Lektion09.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lektion 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funktionen als Argumente\n",
    "\n",
    "\"Functions are first class citizens\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def komposition(f, g):\n",
    "    \"gibt die Funktion f ∘ g zurück\"\n",
    "    def func(x):\n",
    "        return f(g(x))\n",
    "    return func"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABsAAAASCAYAAACq26WdAAAABHNCSVQICAgIfAhkiAAAAIZJREFU\nOI3t1LENwkAMQNEHSoEyADtQRRRMQ8U+DMEaqTIARRTEFsyAQnEpUhApQXeRAvzGxcn+Z9kyCyfH\nbQ7RAVe07x6zSJIdznjgGanmKC4GOlvP+Yu/LAr9bSyE4a5G5tY4fSprsJ+SPJXvnVkK2aaLeYLa\nYIsSd+F6tMLpqnBMJf1RXtvTD+xjlzAcAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$-1$$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = komposition(cos, sqrt)\n",
    "h(pi**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEUAAAAVCAYAAAAQAyPeAAAABHNCSVQICAgIfAhkiAAAA0pJREFU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\nQmCC\n",
      "text/latex": [
       "$$\\cos{\\left (\\sqrt{x} \\right )}$$"
      ],
      "text/plain": [
       "cos(√x)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Symbol('x')\n",
    "h(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jordansche Normalform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}-4 & -2 & -3\\\\5 & 3 & 3\\\\5 & 2 & 4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-4  -2  -3⎤\n",
       "⎢          ⎥\n",
       "⎢5   3   3 ⎥\n",
       "⎢          ⎥\n",
       "⎣5   2   4 ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = Matrix(3, 3, [-4, -2, -3, 5, 3, 3, 5, 2, 4])\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC8AAAATCAYAAAAAn1R6AAAABHNCSVQICAgIfAhkiAAAAdhJREFU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\nnk04hkUp8VNMkeAnsDhUor4lSPQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ 1 : 3\\right \\}$$"
      ],
      "text/plain": [
       "{1: 3}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left ( 1, \\quad 3, \\quad \\left [ \\left[\\begin{matrix}- \\frac{2}{5}\\\\1\\\\0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}- \\frac{3}{5}\\\\0\\\\1\\end{matrix}\\right]\\right ]\\right )\\right ]$$"
      ],
      "text/plain": [
       "⎡⎛1, 3, ⎡⎡-2/5⎤, ⎡-3/5⎤⎤⎞⎤\n",
       "⎢⎜      ⎢⎢    ⎥  ⎢    ⎥⎥⎟⎥\n",
       "⎢⎜      ⎢⎢ 1  ⎥  ⎢ 0  ⎥⎥⎟⎥\n",
       "⎢⎜      ⎢⎢    ⎥  ⎢    ⎥⎥⎟⎥\n",
       "⎣⎝      ⎣⎣ 0  ⎦  ⎣ 1  ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.eigenvects()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das ist einer zu wenig."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "MatrixError",
     "evalue": "Matrix is not diagonalizable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mMatrixError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-3144553eeb69>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mJ\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mC\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdiagonalize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m# MatrixError\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32mC:\\Users\\braun\\Miniconda3\\lib\\site-packages\\sympy\\matrices\\matrices.py\u001b[0m in \u001b[0;36mdiagonalize\u001b[0;34m(self, reals_only, sort, normalize)\u001b[0m\n\u001b[1;32m   3465\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_diagonalizable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mreals_only\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m   3466\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_diagonalize_clear_subproducts\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3467\u001b[0;31m             \u001b[1;32mraise\u001b[0m \u001b[0mMatrixError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Matrix is not diagonalizable\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   3468\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m   3469\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_eigenvects\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mMatrixError\u001b[0m: Matrix is not diagonalizable"
     ]
    }
   ],
   "source": [
    "T, J = C.diagonalize()  # MatrixError"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}- \\frac{38}{3} & \\frac{5}{3} & - \\frac{1}{7}\\\\\\frac{38}{3} & \\frac{2}{3} & - \\frac{8}{7}\\\\\\frac{38}{3} & 1 & 1\\end{matrix}\\right], \\quad \\left[\\begin{matrix}1 & 1 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{matrix}\\right]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡-38/3  5/3  -1/7⎤, ⎡1  1  0⎤⎞\n",
