{2}}{12} \\left(2 x - 1\\right) \\left(3 x + 4\\right)$$"
      ],
      "text/plain": [
       " 2                    \n",
       "x ⋅(2⋅x - 1)⋅(3⋅x + 4)\n",
       "──────────────────────\n",
       "          12          "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(x**4/2 + 5*x**3/12 - x**2/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2}{x + 2} - \\frac{1}{x + 1}$$"
      ],
      "text/plain": [
       "  2       1  \n",
       "───── - ─────\n",
       "x + 2   x + 1"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apart(x/((x+2)*(x+1)), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2 x + 3}{\\left(x + 1\\right) \\left(x + 2\\right)}$$"
      ],
      "text/plain": [
       "    2⋅x + 3    \n",
       "───────────────\n",
       "(x + 1)⋅(x + 2)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "together(1/(x+2) + 1/(x+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$a^{5} + 5 a^{4} \\sqrt{b} + 10 a^{3} b + 10 a^{2} b^{\\frac{3}{2}} + 5 a b^{2} + b^{\\frac{5}{2}}$$"
      ],
      "text/plain": [
       " 5      4          3         2  3/2        2    5/2\n",
       "a  + 5⋅a ⋅√b + 10⋅a ⋅b + 10⋅a ⋅b    + 5⋅a⋅b  + b   "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S('(a+sqrt(b))**5').expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}$$"
      ],
      "text/plain": [
       " 5      4         3  2       2  3        4    5\n",
       "x  + 5⋅x ⋅y + 10⋅x ⋅y  + 10⋅x ⋅y  + 5⋅x⋅y  + y "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expand((x+y)**5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- 4 \\sin^{3}{\\left (x \\right )} + 3 \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "       3              \n",
       "- 4⋅sin (x) + 3⋅sin(x)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expand_trig(sin(3*x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2 \\tan{\\left (\\frac{3 x}{2} \\right )}}{\\tan^{2}{\\left (\\frac{3 x}{2} \\right )} + 1}$$"
      ],
      "text/plain": [
       "       ⎛3⋅x⎞ \n",
       "  2⋅tan⎜───⎟ \n",
       "       ⎝ 2 ⎠ \n",
       "─────────────\n",
       "   2⎛3⋅x⎞    \n",
       "tan ⎜───⎟ + 1\n",
       "    ⎝ 2 ⎠    "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(3*x).rewrite(tan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left(x + 2\\right)^{5}$$"
      ],
      "text/plain": [
       "       5\n",
       "(x + 2) "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((x+y)**5).subs(y, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$y^{\\frac{5}{2}} + 10 y^{\\frac{3}{2}} + 5 \\sqrt{y} + 5 y^{2} + 10 y + 1$$"
      ],
      "text/plain": [
       " 5/2       3/2             2           \n",
       "y    + 10⋅y    + 5⋅√y + 5⋅y  + 10⋅y + 1"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((x+y)**5).subs([(x, 1), (y, sqrt(y))]).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]\n",
      "[(10, 0), (9, 1), (8, 2), (7, 3), (6, 4), (5, 5), (4, 6), (3, 7), (2, 8), (1, 9), (0, 10)]\n"
     ]
    }
   ],
   "source": [
    "p = expand(Poly('x + y') ** 10)\n",
    "print p.coeffs()\n",
    "print p.monoms()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Выражение можно превратить в функцию"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25\n",
      "t**3/3\n"
     ]
    }
   ],
   "source": [
    "f = Lambda(x, x ** 2)\n",
    "print f(5)\n",
    "print integrate(f(t), t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## solve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция `solve` это причина, по которой CAS вообще нужны"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3]\n"
     ]
    }
   ],
   "source": [
    "print solve(x ** 2 - 5 * x + 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left(-\\infty < x \\wedge x < 2\\right) \\vee \\left(3 < x \\wedge x < \\infty\\right)$$"
      ],
      "text/plain": [
       "(-∞ < x ∧ x < 2) ∨ (3 < x ∧ x < ∞)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(x ** 2 - 5 * x + 6 > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{4}{\\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}} - \\frac{1}{3} \\left(- \\frac{1}{2} - \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}$$"
      ],
      "text/plain": [
       "                                                        ___________________\n",
       "                                       ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409 \n",
       "                                       ⎜- ─ - ────⎟⋅3 ╱  ──── + ────────── \n",
       "                 4                     ⎝  2    2  ⎠ ╲╱    2         2      \n",
       "──────────────────────────────────── - ────────────────────────────────────\n",
       "                 ___________________                    3                  \n",
       "⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409                                        \n",
       "⎜- ─ - ────⎟⋅3 ╱  ──── + ──────────                                        \n",
       "⎝  2    2  ⎠ ╲╱    2         2                                             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$- \\frac{1}{3} \\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}} + \\frac{4}{\\left(- \\frac{1}{2} + \\frac{\\sqrt{3} i}{2}\\right) \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}}$$"
      ],
      "text/plain": [
       "                   ___________________                                       \n",
       "  ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409                                        \n",
       "  ⎜- ─ + ────⎟⋅3 ╱  ──── + ──────────                                        \n",
       "  ⎝  2    2  ⎠ ╲╱    2         2                          4                  \n",
       "- ──────────────────────────────────── + ────────────────────────────────────\n",
       "                   3                                      ___________________\n",
       "                                         ⎛  1   √3⋅ⅈ⎞    ╱ 4887   3⋅√2654409 \n",
       "                                         ⎜- ─ + ────⎟⋅3 ╱  ──── + ────────── \n",
       "                                         ⎝  2    2  ⎠ ╲╱    2         2      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$- \\frac{1}{3} \\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}} + \\frac{4}{\\sqrt[3]{\\frac{4887}{2} + \\frac{3 \\sqrt{2654409}}{2}}}$$"
      ],
      "text/plain": [
       "      ___________________                          \n",
       "     ╱ 4887   3⋅√2654409                           \n",
       "  3 ╱  ──── + ──────────                           \n",
       "  ╲╱    2         2                    4           \n",
       "- ─────────────────────── + ───────────────────────\n",
       "             3                  ___________________\n",
       "                               ╱ 4887   3⋅√2654409 \n",
       "                            3 ╱  ──── + ────────── \n",
       "                            ╲╱    2         2      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "map(display, solve(x**3 + 4*x + 181, x));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\frac{\\pi}{4}, \\quad \\frac{3 \\pi}{4}\\right ]$$"
      ],
      "text/plain": [
       "⎡π  3⋅π⎤\n",
       "⎢─, ───⎥\n",
       "⎣4   4 ⎦"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(sin(x) - S('1/sqrt(2)'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left\\{2 n \\pi + \\frac{3 \\pi}{4}\\; |\\; n \\in \\mathbb{Z}\\right\\} \\cup \\left\\{2 n \\pi + \\frac{\\pi}{4}\\; |\\; n \\in \\mathbb{Z}\\right\\}$$"
      ],
      "text/plain": [
       "⎧        3⋅π        ⎫   ⎧        π        ⎫\n",
       "⎨2⋅n⋅π + ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─ | n ∊ ℤ⎬\n",
       "⎩         4         ⎭   ⎩        4        ⎭"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solveset(sin(x) - S('1/sqrt(2)'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- \\operatorname{LambertW}{\\left (e^{2} \\right )} + 2$$"
      ],
      "text/plain": [
       "          ⎛ 2⎞    \n",
       "- LambertW⎝ℯ ⎠ + 2"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(exp(x) + x - 2)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left \\{ x : - \\frac{1}{2}, \\quad y : \\frac{11}{2}\\right \\}$$"
      ],
      "text/plain": [
       "{x: -1/2, y: 11/2}"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([x + y - 5, y - x - 6], (x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Увы, пока что `sympy` не умеет решать системы неравенств, в отличие от Sage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NotImplementedError",
     "evalue": "\ninequality has more than one symbol of interest",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNotImplementedError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-45-3616e9e3c92f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mx\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m6\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Users\\User\\Anaconda2\\lib\\site-packages\\sympy\\solvers\\solvers.pyc\u001b[0m in \u001b[0;36msolve\u001b[1;34m(f, *symbols, **flags)\u001b[0m\n\u001b[0;32m    846\u001b[0m             \u001b[0mf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mas_expr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    847\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mbool\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mBooleanAtom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mfi\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_Relational\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 848\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mreduce_inequalities\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    849\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    850\u001b[0m         \u001b[1;31m# rewrite hyperbolics in terms of exp\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\User\\Anaconda2\\lib\\site-packages\\sympy\\solvers\\inequalities.pyc\u001b[0m in \u001b[0;36mreduce_inequalities\u001b[1;34m(inequalities, symbols)\u001b[0m\n\u001b[0;32m    699\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    700\u001b[0m     \u001b[1;31m# solve system\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 701\u001b[1;33m     \u001b[0mrv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_reduce_inequalities\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minequalities\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    702\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    703\u001b[0m     \u001b[1;31m# restore original symbols and return\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\User\\Anaconda2\\lib\\site-packages\\sympy\\solvers\\inequalities.pyc\u001b[0m in \u001b[0;36m_reduce_inequalities\u001b[1;34m(inequalities, symbols)\u001b[0m\n\u001b[0;32m    620\u001b[0m                 raise NotImplementedError(filldedent('''\n\u001b[0;32m    621\u001b[0m                     \u001b[0minequality\u001b[0m \u001b[0mhas\u001b[0m \u001b[0mmore\u001b[0m \u001b[0mthan\u001b[0m \u001b[0mone\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 622\u001b[1;33m                     symbol of interest'''))\n\u001b[0m\u001b[0;32m    623\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    624\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mexpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_polynomial\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mgen\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNotImplementedError\u001b[0m: \ninequality has more than one symbol of interest"
     ]
    }
   ],
   "source": [
    "solve([x + y > 5, y - x < 6], (x,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Матан"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предел"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(sin(x) / x, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- \\frac{1}{2}$$"
      ],
      "text/plain": [