       "⎜⎢                ⎥  ⎢       ⎥⎟\n",
       "⎜⎢38/3   2/3  -8/7⎥  ⎢0  1  0⎥⎟\n",
       "⎜⎢                ⎥  ⎢       ⎥⎟\n",
       "⎝⎣38/3    1    1  ⎦  ⎣0  0  1⎦⎠"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T, J = C.jordan_form()\n",
    "T, J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T * J * T**(-1) == C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rang einer Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\\\7 & 8 & 9\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1  2  3⎤\n",
       "⎢       ⎥\n",
       "⎢4  5  6⎥\n",
       "⎢       ⎥\n",
       "⎣7  8  9⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = Matrix(3, 3, range(1,10))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAALxJREFU\nKJHF0LFKQgEUh/FfIkjo4JSRi4gvkINDiO8hRG8SREZjb+Dk4pKbiC5CU7sPIDSK4mBLQ9TQHW6H\nCwoO/uEM5+PjnMPhiLQwwgQL9FHNEpuYoZz0JbxhhVqUx2gEdo0fDKP8iQ9cBL7FGnIpuEQFxSB/\n4TxOLuIysKvkjHmUs/KMb9zsE+vY4WmfWMA7Xg5ZP8DjIeID7gO74//r4DZhvcDbcJYCHbxiGsS8\nv/d103CTwKyKm06ZX2eJIzA9eAUpAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.rank()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 x + 2 & 2 y - 2\\\\2 x + 2 & - 2 y + 2\\\\y - 1 & x + 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⋅x + 2  2⋅y - 2 ⎤\n",
       "⎢                 ⎥\n",
       "⎢2⋅x + 2  -2⋅y + 2⎥\n",
       "⎢                 ⎥\n",
       "⎣ y - 1    x + 1  ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "M = Matrix(3, 2, [2*x+2, 2*y-2, 2*x+2, -2*y+2, y-1, x+1])\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAALxJREFU\nKJHF0LFKQgEUh/FfIkjo4JSRi4gvkINDiO8hRG8SREZjb+Dk4pKbiC5CU7sPIDSK4mBLQ9TQHW6H\nCwoO/uEM5+PjnMPhiLQwwgQL9FHNEpuYoZz0JbxhhVqUx2gEdo0fDKP8iQ9cBL7FGnIpuEQFxSB/\n4TxOLuIysKvkjHmUs/KMb9zsE+vY4WmfWMA7Xg5ZP8DjIeID7gO74//r4DZhvcDbcJYCHbxiGsS8\nv/d103CTwKyKm06ZX2eJIzA9eAUpAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2$$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.rank()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Glauben wir das?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mult_zeile(A, zeilennr, faktor):\n",
    "    B = Matrix(A)\n",
    "    def func(b, j):\n",
    "        return b*faktor\n",
    "    B.row_op(zeilennr, func)\n",
    "    return B\n",
    "\n",
    "def add_zeile(A, quell_nr, ziel_nr, faktor):\n",
    "    B = Matrix(A)  \n",
    "    def func(b, j):\n",
    "        return b + B[quell_nr,j]*faktor\n",
    "    B.row_op(ziel_nr, func)\n",
    "    return B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 x + 2 & 2 y - 2\\\\0 & - 4 y + 4\\\\y - 1 & x + 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⋅x + 2  2⋅y - 2 ⎤\n",
       "⎢                 ⎥\n",
       "⎢   0     -4⋅y + 4⎥\n",
       "⎢                 ⎥\n",
       "⎣ y - 1    x + 1  ⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M1 = add_zeile(M, 0, 1, -1)\n",
    "M1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\left(2 x + 2\\right) \\left(y - 1\\right) & \\left(y - 1\\right) \\left(2 y - 2\\right)\\\\0 & - 4 y + 4\\\\\\left(x + 1\\right) \\left(y - 1\\right) & \\left(x + 1\\right)^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡(2⋅x + 2)⋅(y - 1)  (y - 1)⋅(2⋅y - 2)⎤\n",
       "⎢                                    ⎥\n",
       "⎢        0              -4⋅y + 4     ⎥\n",
       "⎢                                    ⎥\n",
       "⎢                              2     ⎥\n",
       "⎣ (x + 1)⋅(y - 1)       (x + 1)      ⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M2 = mult_zeile(M1, 0, y-1)   # nur für y != 1\n",
    "M3 = mult_zeile(M2, 2, x+1)   # nur für x != -1\n",
    "M3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 \\left(x + 1\\right) \\left(y - 1\\right) & 2 \\left(y - 1\\right)^{2}\\\\0 & - 4 \\left(y - 1\\right)\\\\0 & \\left(x + y\\right) \\left(x - y + 2\\right)\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                                2     ⎤\n",
       "⎢2⋅(x + 1)⋅(y - 1)      2⋅(y - 1)      ⎥\n",
       "⎢                                      ⎥\n",
       "⎢        0              -4⋅(y - 1)     ⎥\n",
       "⎢                                      ⎥\n",
       "⎣        0          (x + y)⋅(x - y + 2)⎦"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M4 = add_zeile(M3, 0, 2, -Rational(1,2)).expand()\n",
    "factor(M4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wenn $x\\ne-1$ und $y\\ne1$, dann ist der Rang dieser Matrix gleich 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 2 \\left(y - 1\\right)\\\\0 & - 2 \\left(y - 1\\right)\\\\y - 1 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡  0    2⋅(y - 1) ⎤\n",
       "⎢                 ⎥\n",
       "⎢  0    -2⋅(y - 1)⎥\n",
       "⎢                 ⎥\n",
       "⎣y - 1      0     ⎦"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M5 = M.subs(x, -1)\n",
    "factor(M5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Für $y\\ne1$ ist der Rang dieser Matrix immer noch 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 \\left(x + 1\\right) & 0\\\\2 \\left(x + 1\\right) & 0\\\\0 & x + 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2⋅(x + 1)    0  ⎤\n",
       "⎢                ⎥\n",
       "⎢2⋅(x + 1)    0  ⎥\n",
       "⎢                ⎥\n",
       "⎣    0      x + 1⎦"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M6 = M.subs(y, 1)\n",
    "factor(M6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "dito für $x\\ne-1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 0\\\\0 & 0\\\\0 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0  0⎤\n",
       "⎢    ⎥\n",
       "⎢0  0⎥\n",
       "⎢    ⎥\n",
       "⎣0  0⎦"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M7 = M.subs({x:-1, y:1})\n",
    "M7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kein Fehler von `sympy`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normen von Vektoren und Matrizen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1\\\\2\\\\3\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡1⎤\n",
       "⎢ ⎥\n",
       "⎢2⎥\n",
       "⎢ ⎥\n",
       "⎣3⎦"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Matrix([1,2,3])\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACwAAAAbCAYAAAAH+20UAAAABHNCSVQICAgIfAhkiAAAAd9JREFU\nWIXt10+ITWEcxvGPccdoGrNQI6X8KQklNlaWiNjISimxYkFKLCYbSrEgZZRkM6YUiUSUlEkWVhak\nUFhIs5mdLKaJrsV71JnbPee+554zJ4v73Zzu+z7vc57z3ve8v/fQY35ZUJFPsyKf2niGxXXcqK8C\nj914hZkKvGrhMYbrulnZGd6G9/hZQZZauI+ROm9YZoY3YwrTFWWZdyawMkI3KCybWE5jNKuz2xle\ni1l876DbKuwgmyJ9V+E8BrIEjUijVs7gck7/hqR/Gn8K+J4V/pFMsmZ4Sc6YFUn/pxzNR+zF4Q66\nNPvxspOoNfAg7uBSzphTuBIZIpYh7MHdTsJ04EYS5hsOaV8MlmIN3pbPOIdRXIwRpgP/xgVcxUIc\naaM/ibGy6VrYgl/4WsbkFj6be5obwtMuvMZln+b6cBuLUm1NnMsyy3rprmMddqXajuFmZMhYjgoP\nNBs7ICvwO7zGieT3AHbiSYlwrSzHRkwWGZS3D4/hnlAktguVrcqD+g6sx6NUW39yPSCs7Qk8jDVs\n4Aeu4YXwInbDuPgHXa3LNUzYNW7gOB4oVrHS/PsSya1gCf0t18KM4Ivinz/L8BwfhBlrCmV6Egfb\n6IeTvqlEO4M32NdV6h49/mP+ApcYTY09vX/IAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\sqrt{14}$$"
      ],
      "text/plain": [
       "√14"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACwAAAAbCAYAAAAH+20UAAAABHNCSVQICAgIfAhkiAAAAd9JREFU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\n6IeTvqlEO4M32NdV6h49/mP+ApcYTY09vX/IAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\sqrt{14}$$"
      ],
      "text/plain": [
       "√14"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt((v.T*v)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFU\nKJHN0S1LxEEUxeHHZRHFt2DwA2zR4kszGg0Gi90mJvMGo8kgKPglbH6BTdsWNtgsdgWXFXRFxDX8\nrziMI65tDwzD/O49M8O5/FMT2XkTBxhgOtYJbkrmDVxjKmGXeMJ6yXCGIfYSthPs/AvUkmI3busn\nbC72l9ILJZ3iHWujNDfwgMO/GndxgVs0/UzyV02ihTYWRzVtqVK6KhWXsZqx+TB8YDYvDFSJNBI+\nE4YhFviewxvquEMvMazE3hHzqQd4VWV+nxmO8CyJNo9sH9vxtSU84lgV8bjqE3aWKpLa/9brAAAA\nAElFTkSuQmCC\n",
      "text/latex": [
       "$$3$$"
      ],
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.norm(oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAbCAYAAADMIInqAAAABHNCSVQICAgIfAhkiAAAAnRJREFU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\nHTvf7Y0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\sqrt[4]{2} \\sqrt{7}$$"
      ],
      "text/plain": [
       "4 ___   \n",
       "╲╱ 2 ⋅√7"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.norm(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}-4 & -2 & -3\\\\5 & 3 & 3\\\\5 & 2 & 4\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-4  -2  -3⎤\n",
       "⎢          ⎥\n",
       "⎢5   3   3 ⎥\n",
       "⎢          ⎥\n",
       "⎣5   2   4 ⎦"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADYAAAAbCAYAAAA3d3w1AAAABHNCSVQICAgIfAhkiAAAAipJREFU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\n",
      "text/latex": [
       "$$3 \\sqrt{13}$$"