       "-1/2"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit((cos(x) - 1) / x ** 2, x, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Дифференцирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "expr = sin(x)**2 + 2*cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$2 \\sin{\\left (x \\right )} \\cos{\\left (x \\right )} - 2 \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "2⋅sin(x)⋅cos(x) - 2⋅sin(x)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.diff(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{x} \\cos{\\left (x \\right )} - \\frac{1}{x^{2}} \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "cos(x)   sin(x)\n",
       "────── - ──────\n",
       "  x         2  \n",
       "           x   "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(sin(x) / x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{x \\left(- 2 x - 2\\right)}{\\left(x^{2} + 2 x + 1\\right)^{2}} + \\frac{1}{x^{2} + 2 x + 1}$$"
      ],
      "text/plain": [
       "  x⋅(-2⋅x - 2)         1      \n",
       "─────────────── + ────────────\n",
       "              2    2          \n",
       "⎛ 2          ⎞    x  + 2⋅x + 1\n",
       "⎝x  + 2⋅x + 1⎠                "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x / (x**2 + 2*x + 1), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\sin{\\left (2 x \\right )}, \\quad 2 \\cos{\\left (2 x \\right )}, \\quad - 4 \\sin{\\left (2 x \\right )}, \\quad - 8 \\cos{\\left (2 x \\right )}, \\quad 16 \\sin{\\left (2 x \\right )}\\right ]$$"
      ],
      "text/plain": [
       "[sin(2⋅x), 2⋅cos(2⋅x), -4⋅sin(2⋅x), -8⋅cos(2⋅x), 16⋅sin(2⋅x)]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[diff(sin(2 * x), x, u) for u in range(5)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Интегрирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{x}{2} - \\frac{1}{2} \\sin{\\left (x \\right )} \\cos{\\left (x \\right )} + 2 \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "x   sin(x)⋅cos(x)           \n",
       "─ - ───────────── + 2⋅sin(x)\n",
       "2         2                 "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr.integrate(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\log{\\left (x + 1 \\right )} + \\frac{1}{x + 1}$$"
      ],
      "text/plain": [
       "               1  \n",
       "log(x + 1) + ─────\n",
       "             x + 1"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(x / (x**2 + 2*x + 1), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\operatorname{Si}{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "Si(x)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(sin(x)/x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\operatorname{erf}{\\left (\\frac{\\sqrt{2} x}{2} \\sqrt{\\frac{1}{\\sigma^{2}}} \\right )}}{2 \\sigma \\sqrt{\\frac{1}{\\sigma^{2}}}}$$"
      ],
      "text/plain": [
       "   ⎛          ____⎞\n",
       "   ⎜         ╱ 1  ⎟\n",
       "   ⎜√2⋅x⋅   ╱  ── ⎟\n",
       "   ⎜       ╱    2 ⎟\n",
       "   ⎜     ╲╱    σ  ⎟\n",
       "erf⎜──────────────⎟\n",
       "   ⎝      2       ⎠\n",
       "───────────────────\n",
       "            ____   \n",
       "           ╱ 1     \n",
       "   2⋅σ⋅   ╱  ──    \n",
       "         ╱    2    \n",
       "       ╲╱    σ     "
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma = var('sigma')\n",
    "integrate(exp(-x**2 / 2 / sigma ** 2) / sqrt(2 * pi) / sigma, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\pi$$"
      ],
      "text/plain": [
       "π"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(sin(x)/x, (x, -oo, oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ряд Тейлора"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x + \\frac{x^{3}}{3} + \\frac{2 x^{5}}{15} + \\frac{17 x^{7}}{315} + \\frac{62 x^{9}}{2835} + \\frac{1382 x^{11}}{155925} + \\frac{21844 x^{13}}{6081075} + \\mathcal{O}\\left(x^{15}\\right)$$"
      ],
      "text/plain": [
       "     3      5       7       9         11          13         \n",
       "    x    2⋅x    17⋅x    62⋅x    1382⋅x     21844⋅x      ⎛ 15⎞\n",
       "x + ── + ──── + ───── + ───── + ──────── + ───────── + O⎝x  ⎠\n",
       "    3     15     315     2835    155925     6081075          "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series(tan(x), x, 0, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ряды Фурье"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- 4 \\cos{\\left (x \\right )} + \\cos{\\left (2 x \\right )} + \\frac{\\pi^{2}}{3} + \\ldots$$"
      ],
      "text/plain": [
       "                        2    \n",
       "                       π     \n",
       "-4⋅cos(x) + cos(2⋅x) + ── + …\n",
       "                       3     "
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ser = fourier_series(x**2, (x, -pi, pi))\n",
    "ser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\sqrt{\\pi} e^{- \\pi^{2} k^{2}}$$"
      ],
      "text/plain": [
       "      2  2\n",
       "    -π ⋅k \n",
       "√π⋅ℯ      "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fourier_transform(exp(-x ** 2), x, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$e^{- x^{2}}$$"
      ],
      "text/plain": [
       "   2\n",
       " -x \n",
       "ℯ   "
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_fourier_transform(sqrt(pi)*exp(-(pi*k)**2), k, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kmzrhSA5vgT0LyWx3M1NXZzK+VzTdY4LMTuUwpNAbEU83F565siMH8kqZ63+9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\nIYSDkEIXQggHIYUuhBAOQgpdCCEcxP8DUYwG0nFTeh0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1abfcf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "serfn = lambdify(x, ser.truncate(3))\n",
    "\n",
    "xx = linspace(-numpy.pi, numpy.pi)\n",
    "matplotlib.pyplot.plot(xx, xx ** 2);\n",
    "matplotlib.pyplot.plot(xx, serfn(xx));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Векторные поля"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.vector import CoordSys3D, express, divergence, curl, gradient, scalar_potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$3 \\mathbf{{y}_{R}} + 2 \\mathbf{{z}_{R}}$$"
      ],
      "text/plain": [
       "3⋅R_y + 2⋅R_z"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$(- \\mathbf{{x}_{R}})\\mathbf{\\hat{k}_{R}}$$"
      ],
      "text/plain": [
       "(-R_x) R_k"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = CoordSys3D('R')\n",
    "vector_field = R.x * R.y * R.i + R.y ** 2 * R.j + R.z ** 2 * R.k\n",
    "display(divergence(vector_field))\n",
    "display(curl(vector_field))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$(\\mathbf{{y}_{R}})\\mathbf{\\hat{i}_{R}} + (\\mathbf{{x}_{R}} + 2 \\mathbf{{y}_{R}})\\mathbf{\\hat{j}_{R}} + (2 \\mathbf{{z}_{R}})\\mathbf{\\hat{k}_{R}}$$"
      ],
      "text/plain": [
       "(R_y) R_i + (R_x + 2⋅R_y) R_j + (2⋅R_z) R_k"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar_field = R.x * R.y + R.y ** 2 + R.z ** 2\n",
    "gr = gradient(scalar_field)\n",
    "gr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "print sympy.vector.is_conservative(gr)\n",
    "print sympy.vector.is_solenoidal(gr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\mathbf{{x}_{R}} \\mathbf{{y}_{R}} + \\mathbf{{y}_{R}}^{2} + \\frac{\\mathbf{{z}_{R}}^{2}}{2}$$"
      ],
      "text/plain": [
       "                    2\n",
       "             2   R_z \n",
       "R_x⋅R_y + R_y  + ────\n",
       "                  2  "
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar_potential(R.y * R.i + (R.x + 2 * R.y) * R.j + R.z * R.k, R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Дифференциальные уравнения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$y{\\left (t \\right )} = C_{2} e^{- t} + \\left(C_{1} + \\frac{t}{2}\\right) e^{t}$$"
      ],
      "text/plain": [
       "           -t   ⎛     t⎞  t\n",
       "y(t) = C₂⋅ℯ   + ⎜C₁ + ─⎟⋅ℯ \n",
       "                ⎝     2⎠   "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(y(t).diff(t, t) - y(t) - exp(t), y(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ x{\\left (t \\right )} = 3 C_{1} e^{t} + 3 C_{2} e^{5 t}, \\quad y{\\left (t \\right )} = - C_{1} e^{t} + 3 C_{2} e^{5 t}\\right ]$$"
      ],
      "text/plain": [
       "⎡             t         5⋅t               t         5⋅t⎤\n",
       "⎣x(t) = 3⋅C₁⋅ℯ  + 3⋅C₂⋅ℯ   , y(t) = - C₁⋅ℯ  + 3⋅C₂⋅ℯ   ⎦"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve((Eq(x(t).diff(t), 2 * x(t) + 3 * y(t)), Eq(y(t).diff(t), 1 * x(t) + 4 * y(t))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Урчпы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$f{\\left (x,y \\right )} = F{\\left (3 x - 2 y \\right )} e^{- \\frac{2 x}{13} - \\frac{3 y}{13}}$$"
      ],
      "text/plain": [
       "                          2⋅x   3⋅y\n",
       "                        - ─── - ───\n",
       "                           13    13\n",
       "f(x, y) = F(3⋅x - 2⋅y)⋅ℯ           "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = Function('f')\n",
    "u = f(x, y)\n",
    "u_x = u.diff(x)\n",
    "u_y = u.diff(y)\n",
    "pdsolve(Eq(1 + (2*(u_x/u)) + (3*(u_y/u))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Линал"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Для вещественных чисел в `sympy` определены функции `sign Min Max`, для комплексных `re im arg conjugate Abs`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Матрицы, транспонирование, арифметика, определитель, след, обратная, характеристический полином, собственные значения, жорданова форма, канонический базис"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2 & 3 & 4\\\\2 & 4 & 6 & 8\\\\3 & 6 & 9 & 12\\\\4 & 8 & 12 & 16\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  2  3   4 ⎤\n",
       "⎢            ⎥\n",
       "⎢2  4  6   8 ⎥\n",
       "⎢            ⎥\n",
       "⎢3  6  9   12⎥\n",
       "⎢            ⎥\n",
       "⎣4  8  12  16⎦"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix(4,4, lambda i,j: (i+1)*(j+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 3\\\\2 & 4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  3⎤\n",
       "⎢    ⎥\n",
       "⎣2  4⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}7 & 10\\\\15 & 22\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡7   10⎤\n",
       "⎢      ⎥\n",
       "⎣15  22⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 4\\\\9 & 16\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  4 ⎤\n",
       "⎢     ⎥\n",
       "⎣9  16⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M = Matrix([[1,2],[3,4]])\n",
    "display(M.T)\n",
    "display(M * M)\n",
    "display(M.multiply_elementwise(M))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{2} & \\frac{1}{2} & 0\\\\\\frac{1}{2} & 0 & \\frac{1}{2}\\\\0 & \\frac{1}{2} & \\frac{1}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1/2  1/2   0 ⎤\n",
       "⎢             ⎥\n",
       "⎢1/2   0   1/2⎥\n",
       "⎢             ⎥\n",
       "⎣ 0   1/2  1/2⎦"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Matrix([[S('1/2'), S('1/2'), S('0')], [S('1/2'), S('0'), S('1/2')], [S('0'), S('1/2'), S('1/2')]])\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( - \\frac{1}{4}, \\quad 1\\right )$$"
      ],
      "text/plain": [
       "(-1/4, 1)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "det(m), trace(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 1 & -1\\\\1 & -1 & 1\\\\-1 & 1 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1   1   -1⎤\n",
       "⎢          ⎥\n",
       "⎢1   -1  1 ⎥\n",
       "⎢          ⎥\n",
       "⎣-1  1   1 ⎦"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 1\\\\1 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  1⎤\n",
       "⎢    ⎥\n",
       "⎣1  0⎦"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM = Matrix([[1,1],[1,0]])\n",
    "FiboM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 1\\\\1 & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0  1 ⎤\n",
       "⎢     ⎥\n",
       "⎣1  -1⎦"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM ** (-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}34 & 21\\\\21 & 13\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡34  21⎤\n",
       "⎢      ⎥\n",
       "⎣21  13⎦"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM ** 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1 1\n"