      ],
      "text/plain": [
       "3⋅√13"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.norm()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Frobeniusnorm ist submultiplikativ, also $\\left\\Vert A B \\right\\Vert \\le \\left\\Vert A \\right\\Vert \\left\\Vert B \\right\\Vert$.  Sie ist aber keine Matrixnorm im Sinne der Analysis II. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIEAAAAlCAYAAABlLYqoAAAABHNCSVQICAgIfAhkiAAABWBJREFU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\nMGn8CkcijBqVX3AAAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\sqrt{\\sqrt{3363} + 58}$$"
      ],
      "text/plain": [
       "  ____________\n",
       "╲╱ √3363 + 58 "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.norm(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAAfCAYAAADgBaa3AAAABHNCSVQICAgIfAhkiAAABzNJREFU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\niqIoiqIoiqIoiqIoyeV/x2ZxcKvlSh0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left \\{ 1 : 1, \\quad - \\sqrt{3363} + 58 : 1, \\quad \\sqrt{3363} + 58 : 1\\right \\}$$"
      ],
      "text/plain": [
       "{1: 1, -√3363 + 58: 1, √3363 + 58: 1}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(C.T*C).eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAAAWCAYAAABjYE+sAAAABHNCSVQICAgIfAhkiAAACSFJREFU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\n1cQHbAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( 10.816653826392, \\quad 10.7699293716158\\right )$$"
      ],
      "text/plain": [
       "(10.816653826392, 10.7699293716158)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.norm().n(), C.norm(2).n()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kreuzprodukt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}12\\\\-6\\\\0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡12⎤\n",
       "⎢  ⎥\n",
       "⎢-6⎥\n",
       "⎢  ⎥\n",
       "⎣0 ⎦"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = Matrix([-1,-2,3])\n",
    "z = v.cross(w)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "[0]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.T*z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "[0]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.T*z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Kreuzprodukt $v \\times w$ steht senkrecht auf $v$ und $w$.  Seine euklidische Norm ist gleich dem Flächeninhalt des von $v$ und $w$ aufgespannten Parallelogramms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "z = Symbol('z')\n",
    "var = [x,y,z]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGMAAAAbCAYAAABoSjE5AAAABHNCSVQICAgIfAhkiAAAAzRJREFU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\nKPLI+bGXVlFRUVFRUVHRBlwCbjWc8KM5U44AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$e^{x^{2} + 2 y^{2} + 3 z^{2}}$$"
      ],
      "text/plain": [
       "  2      2      2\n",
       " x  + 2⋅y  + 3⋅z \n",
       "ℯ                "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = exp(x**2 + 2*y**2 + 3*z**2)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 x e^{x^{2} + 2 y^{2} + 3 z^{2}}\\\\4 y e^{x^{2} + 2 y^{2} + 3 z^{2}}\\\\6 z e^{x^{2} + 2 y^{2} + 3 z^{2}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      2      2      2⎤\n",
       "⎢     x  + 2⋅y  + 3⋅z ⎥\n",
       "⎢2⋅x⋅ℯ                ⎥\n",
       "⎢                     ⎥\n",
       "⎢      2      2      2⎥\n",
       "⎢     x  + 2⋅y  + 3⋅z ⎥\n",
       "⎢4⋅y⋅ℯ                ⎥\n",
       "⎢                     ⎥\n",
       "⎢      2      2      2⎥\n",
       "⎢     x  + 2⋅y  + 3⋅z ⎥\n",
       "⎣6⋅z⋅ℯ                ⎦"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gr = Matrix([f.diff(t) for t in var])\n",
    "gr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sympy hat eine Funktion gradient, aber nur in 3D.  Man beachte aber den nächsten Abschnitt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Jacobi- und Hessematrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 x e^{x^{2} + 2 y^{2} + 3 z^{2}} & 4 y e^{x^{2} + 2 y^{2} + 3 z^{2}} & 6 z e^{x^{2} + 2 y^{2} + 3 z^{2}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡      2      2      2        2      2      2        2      2      2⎤\n",
       "⎢     x  + 2⋅y  + 3⋅z        x  + 2⋅y  + 3⋅z        x  + 2⋅y  + 3⋅z ⎥\n",
       "⎣2⋅x⋅ℯ                  4⋅y⋅ℯ                  6⋅z⋅ℯ                ⎦"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J = Matrix([f]).jacobian(var)\n",