     ]
    }
   ],
   "source": [
    "print FiboM.det(), FiboM.trace()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\operatorname{PurePoly}{\\left( \\lambda^{2} - \\lambda - 1, \\lambda, domain=\\mathbb{Z} \\right)}$$"
      ],
      "text/plain": [
       "PurePoly(lamda**2 - lamda - 1, lamda, domain='ZZ')"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM.charpoly(var('lamda'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{-sqrt(5)/2 + 1/2: 1, 1/2 + sqrt(5)/2: 1}"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM.eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1/2 + sqrt(5)/2, 1, [Matrix([\n",
       "   [-1/(-sqrt(5)/2 + 1/2)],\n",
       "   [                    1]])]), (-sqrt(5)/2 + 1/2, 1, [Matrix([\n",
       "   [-1/(1/2 + sqrt(5)/2)],\n",
       "   [                   1]])])]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FiboM.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{2} + \\frac{\\sqrt{5}}{2} & 0\\\\0 & - \\frac{\\sqrt{5}}{2} + \\frac{1}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1   √5          ⎤\n",
       "⎢─ + ──     0    ⎥\n",
       "⎢2   2           ⎥\n",
       "⎢                ⎥\n",
       "⎢          √5   1⎥\n",
       "⎢  0     - ── + ─⎥\n",
       "⎣          2    2⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{1}{2} + \\frac{\\sqrt{5}}{2} & - \\frac{\\sqrt{5}}{2} + \\frac{1}{2}\\\\1 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1   √5    √5   1⎤\n",
       "⎢─ + ──  - ── + ─⎥\n",
       "⎢2   2     2    2⎥\n",
       "⎢                ⎥\n",
       "⎣  1        1    ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kb, jf = simplify(FiboM.jordan_form())\n",
    "display(jf)\n",
    "display(kb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 1\\\\1 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  1⎤\n",
       "⎢    ⎥\n",
       "⎣1  0⎦"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(kb * jf * kb.inv())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{2^{- k}}{5} \\sqrt{5} \\left(\\left(1 + \\sqrt{5}\\right)^{k} - \\left(- \\sqrt{5} + 1\\right)^{k}\\right)$$"
      ],
      "text/plain": [
       " -k    ⎛        k            k⎞\n",
       "2  ⋅√5⋅⎝(1 + √5)  - (-√5 + 1) ⎠\n",
       "───────────────────────────────\n",
       "               5               "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(kb * (jf ** k) * kb.inv())[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([y1*z2 - y2*z1, -x1*z2 + x2*z1, x1*y2 - x2*y1], dtype=object)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1, y1, z1, x2, y2, z2 = var('x1 y1 z1 x2 y2 z2')\n",
    "cross([x1,y1,z1], [x2,y2,z2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\sqrt{\\left|{a_{0}}\\right|^{2} + \\left|{a_{1}}\\right|^{2} + \\left|{a_{2}}\\right|^{2}}$$"
      ],
      "text/plain": [
       "   _______________________\n",
       "  ╱     2       2       2 \n",
       "╲╱  │a₀│  + │a₁│  + │a₂│  "
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix(symarray('a', (3,))).norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\sqrt{\\left|{x_{1}}\\right|^{2} + \\left|{y_{1}}\\right|^{2} + \\left|{z_{1}}\\right|^{2}}$$"
      ],
      "text/plain": [
       "   _______________________\n",
       "  ╱     2       2       2 \n",
       "╲╱  │x₁│  + │y₁│  + │z₁│  "
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix([x1,y1,z1]).norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$X_{1, 0} Y_{0, 2} + X_{1, 1} Y_{1, 2} + X_{1, 2} Y_{2, 2}$$"
      ],
      "text/plain": [
       "X₁₀⋅Y₀₂ + X₁₁⋅Y₁₂ + X₁₂⋅Y₂₂"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = MatrixSymbol('X', 3, 3)\n",
    "Y = MatrixSymbol('Y', 3, 3)\n",
    "(X * Y)[1, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Конкретная математика"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Суммирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{n^{3}}{3} + \\frac{n^{2}}{2} + \\frac{n}{6}$$"
      ],
      "text/plain": [
       " 3    2    \n",
       "n    n    n\n",
       "── + ── + ─\n",
       "3    2    6"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summation(k ** 2, (k, 1, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{cases} \\frac{1}{- x + 1} & \\text{for}\\: \\left|{x}\\right| < 1 \\\\\\sum_{k=0}^{\\infty} x^{k} & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "⎧   1                 \n",
       "⎪ ──────   for │x│ < 1\n",
       "⎪ -x + 1              \n",
       "⎪                     \n",
       "⎪  ∞                  \n",
       "⎪ ___                 \n",
       "⎨ ╲                   \n",
       "⎪  ╲    k             \n",
       "⎪  ╱   x    otherwise \n",
       "⎪ ╱                   \n",
       "⎪ ‾‾‾                 \n",
       "⎪k = 0                \n",
       "⎩                     "
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summation(x ** k, (k, 0, oo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Не все суммы поддаются движку sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\sum_{\\substack{1 \\leq x \\leq A\\\\1 \\leq y \\leq B}} \\left|{x - y}\\right|$$"
      ],
      "text/plain": [
       "  B     A          \n",
       " ___   ___         \n",
       " ╲     ╲           \n",
       "  ╲     ╲   │x - y│\n",
       "  ╱     ╱          \n",
       " ╱     ╱           \n",
       " ‾‾‾   ‾‾‾         \n",
       "y = 1 x = 1        "
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A, B = var('A B', positive=True, integer=True)\n",
    "summation(Abs(x - y), (x, 1, A), (y, 1, B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Решение рекуррентности (вывод формулы Бине)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{5}}{5} \\left(\\frac{1}{2} + \\frac{\\sqrt{5}}{2}\\right)^{n} - \\frac{\\sqrt{5}}{5} \\left(- \\frac{\\sqrt{5}}{2} + \\frac{1}{2}\\right)^{n}$$"
      ],
      "text/plain": [
       "           n                n\n",
       "   ⎛1   √5⎞       ⎛  √5   1⎞ \n",
       "√5⋅⎜─ + ──⎟    √5⋅⎜- ── + ─⎟ \n",
       "   ⎝2   2 ⎠       ⎝  2    2⎠ \n",
       "──────────── - ──────────────\n",
       "     5               5       "
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsolve(y(n+2)-y(n+1)-y(n), y(n), {y(0): 0, y(1): 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Цепная дробь"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ 0, \\quad 2, \\quad 1, \\quad 2\\right ]$$"
      ],
      "text/plain": [
       "[0, 2, 1, 2]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(continued_fraction_iterator(Rational(3, 8)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{3}{8} = 0 + \\frac{1}{2 + \\frac{1}{1 + \\frac{1}{2}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ 3, \\quad \\frac{22}{7}, \\quad \\frac{333}{106}, \\quad \\frac{355}{113}, \\quad \\frac{103993}{33102}, \\quad \\frac{104348}{33215}, \\quad \\frac{208341}{66317}, \\quad \\frac{312689}{99532}, \\quad \\frac{833719}{265381}, \\quad \\frac{1146408}{364913}\\right ]$$"
      ],
      "text/plain": [
       "⎡         333  355  103993  104348  208341  312689  833719  1146408⎤\n",
       "⎢3, 22/7, ───, ───, ──────, ──────, ──────, ──────, ──────, ───────⎥\n",
       "⎣         106  113  33102   33215   66317   99532   265381   364913⎦"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(itertools.islice(continued_fraction_convergents(continued_fraction_iterator(pi)), 0, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(q & r) | (r & ~p)\n",
      "[{p: False, r: True, q: True}, {p: False, r: True, q: False}, {p: True, r: True, q: True}]\n"
     ]
    }
   ],
   "source": [
    "p, q, r = var('p q r')\n",
    "k2 = to_dnf((p >> q) & r)\n",
    "print k2\n",
    "print list(satisfiable(k2, all_models=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Теория чисел"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 1, 1, 0, 1]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits(13, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "168\n",
      "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]\n"
     ]
    }
   ],
   "source": [
    "print primepi(1000)\n",
    "print list(primerange(1, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "541\n",
      "True\n",
      "1000000007\n"
     ]
    }
   ],
   "source": [
    "print prime(100)\n",
    "print isprime(2 ** 127 - 1)\n",
    "print nextprime(1000000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2048953: 1, 3: 3, 1532117: 1}\n"
     ]
    }
   ],
   "source": [
    "print factorint(84759364534527)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 298 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{193707721: 1, 761838257287L: 1}"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "factorint(2 ** 67 - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Профессор Коул к 1903 году потратил на это «все воскресенья в течение трех лет»."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 (-5, 18, 4) 4\n"
     ]
    }
   ],
   "source": [
    "print gcd(244, 68), gcdex(244, 68), -5 * 244 + 18 * 68"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "220 284\n"
     ]
    }
   ],
   "source": [
    "print sum(divisors(284)[:-1]), sum(divisors(220)[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 28\n",
      "[1, 2, 3, 4, 6, 12]\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print divisor_count(12), divisor_sigma(12)\n",
    "print divisors(12)\n",
    "print totient(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Китайская теорема"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(639985, 912285)\n",
      "49 76 65 912285\n"
     ]
    }
   ],
   "source": [
    "from sympy.ntheory.modular import crt\n",
    "print crt([99, 97, 95], [49, 76, 65])\n",
    "print 639985 % 99, 639985 % 97, 639985 % 95, 99 * 97 * 95"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проверка обращения Мёбиуса $G(n) = \\sum_{d|n} F(d) \\Leftrightarrow F(n) = \\sum_{d|n} \\mu(d) G(\\frac{n}{d})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{array}{cccccccccccccccccccc}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & -1 & -1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & -1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & -1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & -1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\-1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\0 & 1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\end{array}\\right]$$"
      ],
      "text/plain": [
       "⎡1   0   0   0   0   0   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎤\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  1   0   0   0   0   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   1   0   0   0   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   -1  0   1   0   0   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   1   0   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢1   -1  -1  0   0   1   0   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   0   0   1   0   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   0   0   -1  0   0   0   1   0   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   0   -1  0   0   0   0   0   1   0   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢1   -1  0   0   -1  0   0   0   0   1   0  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   0   0   0   0   0   0   1  0  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   1   0   -1  0   -1  0   0   0   0   0  1  0  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   0   0   0   0   0   0   0  0  1  0  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢1   -1  0   0   0   0   -1  0   0   0   0  0  0  1  0  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢1   0   -1  0   -1  0   0   0   0   0   0  0  0  0  1  0  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   0   0   0   0   0   0   -1  0   0   0  0  0  0  0  1  0  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   0   0   0   0   0   0   0  0  0  0  0  0  1  0  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢0   0   1   0   0   -1  0   0   -1  0   0  0  0  0  0  0  0  1  0  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎢-1  0   0   0   0   0   0   0   0   0   0  0  0  0  0  0  0  0  1  0⎥\n",
       "⎢                                                                    ⎥\n",
       "⎣0   1   0   -1  0   0   0   0   0   -1  0  0  0  0  0  0  0  0  0  1⎦"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j_divides_i = Matrix(fromfunction(lambda i,j: where((i+1) % (j+1) == 0, 1, 0), (20, 20)))\n",
    "inv_j_divides_i = j_divides_i.inv()\n",
    "inv_j_divides_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mo = [[int(mobius((i + 1) / (j + 1))) if (i + 1) % (j + 1) == 0 else 0 for j in range(20)] for i in range(20)]\n",
    "Matrix(mo) == inv_j_divides_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left\\{\\left ( 3 t_{0} - 5, \\quad - 2 t_{0} + 5\\right )\\right\\}$$"
      ],
      "text/plain": [
       "set([(3⋅t₀ - 5, -2⋅t₀ + 5)])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diophantine(2*x + 3*y - 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(2, 1), (5, 1)}"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diophantine(x**2 - 4*x*y + 8*y**2 - 3*x + 7*y - 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7348655773126303755629132256340558924373328617090197171706667985290133761074361570679971146341442904888591341841287254965947859225905297999477796015919477067007270662755471894303543848700521290783297130156224163076157960251257693490144231567905196959807936667239827765383424517553637410148296202159548497638625891934215562498854803999087988746111891278525153998140276439504335166247691283287982071011L, 13368210114309858110490408377394654362940185298164216827948999032605862717288140668701831983256694918479543797066513434530829632365715334435258980969002310473634736670934466710096296555376044613951842365465867556366705263409477296458008936007006429171666426262499427073084651776609218709214727849066557411083083942753965341146350258607478649802267967135142551807477661688074367083808666023441349174043384L)\n",
      "Wall time: 20.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "a = 30741415699351712223222592216948664852787225938672761888182663459401433940293299920472821794247792558438137266179003170954852009167996\n",
    "b = 5493768938913164268735898548345740984062864198582915532893452862692397723477349340213609803716310002722689784104429402408034399680657214203589114662020419403506380275921075865806868813167390548527002018378296772011002830464813992537445273710373363121247809539380530302504021135339366740636410963119289644130568327436166142653219502858785723203265988729334812946807271940413511096470449043813939925759131485224930805050595388961884769573807597931344321170355620526497042548348665782820474459300583235597864519400688289208986957832681459966933968204573143630154199268824952951642924625108969237666308633980889261559554117298872683137210357137988177192697560524562835477922442010038014370796719316949327823897102946508453004777622812045656957796013010907193455701053005247975317200627083352360327185314875288693488759973999715297338413318230762734322668133288476183336301663326505090120348966948964517423252467946014780068274519231694498484297\n",
    "print max(list(diophantine(x**2 + a*(y**2) - b)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Перестановки"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.combinatorics import Permutation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1 3) (0 1 2 3)\n"
     ]
    }
   ],
   "source": [
    "p = Permutation([0, 3, 2, 1])\n",
    "q = Permutation([1, 2, 3, 0])\n",
    "print p, q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "[0, 1, 3, 4, 2]\n"
     ]
    }
   ],
   "source": [
    "print Permutation([0,1,2,4,3]).rank()\n",
    "print Permutation.unrank_lex(5, 3).array_form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 {1: 2, 2: 1} {4: 1}\n"
     ]
    }
   ],
   "source": [
    "print p.cycles, p.cycle_structure, q.cycle_structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 False 1\n"
     ]
    }
   ],
   "source": [
    "print p.inversions(), p.is_even, p.parity()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3] [0, 1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "print p.support(), q.support()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 4\n"
     ]
    }
   ],
   "source": [
    "print p.order(), q.order()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 0, 5, 1, 2, 3]"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(Permutation.from_sequence('eafbcd'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 [1, 0, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "print p.rank(), p.next_lex().array_form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 0, 3, 2] [3, 2, 1, 0]\n"
     ]
    }
   ],
   "source": [
    "print list(p * q), list(q * p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 3), (0, 2), (0, 1)]"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.transpositions()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 0, 1] [2, 3, 0, 1] [[0, 2], [1, 3]] [2, 3, 0, 1]\n"
     ]
    }
   ],
   "source": [
    "pp = Permutation(0, 2)(1, 3)\n",
    "print pp(range(4)), pp.list(), pp.cyclic_form, pp.array_form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 2, 1, 3, 4]"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Permutation([[1,2]], size=5).list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 2]] [[0], [1, 2], [3], [4]]\n"
     ]
    }
   ],
   "source": [
    "print Permutation([[1,2]], size=5).cyclic_form, Permutation([[1,2]], size=5).full_cyclic_form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Permutation(0, 4) == Permutation([4, 1, 2, 3, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.length()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 3, 2, 1]"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[i ^ p ** 3 for i in range(4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([3, 2, 1, 0], [1, 0, 3, 2])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q(p(range(4))), (p * q)(range(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Группы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Permutation(4), Permutation(0, 4)(1, 3), Permutation(0, 1, 2, 3, 4), Permutation(1, 4)(2, 3), Permutation(0, 2, 4, 1, 3), Permutation(0, 1)(2, 4), Permutation(0, 3, 1, 4, 2), Permutation(0, 2)(3, 4), Permutation(0, 4, 3, 2, 1), Permutation(4)(0, 3)(1, 2)]\n"
     ]
    }
   ],
   "source": [
    "print list(sympy.combinatorics.dihedral(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symmetric 120\n",
      "cyclic 5\n",
      "alternating 60\n",
      "dihedral 10\n"
     ]
    }
   ],
   "source": [
    "for gr in 'symmetric cyclic alternating dihedral'.split():\n",
    "    print gr, len(list(getattr(sympy.combinatorics, gr)(5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мультипликативная группа, порядок элемента в $Z_n^*$, степень по модулю, корень по вычету, дискретный логарифм"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "376"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pow(2, 100, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$2^{504} \\equiv 1 \\pmod{1009} \\\\\n",
    "2^{503} \\equiv 2^{-1} \\equiv 505 \\pmod{1009}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 504 505 505\n"
     ]
    }
   ],
   "source": [
    "print pow(2, 504, 1009), n_order(2, 1009), mod_inverse(2, 1009), pow(2, 504-1, 1009)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 503\n"
     ]
    }
   ],
   "source": [
    "print nthroot_mod(505, 503, 1009), discrete_log(1009, 2, 505)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Комбинаторика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]\n"
     ]
    }
   ],
   "source": [
    "print [fibonacci(k) for k in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000\n",
      "34332795984163804765195977526776142032365783805375784983543400282685180793327632432791396429850988990237345920155783984828001486412574060553756854137069878601\n"
     ]
    }
   ],
   "source": [
    "print factorial(100)\n",
    "print subfactorial(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]\n"
     ]
    }
   ],
   "source": [
    "print [binomial(10, k) for k in range(11)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Число Каталана — число правильных скобочных последовательностей длины $2n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]\n"
     ]
    }
   ],
   "source": [
    "print [catalan(k) for k in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Числа Стирлинга 1-го рода $\\left[ n \\atop k \\right]$ — коэффициенты при $x^k$ разложения $x^{\\underline{n}} = x (x-1) \\ldots (x-n+1)$.\n",
    "\n",
    "Числа Стирлинга 2-го рода  $\\left\\{ {n \\atop k} \\right\\}$ — коэффициенты при $x^{\\underline{k}}$ разложения $x^n$. Заодно число разбиений множества размера $n$ на $k$ непустых подмножеств."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{10} - 45 x^{9} + 870 x^{8} - 9450 x^{7} + 63273 x^{6} - 269325 x^{5} + 723680 x^{4} - 1172700 x^{3} + 1026576 x^{2} - 362880 x$$"
      ],
      "text/plain": [
       " 10       9        8         7          6           5           4            3\n",
       "x   - 45⋅x  + 870⋅x  - 9450⋅x  + 63273⋅x  - 269325⋅x  + 723680⋅x  - 1172700⋅x \n",
       "\n",
       "            2           \n",
       " + 1026576⋅x  - 362880⋅x"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = var('k')\n",
    "expand(product(x-k, (k, 0, 9)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 362880, 1026576, 1172700, 723680, 269325, 63273, 9450, 870, 45, 1]\n"
     ]
    }
   ],
   "source": [
    "print [sympy.combinatorial.numbers.stirling(10, k, kind=1) for k in range(11)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1]\n"
     ]
    }
   ],
   "source": [
    "print [sympy.combinatorial.numbers.stirling(10, k, kind=2) for k in range(11)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Число Белла — число разбиений множества размера $n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147]\n"
     ]
    }
   ],
   "source": [
    "print [sympy.combinatorial.numbers.bell(k) for k in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Числа Бернулли известны прежде всего из-за их роли в формуле Фаульхабера https://en.wikipedia.org/wiki/Faulhaber%27s_formula о закрытой форме суммы $\\sum_{k=1}^n k^p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, -1/2, 1/6, 0, -1/30, 0, 1/42, 0, -1/30, 0]\n"
     ]
    }
   ],
   "source": [
    "print [bernoulli(k) for k in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Число разбиений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "204226"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npartitions(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1, 1, 1, 1]\n",
      "[2, 1, 1, 1, 1]\n",
      "[2, 2, 1, 1]\n",
      "[2, 2, 2]\n",
      "[3, 1, 1, 1]\n",
      "[3, 2, 1]\n",
      "[3, 3]\n",
      "[4, 1, 1]\n",
      "[4, 2]\n",
      "[5, 1]\n",
      "[6]\n"
     ]
    }
   ],
   "source": [
    "import sympy.combinatorics\n",
    "pa = sympy.combinatorics.partitions.IntegerPartition([1] * 6)\n",
    "while True:\n",
    "    print pa.partition\n",
    "    if len(pa.partition) == 1: break\n",
    "    pa = pa.next_lex()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['0000', '0001', '0011', '0010', '0110', '0111', '0101', '0100', '1100', '1101', '1111', '1110', '1010', '1011', '1001', '1000']\n"
     ]
    }
   ],
   "source": [
    "print list(sympy.combinatorics.subsets.GrayCode(4).generate_gray())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 []\n",
      "1 ['d']\n",
      "2 ['c', 'd']\n",
      "3 ['c']\n",
      "4 ['b', 'c']\n",
      "5 ['b', 'c', 'd']\n",
      "6 ['b', 'd']\n",
      "7 ['b']\n",
      "8 ['a', 'b']\n",
      "9 ['a', 'b', 'd']\n",
      "10 ['a', 'b', 'c', 'd']\n",
      "11 ['a', 'b', 'c']\n",
      "12 ['a', 'c']\n",
      "13 ['a', 'c', 'd']\n",
      "14 ['a', 'd']\n",
      "15 ['a']\n"
     ]
    }
   ],
   "source": [
    "ss = sympy.combinatorics.Subset([], 'abcd')\n",
    "while True:\n",