    "J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}2 \\left(2 x^{2} + 1\\right) e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 8 x y e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 12 x z e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}}\\\\8 x y e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 4 \\left(4 y^{2} + 1\\right) e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 24 y z e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}}\\\\12 x z e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 24 y z e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}} & 6 \\left(6 z^{2} + 1\\right) e^{x^{2}} e^{2 y^{2}} e^{3 z^{2}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡              ⎛ 2⎞     2     2            ⎛ 2⎞     2     2                 ⎛ \n",
       "⎢  ⎛   2    ⎞  ⎝x ⎠  2⋅y   3⋅z             ⎝x ⎠  2⋅y   3⋅z                  ⎝x\n",
       "⎢2⋅⎝2⋅x  + 1⎠⋅ℯ    ⋅ℯ    ⋅ℯ         8⋅x⋅y⋅ℯ    ⋅ℯ    ⋅ℯ             12⋅x⋅z⋅ℯ  \n",
       "⎢                                                                             \n",
       "⎢          ⎛ 2⎞     2     2                    ⎛ 2⎞     2     2             ⎛ \n",
       "⎢          ⎝x ⎠  2⋅y   3⋅z         ⎛   2    ⎞  ⎝x ⎠  2⋅y   3⋅z              ⎝x\n",
       "⎢   8⋅x⋅y⋅ℯ    ⋅ℯ    ⋅ℯ          4⋅⎝4⋅y  + 1⎠⋅ℯ    ⋅ℯ    ⋅ℯ         24⋅y⋅z⋅ℯ  \n",
       "⎢                                                                             \n",
       "⎢           ⎛ 2⎞     2     2                ⎛ 2⎞     2     2                  \n",
       "⎢           ⎝x ⎠  2⋅y   3⋅z                 ⎝x ⎠  2⋅y   3⋅z        ⎛   2    ⎞ \n",
       "⎣   12⋅x⋅z⋅ℯ    ⋅ℯ    ⋅ℯ            24⋅y⋅z⋅ℯ    ⋅ℯ    ⋅ℯ         6⋅⎝6⋅z  + 1⎠⋅\n",
       "\n",
       "2⎞     2     2   ⎤\n",
       " ⎠  2⋅y   3⋅z    ⎥\n",
       "  ⋅ℯ    ⋅ℯ       ⎥\n",
       "                 ⎥\n",
       "2⎞     2     2   ⎥\n",
       " ⎠  2⋅y   3⋅z    ⎥\n",
       "  ⋅ℯ    ⋅ℯ       ⎥\n",
       "                 ⎥\n",
       " ⎛ 2⎞     2     2⎥\n",
       " ⎝x ⎠  2⋅y   3⋅z ⎥\n",
       "ℯ    ⋅ℯ    ⋅ℯ    ⎦"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = factor(gr.jacobian(var))\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das ist die Hesse Matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(hessian(f, var)) == H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEUAAAAWCAYAAACWl1FwAAAABHNCSVQICAgIfAhkiAAAA0dJREFU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\n",
      "text/latex": [
       "$$f{\\left (x,y,z \\right )}$$"
      ],
      "text/plain": [
       "f(x, y, z)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = Function('f')\n",
    "f(*var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{\\partial^{2}}{\\partial x^{2}}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial x\\partial y}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial x\\partial z}  f{\\left (x,y,z \\right )}\\\\\\frac{\\partial^{2}}{\\partial x\\partial y}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial y^{2}}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial y\\partial z}  f{\\left (x,y,z \\right )}\\\\\\frac{\\partial^{2}}{\\partial x\\partial z}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial y\\partial z}  f{\\left (x,y,z \\right )} & \\frac{\\partial^{2}}{\\partial z^{2}}  f{\\left (x,y,z \\right )}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡   2                  2                  2             ⎤\n",
       "⎢  ∂                  ∂                  ∂              ⎥\n",
       "⎢ ───(f(x, y, z))   ─────(f(x, y, z))  ─────(f(x, y, z))⎥\n",
       "⎢   2               ∂y ∂x              ∂z ∂x            ⎥\n",
       "⎢ ∂x                                                    ⎥\n",
       "⎢                                                       ⎥\n",
       "⎢   2                  2                  2             ⎥\n",
       "⎢  ∂                  ∂                  ∂              ⎥\n",
       "⎢─────(f(x, y, z))   ───(f(x, y, z))   ─────(f(x, y, z))⎥\n",
       "⎢∂y ∂x                 2               ∂z ∂y            ⎥\n",
       "⎢                    ∂y                                 ⎥\n",
       "⎢                                                       ⎥\n",
       "⎢   2                  2                  2             ⎥\n",
       "⎢  ∂                  ∂                  ∂              ⎥\n",