    "    print ss.rank_gray, ss.subset\n",
    "    ss = ss.next_gray()\n",
    "    if ss.subset == []: break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 []\n",
      "1 ['d']\n",
      "2 ['c']\n",
      "3 ['c', 'd']\n",
      "4 ['b']\n",
      "5 ['b', 'd']\n",
      "6 ['b', 'c']\n",
      "7 ['b', 'c', 'd']\n",
      "8 ['a']\n",
      "9 ['a', 'd']\n",
      "10 ['a', 'c']\n",
      "11 ['a', 'c', 'd']\n",
      "12 ['a', 'b']\n",
      "13 ['a', 'b', 'd']\n",
      "14 ['a', 'b', 'c']\n",
      "15 ['a', 'b', 'c', 'd']\n"
     ]
    }
   ],
   "source": [
    "ss = sympy.combinatorics.Subset([], 'abcd')\n",
    "while True:\n",
    "    print ss.rank_binary, ss.subset\n",
    "    ss = ss.next_binary()\n",
    "    if ss.subset == []:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'c'), ('b', 'd'), ('c', 'd')]"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(sympy.combinatorics.subsets.ksubsets('abcd', 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Геометрия"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line2D(Point2D(1, 1), Point2D(2, 7/5))\n"
     ]
    }
   ],
   "source": [
    "print Line(Point(1,1), slope=S('2/5'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point2D(1/2, 1/2)\n"
     ]
    }
   ],
   "source": [
    "print Segment(Point(0,0), Point(1,1)).midpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n",
      "\n",
      "Triangle(Point2D(0, 0), Point2D(3, 0), Point2D(0, 4))\n",
      "6 12\n",
      "{Point2D(3, 0): acos(3/5), Point2D(0, 0): pi/2, Point2D(0, 4): acos(4/5)}\n",
      "\n",
      "Медианы\n",
      "{Point2D(3, 0): Segment2D(Point2D(0, 2), Point2D(3, 0)), Point2D(0, 0): Segment2D(Point2D(0, 0), Point2D(3/2, 2)), Point2D(0, 4): Segment2D(Point2D(0, 4), Point2D(3/2, 0))}\n",
      "True\n",
      "Point2D(1, 4/3)\n",
      "\n",
      "Высоты\n",
      "{Point2D(3, 0): Segment2D(Point2D(0, 0), Point2D(3, 0)), Point2D(0, 0): Segment2D(Point2D(0, 0), Point2D(48/25, 36/25)), Point2D(0, 4): Segment2D(Point2D(0, 0), Point2D(0, 4))}\n",
      "True\n",
      "[Point2D(0, 0)]\n",
      "\n",
      "Биссектрисы\n",
      "{Point2D(3, 0): Segment2D(Point2D(0, 3/2), Point2D(3, 0)), Point2D(0, 0): Segment2D(Point2D(0, 0), Point2D(12/7, 12/7)), Point2D(0, 4): Segment2D(Point2D(0, 4), Point2D(4/3, 0))}\n",
      "True\n",
      "[Point2D(1, 1)]\n",
      "Вписанная окружность Point2D(1, 1) 1 Circle(Point2D(1, 1), 1)\n",
      "\n",
      "{Point2D(3/2, 2)}\n",
      "Описанная окружность Point2D(3/2, 2) 5/2 Circle(Point2D(3/2, 2), 5/2)\n",
      "\n",
      "(0, 0, 3, 4)\n"
     ]
    }
   ],
   "source": [
    "A = Point(0,0)\n",
    "B = Point(3,0)\n",
    "C = Point(0,4)\n",
    "print Point.is_collinear(A, B, C)\n",
    "print Line(A, B).is_perpendicular(Line(A, C))\n",
    "print\n",
    "\n",
    "t = Triangle(A, B, C)\n",
    "print t\n",
    "print t.area, t.perimeter\n",
    "print t.angles\n",
    "print\n",
    "\n",
    "print 'Медианы'\n",
    "print t.medians\n",
    "print Line.are_concurrent(t.medians.values())\n",
    "print t.centroid # intersection(t.medians.values()[0], t.medians.values()[1])\n",
    "print\n",
    "\n",
    "print 'Высоты'\n",
    "print t.altitudes\n",
    "print Line.are_concurrent(t.altitudes.values())\n",
    "print intersection(t.altitudes.values()[0], t.altitudes.values()[1])\n",
    "print\n",
    "\n",
    "print 'Биссектрисы'\n",
    "print t.bisectors()\n",
    "print Line.are_concurrent(t.bisectors().values())\n",
    "print intersection(t.bisectors().values()[0], t.bisectors().values()[1])\n",
    "print 'Вписанная окружность', t.incenter, t.inradius, t.incircle\n",
    "print\n",
    "\n",
    "AB = Segment(A, B)\n",
    "AC = Segment(A, C)\n",
    "print AB.perpendicular_line(AB.midpoint).intersect(AC.perpendicular_line(AC.midpoint))\n",
    "print 'Описанная окружность', t.circumcenter, t.circumradius, t.circumcircle\n",
    "print\n",
    "\n",
    "print t.bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\operatorname{acos}{\\left (- \\frac{3}{5} \\right )}$$"
      ],
      "text/plain": [
       "acos(-3/5)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Line(A, B).angle_between(Line(B, C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point2D(-3*t + 3, 4*t)\n"
     ]
    }
   ],
   "source": [
    "print Line(B, C).arbitrary_point()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$4$$"
      ],
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Line(A, B).distance(Point(C))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$5$$"
      ],
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Segment(B, C).length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\sqrt{2}$$"
      ],
      "text/plain": [
       "√2"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ray(A, B).distance(Point(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{12}{5}$$"
      ],
      "text/plain": [
       "12/5"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Segment(B, C).distance(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line2D(Point2D(5, 5), Point2D(8, 1))\n",
      "Line2D(Point2D(5, 5), Point2D(9, 8))\n",
      "Segment2D(Point2D(33/25, 56/25), Point2D(5, 5))\n"
     ]
    }
   ],
   "source": [
    "print Segment(B, C).parallel_line(Point(5,5))\n",
    "print Segment(B, C).perpendicular_line(Point(5,5))\n",
    "print Segment(B, C).perpendicular_segment(Point(5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point2D(33/25, 56/25)\n"
     ]
    }
   ],
   "source": [
    "print Line(B, C).projection(Point(5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Segment2D(Point2D(6/5, 12/5), Point2D(33/25, 56/25))\n"
     ]
    }
   ],
   "source": [
    "print Line(B, C).projection(Segment(Point(5,5), Point(6,6)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line2D(Point2D(3/2, 0), Point2D(3/2, 1))\n"
     ]
    }
   ],
   "source": [
    "print AB.perpendicular_bisector()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle(Point2D(0, 0), Point2D(3/2, 3*sqrt(3)/2), Point2D(-2*sqrt(3), 2))\n"
     ]
    }
   ],
   "source": [
    "print t.rotate(pi/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4*x + 3*y - 12 (4, 3, -12)\n",
      "{Point2D(3, 0)}\n"
     ]
    }
   ],
   "source": [
    "L = Line(C, B)\n",
    "L2 = Line(A, B)\n",
    "print L.equation(), L.coefficients\n",
    "print L.intersect(L2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Задача с тестового тура ПВГ: В равнобедренном треугольнике известно основание $b=126$ и медиана $m_a = \\frac{\\sqrt{35997}}{2}$, проведенная к боковой стороне. Найдите расстояние между центрами вписанной и описанной окружностей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h = 16\n",
      "3965/32\n"
     ]
    }
   ],
   "source": [
    "h = var('h')\n",
    "A = Point(0, 0)\n",
    "B = Point(63, h)\n",
    "C = Point(126, 0)\n",
    "T = Triangle(A, B, C)\n",
    "hh = max(solve(T.medians[A].length - sqrt(35977) / 2))\n",
    "print 'h =', hh\n",
    "B = Point(63, hh)\n",
    "T = Triangle(A, B, C)\n",
    "print Segment(T.incircle.center, T.circumcircle.center).length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left(x - 5\\right)^{2} + \\left(\\frac{y}{2} - \\frac{5}{2}\\right)^{2} - 1$$"
      ],
      "text/plain": [
       "                  2    \n",
       "       2   ⎛y   5⎞     \n",
       "(x - 5)  + ⎜─ - ─⎟  - 1\n",
       "           ⎝2   2⎠     "
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el = Ellipse(Point(5,5), 1, 2)\n",
    "el.equation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ellipse(Point2D(-5, 5), 2, 1)\n"
     ]
    }
   ],
   "source": [
    "print el.rotate(pi/2, Point(0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Point2D(-32*sqrt(5)/89 + 430/89, -40*sqrt(5)/89 + 493/89), Point2D(32*sqrt(5)/89 + 430/89, 40*sqrt(5)/89 + 493/89)]\n"
     ]
    }
   ],
   "source": [
    "print intersection(el, Line(Point(2,2), Point(6,7)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\emptyset$$"
      ],
      "text/plain": [
       "∅"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el.intersect(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- \\frac{2 \\sqrt{5}}{5} + 5$$"
      ],
      "text/plain": [
       "  2⋅√5    \n",
       "- ──── + 5\n",
       "   5      "
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(el.intersect(Line(Point(0,0), Point(5,5))))[0].x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$2 \\pi$$"
      ],
      "text/plain": [
       "2⋅π"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el.area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$8 \\int_{0}^{1} \\sqrt{\\frac{- \\frac{3 x^{2}}{4} + 1}{- x^{2} + 1}}\\, dx$$"
      ],
      "text/plain": [
       "  1                        \n",
       "  ⌠                        \n",
       "  ⎮         ____________   \n",
       "  ⎮        ╱      2        \n",
       "  ⎮       ╱    3⋅x         \n",
       "  ⎮      ╱   - ──── + 1    \n",
       "  ⎮     ╱       4          \n",
       "8⋅⎮    ╱     ──────────  dx\n",
       "  ⎮   ╱          2         \n",
       "  ⎮ ╲╱        - x  + 1     \n",
       "  ⌡                        \n",
       "  0                        "
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el.circumference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{3}}{2}$$"
      ],
      "text/plain": [
       "√3\n",
       "──\n",
       "2 "
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "el.eccentricity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Point2D(5, -sqrt(3) + 5), Point2D(5, sqrt(3) + 5))\n"
     ]
    }
   ],
   "source": [
    "print el.foci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Line2D(Point2D(5, 3), Point2D(3, 3))]\n"
     ]
    }
   ],
   "source": [
    "print el.tangent_lines(Point(5,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle(Point2D(0, 0), Point2D(3, 0), Point2D(0, 4))\n"
     ]
    }
   ],
   "source": [
    "print t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$2 \\sqrt{3}$$"
      ],
      "text/plain": [
       "2⋅√3"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Plane(Point(1,2,3), normal_vector=(1,1,1)).distance(Point(0,0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- 3 x + 5 y - 6 z + 5$$"
      ],
      "text/plain": [
       "-3⋅x + 5⋅y - 6⋅z + 5"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi1 = Plane(Point(1,2,2), Point(2,5,4), Point(3,2,1))\n",
    "pi1.equation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- \\operatorname{asin}{\\left (\\frac{11 \\sqrt{35}}{210} \\right )}$$"
      ],
      "text/plain": [
       "     ⎛11⋅√35⎞\n",
       "-asin⎜──────⎟\n",
       "     ⎝ 210  ⎠"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi1.angle_between(Line(Point(1,2,3), Point(5,1,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\operatorname{acos}{\\left (\\frac{73 \\sqrt{14630}}{14630} \\right )}$$"
      ],
      "text/plain": [
       "    ⎛73⋅√14630⎞\n",
       "acos⎜─────────⎟\n",
       "    ⎝  14630  ⎠"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi2 = Plane(Point(1,2,2), Point(2,5,4), Point(3,2,1))\n",
    "pi3 = Plane(Point(1,2,3), Point(5,1,2), Point(-1,2,0))\n",
    "pi2.angle_between(pi3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "73 (-3, 5, -6) (3, 14, -2)\n"
     ]
    }
   ],
   "source": [
    "print dot(pi2.normal_vector, pi3.normal_vector), pi2.normal_vector, pi3.normal_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point3D(3/14, -5/14, 3/7)\n"
     ]
    }
   ],
   "source": [
    "print pi2.projection(Point(0,0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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Lqhz+3f1G2NxaLmEjUpPlgsfltDPuC+ILhCx5ykDf6ATNZ4xb3+9dMsKmalUO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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b5112b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(0)\n",
    "xy = numpy.random.rand(12, 2)\n",
    "points = [Point(x,y) for x,y in xy]\n",
    "\n",
    "poly = convex_hull(*points)\n",
    "print len(poly.vertices)\n",
    "\n",
    "xx = list([float(pt.x) for pt in poly.vertices])\n",