       "⎢─────(f(x, y, z))  ─────(f(x, y, z))   ───(f(x, y, z)) ⎥\n",
       "⎢∂z ∂x              ∂z ∂y                 2             ⎥\n",
       "⎣                                       ∂z              ⎦"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hessian(f(x,y,z), var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definitheit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}6 e^{4} & 0 & - 12 e^{4}\\\\0 & 4 e^{4} & 0\\\\- 12 e^{4} & 0 & 42 e^{4}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡    4              4⎤\n",
       "⎢ 6⋅ℯ     0    -12⋅ℯ ⎥\n",
       "⎢                    ⎥\n",
       "⎢           4        ⎥\n",
       "⎢  0     4⋅ℯ     0   ⎥\n",
       "⎢                    ⎥\n",
       "⎢     4            4 ⎥\n",
       "⎣-12⋅ℯ    0    42⋅ℯ  ⎦"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1 = H.subs({x:1, y:0, z:-1})\n",
    "H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1.is_positive   # falscher Befehl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADgAAAAWCAYAAACVIF9YAAAABHNCSVQICAgIfAhkiAAAAuJJREFU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\newAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$432 e^{12}$$"
      ],
      "text/plain": [
       "     12\n",
       "432⋅ℯ  "
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAAfCAYAAADUfGerAAAABHNCSVQICAgIfAhkiAAACzRJREFU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\ngUAgEAgEAoFAILB38D+S8adKR5JP2wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( - 6 \\sqrt{13} e^{4} + 24 e^{4}, \\quad 129.217023855597\\right )$$"
      ],
      "text/plain": [
       "⎛         4       4                  ⎞\n",
       "⎝- 6⋅√13⋅ℯ  + 24⋅ℯ , 129.217023855597⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU8AAAAfCAYAAABnNE+xAAAABHNCSVQICAgIfAhkiAAACehJREFU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\nnYFnNicTwlKBQCAQCAQCgUAgEAgciPwf+/2ATp5iyaMAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( 6 \\sqrt{13} e^{4} + 24 e^{4}, \\quad 2491.49417773533\\right )$$"
      ],
      "text/plain": [
       "⎛       4       4                  ⎞\n",
       "⎝6⋅√13⋅ℯ  + 24⋅ℯ , 2491.49417773533⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAAAaCAYAAABM+EvnAAAABHNCSVQICAgIfAhkiAAACN1JREFU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\nRK5CYII=\n",
      "text/latex": [
       "$$\\left ( 4 e^{4}, \\quad 218.392600132577\\right )$$"
      ],
      "text/plain": [
       "⎛   4                  ⎞\n",
       "⎝4⋅ℯ , 218.392600132577⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for tmp in H1.eigenvals():\n",
    "    display((tmp, tmp.n()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ImmutableMatrix(eye(3)).is_positive  # das ist nicht die \n",
    "# Antwort auf unsere Frage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hurwitz Kriterium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB4AAAAWCAYAAADXYyzPAAAABHNCSVQICAgIfAhkiAAAAb1JREFU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\nRK5CYII=\n",
      "text/latex": [
       "$$6 e^{4}$$"
      ],
      "text/plain": [
       "   4\n",
       "6⋅ℯ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAWCAYAAABDhYU9AAAABHNCSVQICAgIfAhkiAAAAhdJREFU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\nUx1Ck27HPqG/5SrC//iPAcdPar5vImsWTh0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$24 e^{8}$$"
      ],
      "text/plain": [
       "    8\n",
       "24⋅ℯ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADgAAAAWCAYAAACVIF9YAAAABHNCSVQICAgIfAhkiAAAAuJJREFU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\newAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$432 e^{12}$$"
      ],
      "text/plain": [
       "     12\n",
       "432⋅ℯ  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for j in range(1,4):\n",
    "    minor = H1[0:j, 0:j]\n",
    "    display(minor.det())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also positiv definit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAAWCAYAAABUpxX0AAAABHNCSVQICAgIfAhkiAAAAdhJREFU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\nS+HzyYxa5jGPOYU/z1VTjmrpX0wAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- 6 e^{4}$$"
      ],
      "text/plain": [
       "    4\n",
       "-6⋅ℯ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAWCAYAAABDhYU9AAAABHNCSVQICAgIfAhkiAAAAhdJREFU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\nUx1Ck27HPqG/5SrC//iPAcdPar5vImsWTh0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$24 e^{8}$$"
      ],
      "text/plain": [
       "    8\n",
       "24⋅ℯ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEgAAAAWCAYAAABjadrAAAAABHNCSVQICAgIfAhkiAAAAwtJREFU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\n",
      "text/latex": [
       "$$- 432 e^{12}$$"
      ],
      "text/plain": [
       "      12\n",
       "-432⋅ℯ  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for j in range(1,4):\n",
    "    minor = -H1[0:j, 0:j]\n",
    "    display(minor.det())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hurwitz-Kriterium\n",
    "\n",
    "Es sei $M \\in \\mathbb R^{n\\times n}$ eine symmetrische Matrix.\n",
    "\n",
    "* $M$ ist genau dann positiv definit, wenn alle Unterdeterminanten entlang der Hauptdiagonale positiv sind.\n",
    "* $M$ ist genau dann negativ definit, wenn die geraden Unterdeterminanten positiv und die ungeraden negativ sind.\n",
    "* Wenn eine gerade Unterdeterminante negativ ist, dann ist $M$ indefinit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extremwerte in mehreren Veränderlichen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASIAAAAbCAYAAADYvIJnAAAABHNCSVQICAgIfAhkiAAABidJREFU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\n",
      "text/latex": [
       "$$- \\frac{x^{4}}{2} + x^{3} - x^{2} y^{2} - 3 x y^{2} - \\frac{y^{4}}{2}$$"
      ],
      "text/plain": [
       "   4                          4\n",
       "  x     3    2  2        2   y \n",
       "- ── + x  - x ⋅y  - 3⋅x⋅y  - ──\n",
       "  2                          2 "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = -x**4/2 - x**2*y**2 - y**4/2 + x**3 - 3*x*y**2\n",
    "fn = lambdify((x,y), f)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-5, 5)\n",
    "yn = np.linspace(-5, 5)\n",
    "X, Y = np.meshgrid(xn, yn)\n",
    "W = fn(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J/SDLLJISMCCVqFQhEwEkmJUq8XybNAxwxkdRHZ+0HSBcl+KkhwojVBBiVatg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\ndayIpKeVBi0a+fxWj5APvhvlGkR6NMncmL7v02636ff7uK7LwsJC4t+7m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Lv3GfioDGgQ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v3+Y7uj/77DPMnTsXPj4+bXS6fX19LaYRxQ6Fu4FyEaWzJCOlxJqZXGsQpq45xF3Ijkp1C8sE\nEx4PxQfbbiAkSOVWzljYiS8Uiqmrq8ORI0dw/vx5ZGZmIjExEbm5ucjNzUVOTg6qqqrkNl0SxL0K\nFGmhEbKAffv2ISUlBRkZGUhKSoJOp8P58+fx3HPPyW3aQwfnJIQ63Tk5OSgqKsLAgQONGsaEOt2W\nFr57enrCy8vLrWrF9uwqlgJrU93WZCZMlQkMRIGXZ+VjQIwvVi91fdlF4WsQlgkIITh+/DhSU1MR\nGxuLv/71r+jevbvc5lJcE5qythaWZdG7d2+sXr0aycnJcptDMYE1Ot1cTbq8vBx79uzBzJkzERAQ\nYOSgFQpFm7lTV0xdS7mruKPYm+pmWRZardZkmWDHnjIoFAymPt9DltdkLeZeg1arxdtvv41du3Zh\nw4YNePnll93qsEdxOjRlbS1nzpxBeXk5AGDkyJG4desWYmNj8Ze//AVDhgyR2ToK0JI+DQwMxOOP\nP47HH38cgLFOd3Z2NtasWYO8vDwAQO/evREaGorHHnuM1+nmGsa4cSEOKRrGpEIcUcrdfQxYl+oW\nvqecQzYYDGAYBmq1uk1kP+Hxrii53uDU12EL4r8DV+oghCA3NxczZsxAVFQU8vLyEBkZKbe57bJp\n0yasW7cOt27dwvDhw7Fx40ZoNBq5zaIIoBHyA/bs2YMXX3wRUVFR2LBhA6KiorBu3Tr8+9//xpUr\nVxAYGCi3iZR2+O677/D666/j9u3bmDZtGvr06cPX8O7cuYMRI0bwzWIJCQkIDw9vs+3KVMOYMzuQ\nnb2rWGoMBgOam5v58TUhplLdAFzy9QmzE8K/Q1NTEzIyMrBlyxasWbMGM2bMcIuoeM+ePZg2bRq2\nbNmChIQEbNiwAXv37kVRURFCQ0Pb/wEUKaAp6+XLl+Pdd981+zzDMLh06RL++9//YsqUKdi6dSte\nf/11AC27b3v27Ik///nPeOONN5xlMsVODh06hI0bN2LTpk3o06cP/3h7Ot1cLTo2Nhbe3t7tpmWF\ns9FSIVR5clW1sPYQR5TcTK4raEvb8hq4mr1wLI4QUdkXcAAAEBdJREFUggsXLuCNN95AQEAAtm/f\njr59+8pmp62MGjUKiYmJ+OCDDwC0vM7IyEikp6djyZIlMlv30EAdclVVVbsdjn369MGJEyeQlJSE\nEydOYPTo0fxzo0aNwuOPP47Vq1c72lSKBBBC2r2hi3W6uVq0OZ1u8eypWGJRmO621ZlwI11y7iqW\nAlsie0va0uKubmeWD8zV7PV6Pd5//32sX78ef/rTnzB//ny3OizpdDqo1Wrs27cPEydO5B9PTk5G\nTU0NvvzySxmte6igNeSQkBCEhIS0+3VxcXHw8vJCYWEh75B1Oh2uXbuGqKgoR5tJkQhrHBnDMPD0\n9ERcXBzi4uIwa9asNjrde/fuxZIlS6BQKIyi6Li4OPj7+xt1dHNzwYBtDWOusqu4I4hncq0ZKeMW\njgjr4uIourm52e55c3tegzAqFtbsi4qKMGPGDBgMBpw4cQKPPPKIZL/XWVRWVoJlWXTr1s3o8W7d\nuqGwsFAmqyim6PQO2Vq6dOmCmTNnYtWqVejZsyeioqLw3nvvgWEYPP/887LZ1dzcjISEBBQUFCAv\nLw/Dhg2TzZbODMMwCAkJwZNPPoknn3wSQEvEVFhYiOzsbGRnZ2PVqlW4cOEC+vbta6Qwxul0m2oY\nMzXHC8BolEmtVssmZdkRzM3k2oM9spVSpLoNBgO0Wm2bqJhlWWzevBnvvPMO5s+fjxUrVjhl3Izy\ncEMdsoB169ZBpVJh6tSpaGhoQGJiIn744QcEBATIZtOSJUvQs2dPnDt3TjYbHlaUSiUGDx6MwYMH\n49VXX22j0/3DDz9g7dq1RjrdnJMOCwszG/FxcDVKV15JaQp7omJbsaer25ZUt3jnsrALvLS0FKmp\nqaisrMR3332HuLg4t/r7iAkNDYVSqURFRYXR4xUVFXRm2sXo9DVkd+bbb7/FokWLsG/fPgwePJhG\nyC6ItTrdAwYMwI4dO+Dl5YUXX3yRb3bicGTDmJTo9XpotVqXqXebahhrL9VtbueywWDAZ599hhUr\nVuCNN97A