    "yy = list([float(pt.y) for pt in poly.vertices])\n",
    "\n",
    "matplotlib.pyplot.gca().set_aspect('equal')\n",
    "matplotlib.pyplot.scatter([pt.x for pt in points], [pt.y for pt in points]);\n",
    "matplotlib.pyplot.plot(xx + xx[0:1], yy + yy[0:1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Графики"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Библиотека `sympy` умеет рисовать графики, используя библиотеку `matplotlib`, немного оборачивая ее для автоматического выбора диапазона, адаптивного числа точек, перенесения осей в 0, а заодно и затрудняя использование возможностей `matplotlib`, для которых обертки нет. Манки-патч в функции `plot_plus` немного решает эту проблему для самых вопиющих вещей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_plus(plot_fn, *args, **kwargs):\n",
    "    parse_args = {'set_aspect', 'figsize'}\n",
    "    if set(kwargs.keys()) & parse_args:\n",
    "        kw = {k:v for k,v in kwargs.items() if k not in parse_args}\n",
    "        kw['show'] = False\n",
    "        p = plot_fn(*args, **kw)\n",
    "        p._backend = p.backend(p)\n",
    "        if 'figsize' in kwargs:\n",
    "            p._backend.fig.set_size_inches(kwargs['figsize'])\n",
    "        if 'set_aspect' in kwargs:\n",
    "            p._backend.ax.set_aspect(kwargs['set_aspect'])\n",
    "        p._backend.show()\n",
    "        return p\n",
    "    else:\n",
    "        return plot_fn(*args, **kwargs)\n",
    "\n",
    "import functools\n",
    "for fn in 'plot plot_parametric plot3d plot3d_parametric_line plot3d_parametric_surface plot_implicit'.split():\n",
    "    globals()[fn] = functools.partial(plot_plus, getattr(sympy.plotting, fn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, y, t, u = var('x y t u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dqqo8tHQvtQ2yPJ+wbpV1eh5YkkJ2cRVJt/eQ69k1IOVuIYK9XFlwZyxH8s/x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\nj14AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ad76748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x**2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VYgrHgF2dkd+BOppcFT9GhVxQZ+Rn2YHJyCIlSIuPRoOZ24yZgIk7X6YqgaaO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\nXQghVEjCXQghVEjCXQghVOhvYQLnYeSk9+EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d0a87f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sin(x));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ja8/bbIrSBiP5bYs8FdY0c6C0keMVTR33N8YlhbKrsI6Bkf4kheoIaJs402qx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\nhKYVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d378748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, x**2, x**3, (x, -2, 2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PDYX24rc/tiEiIjKlw+UXce5COxYmc+9WuhyLK92QaTED0M/diYu0iIjI5DZqKuHhrMCM\nuIGio5CFYXGlG+LiqMC8JBV2nahFQ2uX6DhERGSj2rr02H7sPGbFB8Hd2VF0HLIwLK50wzJSQ6Az\nyNicrxUdhYiIbNSnx86jvdvAI17pqlhc6YZFBHpBPagfPjhcCVnmIi0iIup7G/O1GNzfA+pB/URH\nIQvE4ko3JT01FKUNbfi6rFF0FCIisjHnLrQhr6wRC5JVkCTu3UpXYnGlmzIrLghero7IyuMiLSIi\n6lub87VwkIB5SUrRUchCsbjSTXFzVmBOohKfHq9BU3u36DhERGQjjEYZm49UYWxkAIJ83ETHIQvF\n4ko3LT01BN16I7YcrRIdhYiIbMTBsxdQ1dTBk7LoB7G40k2LCfZBvMoHWXlcpEVERH1jY34lvF0d\nccfwAaKjkAVjcaVeSU8JxenaFhytbBIdhYiIrFxzhw45x2uQlhgMVyeF6DhkwVhcqVfSEoPh7qzg\nIi0iIrpl24vOo0tv5BGvdF0srtQrni6O+FF8MLYVnkdLp050HCIismIb8ysxdIAn4lU+oqOQhWNx\npV5LTw1Bh86ArYXVoqMQEZGVOlPXgqMVTViYHMK9W+m6WFyp1xJDfDFsoBey8ipFRyEiIiu1MV8L\nhYOEOSO4dytdH4sr9ZokSUhPCcGxqmYcr2oWHYeIiKyM3mDER0eqMDEqAAFeLqLjkBVgcaVbMneE\nCi6ODsg6zEVaZB2WLFmCwMBAxMbGXvX63r174ePjg8TERCQmJuKZZ57puZaTk4OoqChERETg+eef\nN1dkIpu1v6Qe9S1dWMBFWXSDWFzplvi4O2FmXBCyj1ajvVsvOg7RdS1evBg5OTk/+Jpx48ahoKAA\nBQUF+N3vfgcAMBgMWL58OXbs2IETJ05gw4YNOHHihDkiE9msTfla+Hk4Y9KwQNFRyEqwuNItS08J\nQUuXHtuLzouOQnRd48ePh5+f303fl5eXh4iICISHh8PZ2Rnp6enIzs42QUIi+3CxrRufn6jDnEQl\nnB1ZR+jG8HcK3bLUwX4ID/DABu7pSjbi4MGDiI+Px4wZM1BcXAwAqKqqQkjIf36cqVKpUFXFY4+J\neiu7oArdBiMWqnnEK904Fle6Zd8v0jpS0YRvaltExyG6JUlJSaioqEBRURFWrFiBOXPm9Op9MjMz\noVaroVarUV9f38cpiazfxnwtYpXeiA7yFh2FrAiLK/WJ+UkqOCkkjrqS1fP29oanpycAYObMmdDp\ndGhoaIBSqURl5X+2ftNqtVAqr719z9KlS6HRaKDRaBAQEGDy3ETW5ET1JRRXX8KCJI620s1hcaU+\n4e/pgqnDB2LL0Sp06gyi4xD1Wk1NDWRZBvDtvFaj0Qh/f3+kpKSgpKQEZWVl6O7uRlZWFtLS0gSn\nJbJOG/Mr4axwwOxE7t1KN8dRdACyHempIdh+7Dw+K67hH0ZksTIyMrB37140NDRApVJh1apV0Om+\nPbZ42bJl2LRpE15//XU4OjrCzc0NWVlZkCQJjo6OWL16NaZNmwaDwYAlS5YgJiZG8Kchsj7deiOy\nC6oxZXgg+nk4i45DVkb6fmShj/Tpm5F1MRplTPjrHih93ZC1dJToOEQWQ61WQ6PRiI5BZBE+K67B\ng+vz8fbiFEzkNlj2rFfn+3KqAPUZBwcJd6lDcKi0EWUNbaLjEBGRBVr3VTlSB/thXGR/0VHICrG4\nUp9aqA6BwkHiSVpERHSFUzWXcODMBUyMCoSjghWEbh5/11CfGuDtiolRgdicr0W33ig6DhERWZB3\nDpTD1ckBGak84pV6h8WV+lxGaggaWrvxxcla0VGIiMhCNLZ1Y8vRKsxLUsHXnYuyqHdYXKnPTRga\ngIHerthwuPL6LyYiIruwIa8CXXoj7hsdJjoKWTEWV+pzjgoHLFKr8GVJPSob20XHISIiwXQGI9Z9\nVY5xkf0ROcBLdByyYiyuZBKLUr6dv7RRw1FXIiJ79+mx86i91IUlYwaLjkJWjsWVTELVzx3jIgPw\noUYLvYGLtIiI7NlbB8oR3t8DE4by+GO6NSyuZDIZKSGoudSJfd/Ui45CRESCHKm4iMLKJiweEwYH\nh17tOU/Ug8WVTGZy9AD093TGhjxOFyAisldv5ZbBy9UR85NUoqOQDWBxJZNxdnTA/GQV9pyuQ+2l\nTtFxiIjIzM43d2DH8Rqkp4TAw8VRdByyASyuZFLpKaEwGGUu0iIiskPrvjoHWZZx76gw0VHIRrC4\nkkkN7u+BkeF++EBTCaNRFh2HiIjMpKPbgA15FZg6fCBC/NxFxyEbweJKJpeRGorKxg4cONsgOgoR\nEZnJlqNVaGrXYclYboFFfYfFlUxuWsxA+Lo7IYuLtIiI7IIsy3j7QBligr2REtZPdByyISyuZHKu\nTgrMHaHEzhM1uNDaJToOERGZWO6ZBpTUtWLJmMGQJG6BRX2HxZXMIiM1FDqDjM1HtKKjEBGRib19\noBz9PV1wZ0KQ6ChkY1hcySyGDvBCUqgvsg5XQpa5SIuIyFaV1rdi96k63H1bKFwcFaLjkI1hcSWz\nSU8NRWl9G/LKGkVHISIiE3n3YDmcFQ64e2So6Chkg1hcyWzujA+Cl4sjsg5zkRYRkS1q7tBhY74W\ndyYEIdDLVXQcskEsrmQ27s6OSEsMxqfHzqO5XSc6DhER9bGNmkq0dxuwZAy3wCLTYHEls8pIDUWX\n3ogtR7lIi4jIlhiMMt45WI7UMD/EKn1ExyEbxeJKZhWr9EGs0puLtIiIbMyuE7XQXuzAkrFhoqOQ\nDWNxJbNLTwnFqZoWFFQ2iY5CRER95K0DZVD6uuGO4QNFRyEbxuJKZjc7MRhuTgqepEVEZCOKq5uR\nV9aIxaPDoHDggQNkOiyuZHZerk64Mz4I24qq0dqlFx2HiIhu0dsHyuHurMCilBDRUcjGsbiSEOmp\noWjvNmBrQbXoKEREdAvqW7qwtaAaC5JV8HFzEh2HbByLKwmRFOqLoQM8kXW4QnQUIiK6Be9/XYFu\ngxE/HR0mOgrZARZXEkKSJKSnhKJI24zi6mbRcYiIqBe69AasP3QOE6MCMCTAU3QcsgMsriTMvCQl\nnB0duEiLiMhKbS86j4bWLtzHAwfITFhcSRhfd2fMiB2Ijwuq0NFtEB2HiIhugizLeOtAGSICPTEu\nsr/oOGQnWFxJqPSUULR06rH92HnRUYiI6CZozl3E8apLuG9MGCSJW2CRebC4klAjw/0wuL8HsvK4\nSIvMY8mSJQgMDERsbOxVr7/33nuIj49HXFwcRo8ejcLCwp5rYWFhiIuLQ2JiItRqtbkiE1mkt3LL\n4OPmhHkjVKKjkB1hcSWhJEnCXSkh0Jy7iJLaFtFxyA4sXrwYOTk517w+ePBg7Nu3D8eOHcPTTz+N\npUuXXnZ9z549KCgogEajMXVUIoulvdiOz4prkJEaCjdnheg4ZEdYXEm4+UkqODpIyDrMRVpkeuPH\nj4efn981r48ePRr9+vUDAIwcORJardZc0YisxrqvzkGSJNw7apDoKGRnWFxJuAAvF9wxfAA+OqJF\nl56LtMhyrF27FjNmzOh5LEkSpkyZguTkZGRmZgpMRiROW5ceWXkVmB47EMG+bqLjkJ1xFB2ACPj2\nJK0dx2vwWXEt0hKCRcchwp49e7B27Vrk5ub2PJebmwulUom6ujrccccdGDZsGMaPH3/V+zMzM3vK\nbX19vVkyE5nDR0e0uNSpxxJugUUCcMSVLMK4iP4I7++OvafrREchQlFRER544AFkZ2fD39+/53ml\nUgkACAwMxNy5c5GXl3fN91i6dCk0Gg00Gg0CAgJMnpnIHIxGGW8fLEeCygdJob6i45AdYnEli+Dg\nIOGeUWH46EgVNOWNouOQHauoqMC8efOwfv16DB06tOf5trY2tLS09Hy9c+fOa+5MQGSr9pXUo7S+\nDUvGDuYWWCQEpwqQxbgrJQSrd5/By1+UYP39t4mOQzYqIyMDe/fuRUNDA1QqFVatWgWdTgcAWLZs\nGZ555hlcuHABDz30EADA0dERGo0GtbW1mDt3LgBAr9fjxz/+MaZPny7scxCJ8PaBcgR6uWBGbJDo\nKGSnJFmW+/L9+vTNyP68se8snttxCh89NBpJof1ExyHqE2q1mttnkdU7U9eCKX/fj0enDsXDkyJF\nxyHr16she04VIIvyk5GD4OfhjFe+KBEdhYiI/svbB8rh7OiAjNRQ0VHIjrG4kkXxcHHEA+MGY+/p\nehRWNomOQ0REAJrau7H5iBZzE5Xw93QRHYfsGIsrWZx7R4XB192Jo65ERBYi63AlOnVG3Dc2THQU\nsnMsrmRxPF0c8cDYwfjiVB2OVzWLjkNEZNf0BiPWHSzHqHB/DBvoLToO2TkWV7JI944Og7erI17m\nqCsRkVCfFdeiurkTS8bywAESj8WVLJK3qxPuHxuOXSdqUVzNUVciIlHeOlCGUD93TBoWKDoKEYsr\nWa7FY8Lg5eqIf35xRnQUIiK7VFBxEfnnLmLx6DAoHHjgAInH4koWy8fNCfeNGYyc4hqcqrkkOg4R\nkd15Y38pxkb0x0K1SnQUIgAsrmThlowJg6cLR12JiMztdE0LdhyvwYhQX3i5OomOQwSAxZUsnK+7\nMxaPDsOnx8/jm9oW0XGIiOzGP3eXwMNZgSVjuCiLLAeLK1m8+8cOhruTAv/czVFXIiJzOFPXgu3H\nzuPe0WHo5+EsOg5RDxZXsnj9PJxx7+gwfFJUjTN1raLjEBHZvNW7z8DVUYEHuAUWWRgWV7IKD4wd\nDFdHBVbv5r6uRESmVFrfiq2F1bhn1CAe70oWh8WVrIK/pwvuHTUIWwurUVrPUVciIlN5dc9ZOCkc\n8LNx4aKjEF2BxZWsxgPjwuHs6IDVezjXlYjIFM5daMPHBVW4+7ZBCPDiaCtZHhZXshoBXi74yW2D\nkF1QjfKGNtFxiIhszmt7zkLhIOHBCRxtJcvE4kpWZemEcDg6SHiVo65ERH2qsrEdm49okZESggHe\nrqLjEF0ViytZlUAvV/z4tlB8dLQKlY3touMQEdmM1/edhYMkYdntQ0RHIbomFleyOssmDIGCo65E\nRH2muqkDGzWVWKhWIcjHTXQcomticSWrM8DbFRkpIdiUr4X2IkddiYhu1Zp9ZwEAD02MEJyE6Iex\nuJJVWnb7EDhIEl7be1Z0FCIiq1bT3ImsvEosSFZB6cvRVrJsLK5klYJ83LAoRYWNmkpUN3WIjkNE\nZLXe2H8WBlnGQ7dztJUsH4srWa2ff/eH7OscdSUi6pW6lk68/3UF5o1QIsTPXXQcouticSWrpfR1\nw4LkEHxwuBI1zZ2i4xARWZ1/7S+FzmDEcs5tJSvB4kpW7aHbh8Aoyz0LC4iI6MY0tHbh34cqMCdR\nibD+HqLjEN0QFleyaiF+7pifpML7eRWou8RRVyKiG/Xml2Xo1BuwfBJHW8l6sLiS1Xto4hAYjDLe\n2F8qOgoRkVVobOvGuq/K8aP4YAwJ8BQdh+iGsbiS1Rvk74E5iUq89/U51Ld0iY5DRGTx3sotQ4fO\ngIc52kpWhsWVbMLDkyLQrTfiX19y1JWI6Ic0t+vwzsFyzIwNwtABXqLjEN0UFleyCYP7e2B2ohLr\nvzqHhlaOuhIRXctbB8rQ2qXnaCtZJRZXshkPT4pAp96AN78sEx2FiMgiXerU4a0DZZgWMwDRQd6i\n4xDdNBZXshlDAjzxo/hgrPuqHI1t3aLjEBFZnHcOlKOlU48VkyJFRyHqFRZXsikrJkWgQ2fA2lzO\ndaWrW7JkCQIDAxEbG3vV67IsY+XKlYiIiEB8fDyOHDnScy0nJwdRUVGIiIjA888/b67IRH2ipVOH\ntbllmBIdiFilj+g4RL3C4ko2JXKAF2bGBeHdg+fQ1M5RV7rS4sWLkZOTc83rO3bsQElJCUpKSpCZ\nmYmf//znAACDwYDly5djx44dOHHiBDZs2IATJ06YKzbRLVv31Tk0d+g42kpWjcWVbM7KSZFo7dLj\nrVzOdaUrjR8/Hn5+fte8np2djXvvvReSJGHkyJFoamrC+fPnkZeXh4iICISHh8PZ2Rnp6enIzs42\nY3Ki3mvr0uPNL0txe1QAEkJ8Rcch6jUWV7I5UQO9MCN2IN4+UI7mdp3oOGRlqqqqEBIS0vNYpVKh\nqqrqms8Ezi44AAAgAElEQVQTWYN/HzqHi+0cbSXrx+JKNmnFpEi0dOnx9kGOupIYmZmZUKvVUKvV\nqK+vFx2H7FhHtwGZ+0sxLrI/kgf1Ex2H6JawuJJNGh7sjanDB+Ct3DJc6uSoK904pVKJysrKnsda\nrRZKpfKaz1/L0qVLodFooNFoEBAQYNLMRD/kva/P4UJbN1ZO5mgrWT8WV7JZKydH4lKnHu8eKBcd\nhaxIWloa1q1bB1mWcejQIfj4+CAoKAgpKSkoKSlBWVkZuru7kZWVhbS0NNFxiX5Qp86AN/aXYlS4\nP1LCrj23m8haOIoOQGQqsUofTIkOxJu5ZVg8Jgxerk6iI5EFyMjIwN69e9HQ0ACVSoVVq1ZBp/t2\nVH7ZsmWYOXMmPv30U0RERMDd3R1vv/02AMDR0RGrV6/GtGnTYDAYsGTJEsTExIj8KETXlZVXgfqW\nLrySPkJ0FKI+Icmy3Jfv16dvRnSrirRNSFt9AI9Ni8LyiTzekMRQq9XQaDSiY5Cd6dQZMOHFPRjk\n54EPHhwJSZJERyL6b736DcmpAmTT4lW+mBgVgDe/LEVbl150HCIis9mYr0XtpS6snBzJ0ko2g8WV\nbN7KyZG42K7D+kPnREchIjKLbr0Rr+85g6RQX4yJ8Bcdh6jPsLiSzRsR2g/jhwbgX/tL0d7NUVci\nsn2bj2hR3dzJ0VayOSyuZBcemRyJC23deO9QhegoREQmpTMY8eqeM0hQ+WDCUG7FRraFxZXsQvKg\nfhgb0R9v7D+Ljm6D6DhERCaz5WgVtBc7ONpKNonFlezGI1Mi0dDajffzOOpKRLZJ/91oa0ywNyYN\nCxQdh6jPsbiS3UgJ88OocH+s2XcWnTqOuhKR7dlaWI1zF9o52ko2i8WV7MojUyJR39KFLI66EpGN\nMRhlrN59BsMGeuGO6AGi4xCZBIsr2ZWR4f5IHeyH1znqSkQ25pOiapQ2tGHl5Eg4OHC0lWwTiyvZ\nnV9MjkTtpS5s1FSKjkJE1CeMRhn/3H0GkYGemB4zUHQcIpNhcSW7M2qIP9SD+uG1vWfRpeeoKxFZ\nv0+Pn8eZulas4Ggr2TgWV7I7kiThkSmRON/ciU35WtFxiIhuic5gxJv7yzArLgiz4oJExyEyKRZX\nsktjI/pjRKgvXttzFt16o+g4RES9lnW4EgXaJswZoYSCo61k41hcyS5JkoRHJkeiqqkDHx3hqCsR\nWaeWTh3+sesbjAz3w5Ro7ttKto/FlezWhKEBSFD5YPWeM9AZOOpKRNbn9b1ncaGtG0/NHM59W8ku\nsLiS3fp+rqv2Yge2HK0SHYeI6KZUNXVgbW4Z5o1QIk7lIzoOkVmwuJJdmxgViDilD17dcwZ6jroS\nkRX562enAQCPTosSnITIfFhcya5JkoSVkyNx7kI7sguqRcchIrohRdombDlahQfGDUawr5voOERm\nw+JKdm9KdCCGB3ljNUddicgKyLKMP20/if6ezlg2YYjoOERmxeJKdu/7UdeyhjZ8UnRedBwioh+0\n60Qtvi5rxC+mDIWXq5PoOERmxeJKBGDq8AEYNtALr+wugcEoi45DRHRVOoMRz+84hYhAT6SnhIiO\nQ2R2LK5EABwcvh11La1vw/ZjHHUlIsv0/tcVKG1ow5Mzh8FRwb/Cyf7wdz3Rd6bHDMTUmAHIyqvg\naVpEZHGaO3T4x+ffYPQQf0yM4mEDZJ9YXIm+4+AgISM1FAfPXsC7B8tFxyEiusxre8+gqUOHp2ZF\n87ABslssrkT/ZWJUICZGBeCVL0pQ39IlOg4REQCgsrEdb+eWY94IFWKCedgA2S8WV6L/8ds7h6ND\nZ8Dfdp4WHYWICADw4men4eAAPDptqOgoREKxuBL9jyEBnrhvTBg+0FTimLZZdBwisnMFlU3YWliN\nn40LR5APDxsg+8biSnQVKyZHws/dGau2FUOWuT0WEYnx7WEDJ9Df0wUP8rABIhZXoqvxdnXCY9Oi\noDl3Edt4KAERCfJZcQ0Ol1/Er+4YCk8XR9FxiIRjcSW6hoXqEMQEe+O5T0+io9sgOg4R2Zlu/beH\nDQwd4IlFapXoOEQWgcWV6BoUDhL+kBaD882dWLPvrOg4RGRn/n3oHMovtOOJmdE8bIDoO/xOIPoB\nKWF++FFCMNbsOwvtxXbRcYjITjS36/DK7hKMi+yP24cGiI5DZDFYXImu4zczhkGSgOd2nBIdhfpI\nTk4OoqKiEBERgeeff/6K6y+++CISExORmJiI2NhYKBQKNDY2AgDCwsIQFxeHxMREqNVqc0cnO7F6\nTwmaO3R4YgYPGyD6byyuRNeh9HXDsglDsL3oPL4uvSA6Dt0ig8GA5cuXY8eOHThx4gQ2bNiAEydO\nXPaaxx57DAUFBSgoKMBzzz2HCRMmwM/Pr+f6nj17UFBQAI1GY+74ZAcqLrTj3YPnsDBZheHB3qLj\nEFkUFleiG/Dg+CFQ+rph1bYTMBi5PZY1y8vLQ0REBMLDw+Hs7Iz09HRkZ2df8/UbNmxARkaGGROS\nvXvhs1NQOEj49dQo0VGILA6LK9ENcHNW4ImZw3Di/CV8qKkUHYduQVVVFUJCQnoeq1QqVFVVXfW1\n7e3tyMnJwfz583uekyQJU6ZMQXJyMjIzM6/5/8nMzIRarYZarUZ9fX3ffQCyafnnLmJ70XksHR+O\nAd6uouMQWRwWV6IbNCsuCKlhfnjxs9No7tCJjkNmsG3bNowZM+ayaQK5ubkoKCjAjh078Oqrr2L/\n/v1XvXfp0qXQaDTQaDQICODiGrq+7w8bCPBywdLx4aLjEFkkFleiGyRJEn73o+G42N6NV74oER2H\nekmpVKKy8j+j5lqtFkql8qqvzcrKumKawPevDQwMxNy5c5GXl2e6sGRXPj1WgyMVTXh06lB48LAB\noqticSW6CbFKH6SnhODdg+U4U9cqOg71QkpKCkpKSlBWVobu7m5kZWUhLS3titc1Nzdj3759mD17\nds9zbW1taGlp6fl6586diI2NNVt2sl1degNeyDmFYQO9sCA55Po3ENkpFleim/To1Ci4OSvw7PYT\n138xWRxHR0esXr0a06ZNQ3R0NBYtWoSYmBisWbMGa9as6Xndli1bMHXqVHh4ePQ8V1tbi7FjxyIh\nIQGpqamYNWsWpk+fLuJjkI1Z/9U5VDS248mZ0VA4cPsromuRZLlPV0hzuTXZhTe/LMWz20/ircVq\nTBo2QHQcsnBqtZpbZ9E11bV04r638hCr9MULC+JFxyEyl179C40jrkS9cO+oMIQHeOCPn5xEt94o\nOg4RWbFnPzmJkro2PDiBC7KIrofFlagXnB0d8PSdw1HW0IZ3D5aLjkNEVurLknpsLazGQxOHIDzA\nU3QcIovH4krUSxOjAjFpWCBe+aIE9S1douMQkZXp1Bnw9MfHMbi/B5ZNGCI6DpFVYHElugW/nRWN\nDp0Bf9t5WnQUIrIyr+09i/IL7Xh2TixcnRSi4xBZBRZXolsQHuCJ+8aE4QNNJY5pm0XHISIrcba+\nFWv2nsWcxGCMiegvOg6R1WBxJbpFKyZHwt/DGau2FaOPd+kgIhskyzJ+u+U4XJ0c8NSs4aLjEFkV\nFleiW+Tt6oTHpkVBc+4ithWdFx2HiCzclqNV+Kr0Av5vxjAEeLmIjkNkVVhcifrAguQQxCq98dfP\nTqGtUy86DhFZqKb2bvxp+0mMCPVFRkqo6DhEVofFlagPKBwk/HF2LAxG4K+7uFCLiK7uhZxTaOrQ\n4c9z4+DAE7KIbhqLK1EfGRHaD5OjA/HOwXLkn2sUHYeILEz+uUZsyKvE/WMHIzrIW3QcIqvE4krU\nhx6fPgzBPm54bFMROnUG0XGIyELoDEY8+dFxBPu44pHJkaLjEFktFleiPuTp4ojn58ehtL4NL39R\nIjoOEVmIt3LLcLq2BX9Ii4GHi6PoOERWi8WVqI+NiwzAIrUKmftLubcrEUF7sR3/+LwEdwwfgKkx\nA0XHIbJqLK5EJvDUrOHw93DGY5sK0a03io5DRILIsozfZxdDkoA/pMWIjkNk9VhciUzAx80Jf5ob\nh1M1LXh971nRcYhIkM+Ka/HFqTr8cspQKH3dRMchsnosrkQmcsfwAUhLCMbqPSU4XdMiOg4RmVlr\nlx6rthVj2EAvLB4TJjoOkU1gcSUyoT+kxcDb1QmPbyqE3sApA0T25KVd36DmUif+PC8OTgr+dUvU\nF/idRGRCfh7O+ENaDAq1zVibWyY6DhGZyfGqZrx9oAwZqaFICu0nOg6RzWBxJTKxO+ODMHX4APx9\n1zcorW8VHYeITMxglPHUx8fh5+GM/5s2THQcIpvC4kpkYpIk4dk5sXBxdMD/bS6C0SiLjkREJvR+\nXgUKK5vw21nD4ePuJDoOkU1hcSUyg0BvVzx953AcLr+I9YfOiY5DRCZS09yJTwqrMSbCH7MTg0XH\nIbI5LK5EZrIgWYXxQwPwQs4pVDa2i45DRH1MlmU8vrkIhZVN+PPcOEiSJDoSkc1hcSUyE0mS8Ny8\nOEgAnvjoGGSZUwaIbMn7eRXY/009npwVjUH+HqLjENkkFlciM1L6uuE3M6ORe6YBH2oqRcchoj5y\n7kIb/rT9JMZE+OMntw0SHYfIZrG4EpnZ3amhuG2wH57dfhI1zZ2i4xDRLTIYZTy2sQgKScKLCxLg\n4MApAkSmwuJKZGYODhJemB8PncGIp7ZwygCRtXsrtwx55Y34fVoMgnmsK5FJsbgSCRDW3wOPTo3C\nF6fqsLWwWnQcIuqlktoWvLjzNKZED8D8JKXoOEQ2j8WVSJD7xgxGYogv/rC1GA2tXaLjENFN0hmM\n+NWHhfBwVny78JK7CBCZHIsrkSAKBwkvLohHW5cBv99aLDoOEd2kV/ecwbGqZvxpbhwCvFxExyGy\nCyyuRAJFDvDCyskR2F50HjnHa0THIaIbdEzbjNW7z2B2YjBmxgWJjkNkN1hciQR7cMIQDA/yxtPZ\nx9HU3i06DhFdR6fOgF99WAB/T2c8kxYrOg6RXWFxJRLMSeGAvyyIR2NbN/74yUnRcexCTk4OoqKi\nEBERgeeff/6K63v37oWPjw8SExORmJiIZ5555obvJdv30q5vUFLXiufnx8PH3Ul0HCK74ig6ABEB\nsUof/HzCEKzecwZ3JgRhYlSg6Eg2y2AwYPny5di1axdUKhVSUlKQlpaG4cOHX/a6cePG4ZNPPunV\nvWS7Dpc3IvPLUmSkhvL7lEgAjrgSWYgVkyMQEeiJpz46hpZOneg4NisvLw8REREIDw+Hs7Mz0tPT\nkZ2dbfJ7yfq1denx6w8LoernhqdmRYuOQ2SXWFyJLISLowJ/WRCPUH93rNpWzIMJTKSqqgohISE9\nj1UqFaqqqq543cGDBxEfH48ZM2aguLj4pu4l2/TcjpOovNiOvy5IgKcLf2BJJAKLK5EFSQrth5Hh\n/tiUX4VN+VrRcexWUlISKioqUFRUhBUrVmDOnDk3/R6ZmZlQq9VQq9Wor683QUoyp/3f1OPfhypw\n/5jBuC3cX3QcIrvF4kpkYVZMisSocH/8LrsYJbUtouPYHKVSicrKyp7HWq0WSuXlJx55e3vD09MT\nADBz5kzodDo0NDTc0L3fW7p0KTQaDTQaDQICAkzwSchcGtu68duPjyMi0BOPTosSHYfIrrG4ElkY\nhYOEl9MT4e6swPL3j6Cj2yA6kk1JSUlBSUkJysrK0N3djaysLKSlpV32mpqamp6pGnl5eTAajfD3\n97+he8m2yLKMxzcVQeEA/H1RAlydFKIjEdk1FlciCxTo7YqX7kpESV0rVm3jqVp9ydHREatXr8a0\nadMQHR2NRYsWISYmBmvWrMGaNWsAAJs2bUJsbCwSEhKwcuVKZGVlQZKka95LtutfX5bi85O1uGdk\nGOJVvqLjENk9qY8XgHA1CVEfevGzU3h1z1m8nJ6I2YlX/5E0WT61Wg2NRiM6Bt2kw+WNSM88hKnD\nB+C1u5MgSZLoSES2pFffUBxxJbJgv5wyFOpB/fDkR8dQWt8qOg6R3bjQ2oWH3z+CkH5ueGFBPEsr\nkYVgcSWyYI4KB7ySMQJOjg54+P2j6NRxviuRqRmMMn7xQQEutuvw6t1J8Hbl6VhEloLFlcjCBfu6\n4e+LEnDi/CX8aTuPhCUytX/uLsGXJQ1YlRaDmGAf0XGI6L+wuBJZgUnDBuBn4wZj/aFz+PTYedFx\niGxWbkkDXv6iBPNGKJGeEnL9G4jIrFhciazEY9OGISHEF/+3qQgVF9pFxyGyOTXNnXgk6ygiAjzx\n7NxYzmslskAsrkRWwtnRAaszRgAS8PCGI+jWG0VHIrIZeoMRKzYcQYfOgNd/kgR3Zx7pSmSJWFyJ\nrEiInzteXBCPIm0zXsg5JToOkc14cedpHC6/iOfmxSEi0Et0HCK6BhZXIiszPTYIPx01CGtzy7Dr\nRK3oOERWb9eJWryxrxR33xbK/ZKJLByLK5EVenJWNGKV3nh0YyGqmjpExyGyWpWN7fj1hwWIVXrj\n6TuHi45DRNfB4kpkhVwcFVidkQSDUcbKDUehM3C+K9HN6tIbsPz9I5ABvPbjZLg6KURHIqLrYHEl\nslJh/T3w53lxyD93Ea98XiI6DpHV+fP2kyjSNuOvCxMQ6u8uOg4R3QAumySyYmkJwThb14rM/aUY\nEuiJOSM4P4/oRmwrrMa7X53Dz8YNxrSYgaLjENEN4ogrkZVbPjEC8SofPL6pCPnnGkXHIbJ4Z+tb\n8ZvNRUge1A+PTx8mOg4R3QQWVyIr5+zogDU/SUawryuWrstHZSMPJyC6lo5uA5a/dwQuTgqs/vEI\nOCn41yCRNeF3LJEN6OfhjLWLU6AzGHH/u4fR0qkTHYnI4siyjL/knELlxXb8465EBPm4iY5ERDeJ\nxZXIRgwJ8MTrP0lGaX0bVmw4Cj13GiC6zD8+L8HbB8vxyylDMX5ogOg4RNQLLK5ENmRMRH/8cU4s\n9p6ux7PbT4qOQ2QxNuVr8fIXJViQrML9YweLjkNEvcRdBYhsTEZqKM7WteLN3DIMCfDAPaPCREci\nEurAmQb8ZnMRxkT4489z4yBJkuhIRNRLLK5ENuiJmdEoa2jDH7adwCB/D/5YlOzWN7UtWPbvfIQH\neOC1u5Ph7MgfNBJZM34HE9kghYOElzNGIDLQE8vfO4KS2hbRkYjMrq6lE/e9fRiuTgq8tTgFPm5O\noiMR0S1icSWyUZ4ujnjzp2q4OCmw5N3DuNDaJToSkdm0d+tx/zsaNLZ1462fpkDVjydjEdkCFlci\nG6bq545/3ZuM2ktdWPbvfHTpDaIjEZmcwShj5YYCFFc3458ZIxCn8hEdiYj6CIsrkY0bEdoPf1uY\ngMPlF/HER8cgy7LoSEQm9cdPTuDzk7X4Q1oMpgwfIDoOEfUhLs4isgM/SghGaX0bXvr8G0QEeuKh\n2yNERyIyibdyy/DOwXI8MHYw7uWOGkQ2h8WVyE6snByBs/Wt+EvOaYT398D02CDRkYj61GfFNfjj\n9hOYHjMQT86MFh2HiEyAUwWI7IQkSfjLgngkhfriFx8U4Ji2WXQkoj5TUNmER7KOIkHli5fuSoSD\nA/dqJbJFLK5EdsTVSYE37lHD38MF97+bB21ju+hIRLessrEdD7x7GAFeLnjzp2q4OStERyIiE2Fx\nJbIzAV4ueGtxCiIHeOPet/PQwG2yyIo1t+uw+O08dOuNeHtxKvp7uoiOREQmxOJKZIeiBnrhkcmR\nqG7qwD1r89DcrhMdieimdekNePDfGlQ0tiPzXjUiAj1FRyIiE2NxJbJTqYP98MY9apypa8F97+Sh\nrUsvOhLRDdMbjPh9djFKalvx4oIEjAz3Fx2JiMyAxZXIjk0YGoB/ZoxAQWUTlq7XoFPHAwrI8ukN\nRvzqw0JkHa7EI5MjMGeEUnQkIjITFlciOzc9NggvLkjAgTMX8PD7R6EzGEVHIromg1HGoxsLsbWw\nGr+ZMQz3jh4sOhIRmRGLKxFhfrIKf5wdg89P1uLRjYUwGG37dK2cnBxERUUhIiICzz///BXX33vv\nPcTHxyMuLg6jR49GYWFhz7WwsDDExcUhMTERarXanLHtnsEo47GNhfi4oBqPT4/CsglDREciIjPj\nAQREBAC4Z1QYWrsMeCHnFNydFfjz3DhIku3thWkwGLB8+XLs2rULKpUKKSkpSEtLw/Dhw3teM3jw\nYOzbtw/9+vXDjh07sHTpUnz99dc91/fs2YP+/fuLiG+3DEYZj28qwkdHq/Do1KE8/Y3ITrG4ElGP\nn98+BK1dOry65ywCvVzwiylDba685uXlISIiAuHh4QCA9PR0ZGdnX1ZcR48e3fP1yJEjodVqzZ6T\n/sNolPGbzUXYfESLX90xFA9PihQdiYgE4VQBIrrMo1Oj8Ks7IvHP3Wfwh63FMNrYtIGqqiqEhIT0\nPFapVKiqqrrm69euXYsZM2b0PJYkCVOmTEFycjIyMzNNmpW+La1PfHQMG/O1+MWUSKyczNJKZM84\n4kpEl5EkCSsmRaKlU49/fVmGLr0Rf5obB4UdHqG5Z88erF27Frm5uT3P5ebmQqlUoq6uDnfccQeG\nDRuG8ePHX3FvZmZmT7Gtr683W2ZbYjTKeOrjY/hAU4mVkyLwiylDRUciIsE44kpEV5AkCU/OjMaK\nSRHIOlyJRzcWQm8juw0olUpUVlb2PNZqtVAqr9xOqaioCA888ACys7Ph7+9/2f0AEBgYiLlz5yIv\nL++q/5+lS5dCo9FAo9EgICCgjz+F7TMaZfw2+zg25FXi4YkR+OUdLK1ExOJKRNcgSRJ+PTUKj04d\nii1Hq/BIVoFNbJWVkpKCkpISlJWVobu7G1lZWUhLS7vsNRUVFZg3bx7Wr1+PoUP/U5ja2trQ0tLS\n8/XOnTsRGxtr1vz2QJZl/G7rcbz/dQV+fvsQ/Hqq7c21JqLe4VQBIvpBD0+KhKuTAs9uP4kuvRGv\n3j0CLo4K0bF6zdHREatXr8a0adNgMBiwZMkSxMTEYM2aNQCAZcuW4ZlnnsGFCxfw0EMP9dyj0WhQ\nW1uLuXPnAgD0ej1+/OMfY/r06cI+iy0yGo34/dYT+PehCjw4IRyPT4tiaSWiHpIs9+nCC9taxUFE\nPdZ/VY6ns4sxfmgA3vhJMtycrbe8mptarYZGoxEdw+J16Q14fFMRapo7kRDiiydmDGNpJbJdvfrm\n5lQBIroh94wKw1/mx+PLknrc904eWjp0oiORDWlq78Y9a/OQXVCN8UMDWFqJ6KpYXInohi1KCcE/\n7koEZOCuzEOovdQpOhLZgIoL7Zj3+kEUVDTh5fRELJ8YwdJKRFfF4kpEN2V2ohIP3j4E5y60Yc6r\nB3Cq5pLoSGTFjlRcxNzXDqCxrRv/fuA2zE68cocHIqLvsbgS0U2bGBWID5eNglGWseD1r/BlCfcp\npZu349h5ZGQegoeLIzb/fDRSB/uJjkREFo7FlYh6JSbYB1seGgNVPzfc9/ZhfKipvP5NRPh2u6s3\nvyzFQ+8fwfBgb2x5aDSGBHiKjkVEVoDFlYh6LdjXDR8uG4VRQ/zx+KYi/H3nafTxTiVkY/QGI36X\nXYxnt5/EjNiB2PCzkfD3dBEdi4isBIsrEd0Sb1cnvLU4BYvUKryy+wx+9WEhuvXWf1AB9b22Lj2W\nrs/H+kPn8OD4cKzOSIKrE7dVI6IbxwMIiOiWOSkc8ML8eIT0c8ffdn2D6qZ2vHZ3MkfSqEftpU4s\neecwTp6/hD/OicU9IweJjkREVogjrkTUJyRJworJkXjprgQ4SBLmvHoAx6uaRcciC3Cq5hLmvnoA\nZQ1tWPvTFJZWIuo1Flci6lNzR6jw2PRh0BtlzHv9ID48zEVb9mz/N3VY+PpX0BtlfPjgKEwcFig6\nEhFZMRZXIupzSaH98MmKsUgJ64fHNxfh/zYVoVNnEB2LzMhglPHKFyX47cfFiBrohY+Xj0Gs0kd0\nLCKyciyuRGQS/p4uWLfkNjw8MQIfaCqxYM1BVDa2i45FZlDf0oV73/oaf9/1DUaE+uKd+1IQ7Osm\nOhYR2QCpj7eu4T44RHSFz0/U4pcfFsBBkvCPuxLt7sfFarUaGo1GdAyzOHimASuzCtDSqcOqtBjc\nlRLC41uJ6Gp69QcDR1yJyOSmDB+AT1aMRbCvG+575zBe23OGW2bZGINRxku7vsHda7+Gj5sjsh8e\ng/TUUJZWIupTHHElIrPp1BnwyhcleG3vWUQHeePvixIQHeQtOpbJ2fqIa01zJ375QQG+Kr2AeUlK\n/HF2LDxcuNsiEf2gXv2rlsWViMxuZ3ENntxyDM0dOvxiylA8OD4cjgrb/QGQrRZXWZaxtbAaf9t1\nGgYD8IspkVioDhEdi4isA4srEVmPxrZuPJ19HNuLziMhxBd/W5iAiEDbPK/eFotr3aVOPPXxcew6\nUYsRob7464IEDLHRXz8iMgkWVyKyPtsKq/F09nF0dBvw2LQoLBkzGA4OtjUv0paKqyzL2HK0Cqu2\nnUCnzoBHp0ZhydjBUNjYrxkRmRyLKxFZp7qWTjz50TF8frIOqWF+eHFhPAb5e4iO1WdspbjWNHfi\nyS3HsPtUHdSD+uEvC+IRHsBRViLqFRZXIrJesixj85EqrNpajGEDvXD7sEDcP3YwXJ0UoqPdMmsv\nrgajjI+OaPHMJyegMxjx2LRhWDw6jKOsRHQrWFyJyPpVN3XgbztPY/ORKoT4ueHJGdGYHjvQqrdV\nsubiqilvxB+2FeN41SXMS1Ji5aRIhPW3ndFwIhKGxZWIbMeBMw14ZtsJnK5twW2D/fC7Hw1HTLB1\nHhlqjcX1fHMHnvv0FLYWVmOgtyuemDkMaQnBVv0PCCKyKCyuRGRb9AYjNhyuxN93nkZThw7pKSH4\n9dQo9Pd0ER3tplhTce3UGfCv/aV4be9ZGGQZy8aHY9ntQ+DuzH1ZiahPsbgSkW1q7tDhlS9K8O7B\ncrg5KbBicgR+OioMLlYy/9UaiqvOYMTmfC22FVXjwJkLmBE7EE/OjEaIn7voaERkm1hcici2na1v\nxZXBAdEAAArPSURBVJ+2n8Shsw0I8fPA3SNDsUgdYvELuCy5uOoNRmw5WoVXdpegsrEDiSG++P/2\n7j22yvqO4/j72wstBXqz0BZKLYpVCgoyiogssqGCt+nM5iCLt8nUTRM2lxiQZSNmCSZmW+Kmc4sz\nuESBJRuKiiCoixcEROQ6LparnHIZt3Kn9PDdH33ECm3PKT097en5vJLmPM95fs9zfnzzbc+X5/L7\nTb11AJVl+e3dNRHp3FS4ikhyWLJlH88s2MRn2w9S0D2Dn367Hz8ecTHdO+g0ox2xcK0Ln+GNVdU8\n+14VW/cd48o+OTx+YzmjL++p+1hFJB5UuIpI8nB3lmw5wHPvV/FR1T5yuqbzwHVl3D+yjNysLu3d\nvW/oSIVrzfHTzF6+g5cXb6N7Rjpm8PiN5dxYUaiCVUTiSYWriCSnz3cc5Ln3N7No/R6KsjO5aWAh\nE4aXMqA4u727BnSMwnXTniPMWLyNOStCnDgd5pp++Tx8/aWMLu/Z6WYqE5GEoMJVRJLb+l2HeWNV\nNS9+uJXa8BkGl+Two8pSbh9cTI/M9HbrV3sVruEzznsb9jJj8VY+rtpPRloKdw7pw30jy6jo3TGK\nehFJWipcRUQADh6r5bWVIWYt+5KNe47QNT2V264qZvzwvgwtzYv7JfF4Fq7uztrQYd5cXc2aUA2L\nN++nOCeTe669mPGVpeR361i3UYhI0lLhKiLSkLuzamcNsz/dwdyV1RyrDXNNvzyuvbSAsQOLuKKo\nR1yK2HgUrht3H+HN1dW8saqabfuPk5ZiXF9ewN3D+jJmQCFpqSlt+vkiIi2kwlVEpCnHTtXx1upd\nrNhxgNnLd+IOpflZjB1YyJgBhVxdmktGWtsMq9UWheupujArth/i46p9vLNuN5v2HiXFYOSlBdw+\nuJixA4s63ENqIiINqHAVEYnG7NffZurzswgXDSK1+HK6dOmCO1T2y2dU/4uovDiPF3//FAvmvUlW\nVhYzZsxg6NChAMyfP59JkyYRDoeZOHEikydPjvh5sShcw2ecDbsOs3jzfj6q2seyrQc4cTpMaopx\n65XFVJblMW5QMT17JNasYiKStFS4iohEEg6HKS8vZ+HChZSUlPCtEdfxy+nPs+NUFh9V7aNq71Gy\n0uD46TNcUZxDYZdaVix6jRl/fIryXt0YMqji7L6VlZXMnDmTioqKZj+zpYXrqbowX+w5ytpQDeuq\nD7O2uob1uw5TUZzNih2H6N+rO6P6F3Bd/wKuuSSf7HZ88ExE5AKpcBURieSTTz5h2rRpLFiwAIDp\n06cDMGXKFAD2HD7JQ08+Td4lV+G5JawN1bD/WC1Q/1c249huhlxZQe/crmxbt4LuKad5cMJd5HZN\no1tGGpnpqXRNTyUz+ElNMYYNG8biJcs4URvmWG0dx2vDHK+t48jJ04QOnSR08AShQyfOvuZ0TWdN\nqAaAHhlpDOidzaDeOQwvy2NIaR5FOZnxD5yISGxdUOHaMaeZERFpI6FQiL59+55dLykpYenSpWfX\nC7MzCW9bzsTxNzBq1HDcndE338mEnz/B51v/x6qttdSFnSWb97P7VC/OYHzw0jIy01M4efrMeZ+X\nlZ7CllAN5b9++7xtw8vyWbbtAGbQq0cGfXK7MrhvLoNLsnn4+ksY1DuH0vwsjbMqIhKI6RlXM1sL\nnIzZAZNXAbCvvTuR4BTD2OiMccwDsoHtwXo+0B3Y0aBNf2A3cDRYLwd2AhlR7PuVAqBnsJwOrI5N\n95NWZ8zF9qA4tp5iGBuZ7j6opTvF+ozrSXcfFuNjJh0zW644to5iGBudMY5mdi0wzd3HButTANx9\neoM2fwX+4+4zg/WNwBigLNK+TXxmp4tjvCmGsaE4tp5iGBtmdkFPrGpgPxFJNp8Cl5lZPzPrAowH\n5p7TZi5wr9UbAdS4+64o9xURkTaie1xFJKm4e52ZPQYsAFKBl9x9nZk9Emx/AZgH3AJUAceBB5rb\ntx3+GSIiSSnWhevfYny8ZKU4tp5iGBudMo7uPo/64rThey80WHbg0Wj3jUKnjGOcKYaxoTi2nmIY\nGxcUx1gPhyUiIiIi0iZ0j6uIiIiIJIRWFa5m9oyZbTCz1WY2x8xym2g3zsw2mlmVmUWeHzHJmNkP\nzWydmZ0xsyafVDSzbWa2xsxWXujTeJ1VC2KoXGyGmeWb2UIz+yJ4zWuinXLxHJFyK3jQ69lg+2oz\nG9oe/ezooojjaDOrCXJvpZn9pj362ZGZ2UtmtjcYorKx7crFCKKIofIwAjPra2bvm9l/g+/nSY20\naXEutvaM60JgkLtfBWwCpjTSqVTgOeBmoAKYYGbNz4+YfNYCdwEfRNH2O+4+RENxnCdiDJWLUZkM\nvOvulwHvButNUS4Gosytm4HLgp+HgL/EtZMJoAW/ox8GuTfE3Z+KaycTwwxgXDPblYuRzaD5GILy\nMJI64FfuXgGMAB6Nxd/FVhWu7v6Ou9cFq0uAkkaaDQeq3H2Lu9cCs4A7WvO5nY27r3f3je3dj0QW\nZQyVi5HdAbwcLL8M3NmOfUkk0eTWHcA/vN4SINfMiuPd0Q5Ov6Mx4O4fAAeaaaJcjCCKGEoE7r7L\n3VcEy0eA9UCfc5q1OBdjeY/rT4Dz5zSs7+SXDdZ3cn7HJToOLDKzz8zsofbuTAJSLkZWGIxXCvUz\nRxU20U65+E3R5JbyL7JoYzQyuKz4tpkNjE/XOhXlYmwoD6NkZmXA1cDScza1OBcjDodlZouAokY2\nTXX314M2U6k/JfxKpOMlq2jiGIVR7h4ys17AQjPbEPyvMCnEKIZJr7k4NlxxdzezpoYdSepclHa1\nAih196NmdgvwGvWXGUXiSXkYJTPrDvwL+IW7H27t8SIWru5+Q4QO3Q/cBozxxsfWCgF9G6yXBO8l\nlUhxjPIYoeB1r5nNof6yWtIUCzGIoXKR5uNoZnvMrNjddwWXa/Y2cYykzsVGRJNbyr/IIsao4Ref\nu88zs+fNrMDdNXd89JSLraQ8jI6ZpVNftL7i7v9upEmLc7G1owqMA54Avufux5topikSY8DMuplZ\nj6+WgZuofyBJoqdcjGwucF+wfB9w3pls5WKjWjONrHwtYhzNrMjMLFgeTv332P649zSxKRdbSXkY\nWRCfvwPr3f0PTTRrcS62duasPwMZ1F8qBFji7o+YWW/gRXe/RVMkRmZm3wf+BPQE3jKzle4+tmEc\nqb/XcE4Q5zTgVXef326d7mCiiaFyMSpPA/80sweB7cDdAMrF5rVmGln5WpRx/AHwMzOrA04A45u4\n2pe0zGwmMBooMLOdwG+BdFAuRiuKGCoPI7sOuAdYY2Yrg/eeBErhwnNRM2eJiIiISELQzFkiIiIi\nkhBUuIqIiIhIQlDhKiIiIiIJQYWriIiIiCQEFa4iIiIikhBUuIqIiIhIQlDhKiIiIiIJQYWriIiI\niLQ5M6s0s9VmlhnMwrjOzAa16BiagEBERERE4sHMfgdkAl2Bne4+vUX7q3AVERERkXgwsy7Ap8BJ\nYKS7h1uyv24VEBEREZF4uQjoDvSg/sxri+iMq4iIiIjEhZnNBWYB/YBid3+sJfuntUmvREREREQa\nMLN7gdPu/qqZpQKLzey77v5e1MfQGVcRERERSQS6x1VEREREEoIKVxERERFJCCpcRURERCQhqHAV\nERERkYSgwlVEREREEoIKVxERERFJCCpcRURERCQhqHAVERERkYTwf1Yk6LvcjWJ/AAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d46e2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x ** 2, xlim=(-2,2), ylim=(0,2), set_aspect='equal', figsize=(12,6));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WrVsxYsQI5ObmwmQy4fbbb8dbb7111tcLIeATYByJIgQDSRQiFRUVyMrK6vp5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d471f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(1/x, x, (x, -5, 5), ylim=(-5, 5), set_aspect='equal', figsize=(8,8));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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K4IUfjvHLi75VnaIVQpA68qhzuZOTE0ePHq3ymMTExErPXRTYjUWB3VAqlTz5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\nIQQpENQhhCAFgjrE/wPnAkKmi2ASgQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d356dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_parametric(cos(t * 5) * cos(t), cos(t * 5) * sin(t), set_aspect='equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O5ilkk9oWaTRROmOYcpZF6RxjVSDipWjldBVOGjwe73IrJVorU0t5krYXKLTB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d0aff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3d(sin(x**2 + y**2), (x, -2, 2), (y, -2, 2), nb_of_points_x=200, nb_of_points_y=200);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Oo7SQOU3blXh6+tv5Ow9sXvM+//zzPPPMM2Ov93Zx48YNGo3GpucP8Ku/+qsA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\nByLACjltQrc3D6OHg5acnZUOIhD+P/sZi49P63YjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28525d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot3d_parametric_surface(cos(t), sin(t) * sin(u), sin(t) * cos(u), set_aspect='equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eIriAhwgu4CGCC3jo/1O2MLawbeJ2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x244abd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_implicit(x + y < 2, line_color='yellow', set_aspect='equal');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ExMCzaZOep4O6ulRnVHw8sG2b/ceXjU8H9UvDhqnhkqmpatCD3aOuurqAX/5SrU74m1ue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\nxOASCfT/SIqg6ZMsSZMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d0bc128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_implicit(x ** 2 + y ** 2 + x * y - 2, line_color='red', set_aspect='equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Статистика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sympy.stats\n",
    "from sympy.stats import Normal, Die, P, E, variance, std, cdf, density, sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$p^{5} e^{5 t} + 5 p^{4} \\left(- p + 1\\right) e^{4 t} + 10 p^{3} \\left(p - 1\\right)^{2} e^{3 t} - 10 p^{2} \\left(p - 1\\right)^{3} e^{2 t} + 5 p \\left(p - 1\\right)^{4} e^{t} - \\left(p - 1\\right)^{5}$$"
      ],
      "text/plain": [
       " 5  5⋅t      4           4⋅t       3        2  3⋅t       2        3  2⋅t      \n",
       "p ⋅ℯ    + 5⋅p ⋅(-p + 1)⋅ℯ    + 10⋅p ⋅(p - 1) ⋅ℯ    - 10⋅p ⋅(p - 1) ⋅ℯ    + 5⋅p\n",
       "\n",
       "        4  t          5\n",
       "⋅(p - 1) ⋅ℯ  - (p - 1) "
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p, t = symbols('p t', positive=True, real=True)\n",
    "x = sympy.stats.Binomial('x', 5, p)\n",
    "simplify(E(exp(t*x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Twodices = Die('X', 6) + Die('Y', 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "throws = [int(sample(Twodices)) for i in range(1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{5}{36}$$"
      ],
      "text/plain": [
       "5/36"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(Eq(Twodices, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left \\{ 2 : \\frac{1}{36}, \\quad 3 : \\frac{1}{18}, \\quad 4 : \\frac{1}{12}, \\quad 5 : \\frac{1}{9}, \\quad 6 : \\frac{5}{36}, \\quad 7 : \\frac{1}{6}, \\quad 8 : \\frac{5}{36}, \\quad 9 : \\frac{1}{9}, \\quad 10 : \\frac{1}{12}, \\quad 11 : \\frac{1}{18}, \\quad 12 : \\frac{1}{36}\\right \\}$$"
      ],
      "text/plain": [
       "{2: 1/36, 3: 1/18, 4: 1/12, 5: 1/9, 6: 5/36, 7: 1/6, 8: 5/36, 9: 1/9, 10: 1/12\n",
       ", 11: 1/18, 12: 1/36}"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "twodices = density(Twodices)\n",
    "twodices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJDXu/wCHjUayMJ9SKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d71dd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(throws, range=(0.5, 12.5), bins=12);\n",
    "bar(range(13), [1000 * float(twodices.get(i, 0)) for i in range(13)], color='r', alpha=0.3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 15 225\n",
      "0.000429060333196837\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{30 \\sqrt{\\pi}} e^{- \\frac{1}{450} \\left(x - 100\\right)^{2}}$$"
      ],
      "text/plain": [
       "              2 \n",
       "    -(x - 100)  \n",
       "    ────────────\n",
       "        450     \n",
       "√2⋅ℯ            \n",
       "────────────────\n",
       "     30⋅√π      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{2} \\operatorname{erf}{\\left (\\frac{\\sqrt{2}}{30} \\left(x - 100\\right) \\right )} + \\frac{1}{2}$$"
      ],
      "text/plain": [
       "   ⎛√2⋅(x - 100)⎞    \n",
       "erf⎜────────────⎟    \n",
       "   ⎝     30     ⎠   1\n",
       "───────────────── + ─\n",
       "        2           2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.684456640200, 105.223444284671, 95.7518849755922, 70.4066286794701, 94.4170395543877, 55.4158027715594, 102.657052714370, 116.717820255803, 102.557040346538, 101.089898912479]\n"
     ]
    }
   ],
   "source": [
    "iq = sympy.stats.Normal('iq', 100, 15)\n",
    "print E(iq), std(iq), variance(iq)\n",
    "print N(P(iq > 150))\n",
    "display(density(iq)(x))\n",
    "display(simplify(cdf(iq)(x)))\n",
    "print [sample(iq) for i in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "111.96826841204297"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(E(iq, iq > 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{5 \\sqrt{2}}{6 \\sqrt{\\pi}} \\left(- \\frac{3 \\sqrt{2}}{10} \\sqrt{\\pi} \\operatorname{erf}{\\left (\\frac{5 \\sqrt{2}}{3} \\right )} + \\frac{3 \\sqrt{2}}{10} \\sqrt{\\pi}\\right)$$"
      ],
      "text/plain": [
       "     ⎛             ⎛5⋅√2⎞          ⎞\n",
       "     ⎜  3⋅√2⋅√π⋅erf⎜────⎟          ⎟\n",
       "     ⎜             ⎝ 3  ⎠   3⋅√2⋅√π⎟\n",
       "5⋅√2⋅⎜- ───────────────── + ───────⎟\n",
       "     ⎝          10             10  ⎠\n",
       "────────────────────────────────────\n",
       "                6⋅√π                "
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(iq > 150).rewrite(Integral)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Физика"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.physics import units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.80665*meter/second**2\n"
     ]
    }
   ],
   "source": [
    "print units.acceleration_due_to_gravity.convert_to(units.m / units.s ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "31556925.216*second\n"
     ]
    }
   ],
   "source": [
    "print units.year.convert_to(units.second)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3558179483314*joule\n"
     ]
    }
   ],
   "source": [
    "print units.convert_to(1 * units.pound * units.acceleration_due_to_gravity * 1 * units.foot, units.joule).n()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Третий закон Кеплера"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.28318530717959*venus_a**(3/2)/(sqrt(gravitational_constant)*sqrt(solar_mass))\n",
      "224.662800523082*day\n"
     ]
    }
   ],
   "source": [
    "T = symbols(\"T\")\n",
    "a = units.Quantity('venus_a', units.length, 108208000e3 * units.meter)\n",
    "M = units.Quantity('solar_mass', units.mass, 1.9891e30 * units.kilogram)\n",
    "\n",
    "G = units.gravitational_constant\n",
    "eq = Eq(T**2 / a**3, 4*sympy.pi**2 / G / M)\n",
    "q = solve(eq, T)[1]\n",
    "print q\n",
    "print units.convert_to(q, units.day).n()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Интероп с Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Выражение, результат символьного вычисления, можно сунуть в питон-функцию"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def naive_sum_of_squares(n):\n",
    "    result = 0\n",
    "    for i in range(1, n + 1):\n",
    "        result += i ** 2\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loops, best of 3: 983 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit naive_sum_of_squares(1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fast_naive_sum_of_squares(n):\n",
    "    return sum(arange(1, n + 1) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 4.08 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit fast_naive_sum_of_squares(1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "55.0\n"
     ]
    }
   ],
   "source": [
    "k, n = var('k n')\n",
    "sum_of_squares = lambdify(n, summation(k ** 2, (k, 1, n)))\n",
    "print sum_of_squares(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000 loops, best of 3: 2.41 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit sum_of_squares(1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.54993124494467\n"
     ]
    }
   ],
   "source": [
    "print lambdify(x, Si(x), modules='sympy')(5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Интероп с Maple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Иногда вызов внешней CAS удобнее или быстрее дает ответ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eval_maple(expr):\n",
    "    import os, delegator\n",
    "    cmaple_dir = 'c:\\\\Program Files (x86)\\\\Maple 15\\\\bin.win'\n",
    "    cmaple_exe = 'c:\\\\Program Files (x86)\\\\Maple 15\\\\bin.win\\\\cmaple.exe'\n",
    "    cd = os.getcwdu()\n",
    "    os.chdir(cmaple_dir)\n",
    "    maple = delegator.run([cmaple_exe], block=False)\n",
    "    maple.expect('>')\n",
    "    maple.send('interface(prettyprint=0);')\n",
    "    maple.expect('>')\n",
    "    maple.send(expr)\n",
    "    maple.expect('>')\n",
    "    maple.send('quit();')\n",
    "    os.chdir(cd)\n",
    "    return '\\r\\n'.join(maple.out.splitlines()[3:-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\int \\sin{\\left (e^{x} \\right )}\\, dx$$"
      ],
      "text/plain": [
       "⌠           \n",
       "⎮    ⎛ x⎞   \n",
       "⎮ sin⎝ℯ ⎠ dx\n",
       "⌡           "
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(sin(exp(x)), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\operatorname{Si}{\\left (e^{x} \\right )}$$"
      ],
      "text/plain": [
       "  ⎛ x⎞\n",
       "Si⎝ℯ ⎠"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S(eval_maple('int(sin(exp(x)), x);'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2: 2, 173558250066979L: 1, 29: 1, 49041759323L: 1}\n",
      "Wall time: 2.9 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "print sympy.factorint(987345823683476598732645172)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "``(2)^2*``(29)*``(49041759323)*``(173558250066979)\n",
      "Wall time: 126 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "print eval_maple('ifactor(987345823683476598732645172);')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def parse_ifactor_output(s):\n",
    "    result = {}\n",
    "    import re\n",
    "    s = re.sub('\\s+', '', s)\n",
    "    for item in s.split('*'):\n",
    "        m = re.match('^``\\((\\d+)\\)(?:\\^(\\d+))?$', item)\n",
    "        if not m:\n",
    "            raise Exception('ifactor says ' + s + ', item = ' + item)\n",
    "        base = int(m.groups()[0])\n",
    "        power = int(m.groups()[1]) if m.groups()[1] is not None else 1\n",
    "        result[base] = power\n",
    "    return result\n",
    "\n",
    "def maple_factorint(n):\n",
    "    output = eval_maple('ifactor(%d);' % n)\n",
    "    return parse_ifactor_output(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{2: 2, 173558250066979L: 1, 29: 1, 49041759323L: 1}\n",
      "Wall time: 124 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "print maple_factorint(987345823683476598732645172)"
   ]
  }
 ],
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