22+/DR8fH9lem5SYaurq1asX0tPTsXjxYpmte2igNWR3paKiAikpKTh48GCnuSl0RhiG\nQVRUFKKiojB58mSTOt0ffvgh7ty5A4PBgIkTJyIkJAQajYbX6bYkWdmRhjEpEXeBcx3UcmNrqpuT\nUgVaygZdunQBwzC4efMm5syZgytXruDgwYMYO3asW0fFYhYsWIDk5GTExcXxY09arZaKILkY1CG7\nKK+++irS0tIwYsQIlJaWym0OxUqEOt0jR45EcXExysvLMXz4cLz22msoLy/Hp59+ivT0dCOdbo1G\ng5EjR8LX19doNlrYMCbXiJC5Xb+uiLlUN9d8J8xKJCcnIz8/H4MGDcLZs2eRlJSE7777rlM2cU6a\nNAmVlZVYuXIlKioqEBsbi8OHDyMsLExu0ygCaMraiVg7E/2vf/0L//jHP3D06FEoFApcu3YNffr0\noSlrN4MQgsmTJ+NXv/oV5syZwzsJW3W6AVg1IiR1Y5hwzaO7doEDrQcKAHya3WAw4NChQ/j8889R\nWFiImzdvora2FgAQExODrVu3Yty4cXKaTel80DlkV8Kamejo6GhMmjQJX3/9tdHjLMvCw8MDU6ZM\nQVZWliPNpEiINXPR3NeZ0+kWNoxpNBoEBwdbVTftiMKYO0XF5hCm2YUHCkIIDh06hPT0dIwfPx7v\nv/8+AgICUFJSwr/vs2bN4g9DFIpEUIfsjpSVlfGndQAoLy/H+PHjsW/fPiQkJCAiIkJG6yjOQqzT\nnZOTg/z8fPTq1ctoZ/SQIUOgVCqNZqPFDWPi2WhLv7MzRcXiA0VNTQ2WLl2Kf//738jMzMQf/vAH\ntztoUNwW6pA7A6WlpYiOjpYtZV1aWorVq1fjhx9+wK1bt9CjRw9MmTIFf/zjH+lsphPhIr4zZ84Y\nRdFinW6NRoOIiAgjBy2MojlhDrGmtE6n42vW3t7ebhsVcyNZ4qj46NGjSEtLQ0JCAj7++GO3qp/S\na7BTQLusOwty3hgvX74MQgi2bt2KmJgYnD9/HtOnT4dWq8V7770nm10PG9y87NixYzF27FgAbXW6\nN2/ejBkzZiAwMNDIQY8YMQJeXl5GDWPC7mMOd52NBsyPZNXX12PVqlX44osv8MEHH+Cll15yu9dG\nr8GHAxohU+xi3bp1yMzMRHFxsdymUARYo9PNOerevXvj0KFDqKurw4QJE4xGgoQNY1w07apOTCxU\nwo1kEUKQnZ2NGTNmoF+/fti6dSt69HDt3cu2QK9Bt4NGyBTHcO/ePQQHB8ttBkWENTrd//jHP7B4\n8WLodDpotVr89re/Rffu3dvodLMsy29vAlobxoTiJXI7aXPynY2NjVizZg0++eQTvPvuu5g+fbpb\n1sItQa/BzgeNkCk2U1xcjPj4eKxfvx6vvfaa3OZQbIAQgk8++QQLFy6El5cXpk6divv37yM7OxsX\nLlxATEyMkQSoUKe7ow1jUr8O7rAgXFdJCEFBQQFSUlIQHByMrKwso1WcnQV6DboltKmLYh5r56L7\n9+/PP3bjxg089thjSEpKwubNm51hJkViJk2aBD8/P6xfvx6BgYEA0EanOycnB9nZ2bxOt7Ae3bVr\nV5saxqSOolmWhVarbbPqUafTYd26ddi4cSNWrVqF9PR0l1+TSK/BhwrqkCnmsXZXNLehqLy8HOPG\njcPo0aPpLLQbw617bA9rdbqHDh3Ki21wDpplWf7nmBIvscdJC6NihUIBtVrNO9zLly8jJSUFSqUS\nWVlZGDx4sM0/Xw7oNfhQQR0yRRpu3LiBpKQkaDQafPbZZ7LXDinOx5ROd05ODsrKyjBs2DCjVLdY\np9ucwpi1DWMsy6KhoQEsyxpFxSzL4uOPP8batWuxaNEiLFu2zKrDhjtCr0G3hzpkSscpLy/Hb37z\nG0RHR2PHjh1GaUDx0nNHsWnTJqxbtw63bt3C8OHDsXHjRmg0Gqf8bop5CCG4ffu2kQTo6dOn4ePj\nYxRFjxw5Emq12qhhTK/X8z/HXMMYdwhobGzkR7I4h3v16lWkpqaipqYGO3bsQGxsbKd1Uq5wDVI6\nDHXIlI6zc+fONo0jnCSkMDXpKPbs2YNp06Zhy5Yt/KaavXv3oqioCKGhoQ7//RTrsVanOz4+nq+L\nWmoYMxgMIIRAqVTC19eXbzDbsWMH3nzzTcycOROrVq2Ct7e3XC/ZKch9DVIkgTpkivtjapdrZGQk\n0tPTsWTJEpmto7SHOZ3u5uZmxMXFGTnpkJAQ6HQ6nDx5Ev369YOfnx8AIDMzEzt37sTw4cNx/fp1\nVFVV4bPPPsOjjz7aaaNiSqeDOmSKe6PT6aBWq7Fv3z5MnDiRfzw5ORk1NTX48ssvZbSOYi/mdLrD\nw8Ph7e2NwsJCLF26FEuWLIFKpcKJEyewY8cOFBQU4MqVK3wtecSIEXj11VeRkpIi90uiUNqDCoNQ\n3JvKykqwLNumTtatWzcUFhbKZBWloygUCvTt2xd9+/bFK6+8AoPBgM2bN2Px4sVQqVSYPHkydu/e\njQ8//BBDhw5FdXU1mpubsX37dowZMwb5+fm80Elzc7PcL4dCkQTqkCkUiuxcvXoVc+fOxZQpU7Bh\nwwYEBgbyOt0nTpxAZmYm/vnPfyIgIAAAkJiYiMTERKSnp8tsOYUiHZ1LS47S6QgNDYVSqURFRYXR\n4xUVFejevbtMVlGkJiYmBpcuXUJWVhYvVsIwDHr06IEXXngBR44c4Z2xu9Hc3IzY2FgoFAoUFBTI\nbQ7FhaEOmeLSqFQqxMXF4fvvv+cfI4Tg+++/x+jRo2W0jCI1MTExcpvgEJYsWYKePXvS5jNKu1CH\nTHF5FixYgK1bt+LTTz/F5cuXMXPmTGi1WiQnJzvdlrVr1yIhIQH+/v7o1q0bnn76aRQVFTndDop7\n8O233+I///kP1q1bBxsaaCkPKbSGTHF5Jk2ahMrKSqxcuRIVFRWIjY3F4cOHZVkwf/z4ccyZMwfx\n8fHQ6/VYvnw5nnjiCVy6dAk+Pj5Ot4fiulRUVCAlJQUHDx6knw2KVdCxJwqlA1RWVqJr16748ccf\nMXbsWLnNobgQTz75JH79619j+fLlKC0tRXR0NPLy8jBs2DC5TaPIQ7s1C5qyplA6wL1798AwDN1L\n+5CwfPlyKBQKs/+USiWKiorw4Ycf4v79+1i6dCkA0HQ1xSpohEyh2AkhBBMmTEBdXR2OHTsmtzkU\nJ2DNdqbo6GhMmjQJX3/9tdHjLMvCw8MDU6ZMoZuaHk6oUheF4ihSU1Nx+PBh/PTTTwgPD5fbHIoL\nUVZWhtraWv7/5eXlGD9+PPbt24eEhARERETIaB1FJqhSF4XiCGbPno1Dhw7h+PHj1BlT2tCzZ0+j\n//v6+oIQgj59+lBnTDELdcgUio3Mnj0bBw4cwLFjx9CrVy+5zaG4CXQOmdIetKmLQrGBtLQ0fP75\n59i1axd8fX1RUVGBiooKNDY2ym0aT0ZGBhQKBRYsWCC3KZQHREVFgWVZ2mFNsQitIVMoNqBQKExG\nOllZWZg6daoMFhmTm5uLF154AQEBARg3bhzWr18vt0kUCqUFOvZEoUiJwWAAy7Jt/rmCM75//z5e\nfvllbNu2jdeDplAo7gN1yBRKJ2HWrFmYMGECkpKS5DaFQqHYAW3qolA6AX//+9+Rl5eH06dPy20K\nhUKxExohUyhuTllZGebNm4fPP/8cKpVKbnPcmm+++QajRo2CWq1GcHAwnnnmGblNojxE0KYuCsXN\nOXDgAJ555hkolUpeopFlWTAMA6VSiaamJjpyYwX79u1DSkoKMjIykJSUBJ1Oh/Pnz+O5556T2zRK\n54AqdVEonZ36+nqUlpYaPZacnIxBgwZh2bJlGDRokEyWuQ8sy6J3795YvXq1LGs9KQ8FkjpkCoXi\nJjAMcwTAWUIIHUa2AoZhNABOAXgdQDqA7gDyACwmhFyQ0zbKwwOtIVMonROXOGkzDBPBMMxnDMNU\nMgyjZRgmn2GYkXLbZYI+aIlgVgH4vwCeAnAXwFGGYegMGcUpUIdMoXRCCCFJckfHDxzZTwCaAIwH\nMAjAQrQ4OmfZsJZhGIOFfyzDMP3Rei98hxDyT0LIWQCvouVg87yz7KU83NCxJwqF4iiWAbhOCJku\neKzU3Bc7iHUA2tt1WAKA2/hwiXuQENLMMEwJACpYTnEK1CFTKBRHMQHAvxiG+QLAbwDcAPAxIWSb\nswwghFQBsLzAGADDMP9FSyQ/AMD/e/CYCkBvOP8QQXlIoSlrCoXiKPoASAVQCOAJAH8F8CHDMK/I\napUJCCF1ADIBvM0wzOMP0th/RUvKeq+sxlEeGmiXNYVCcQgMwzQByCGE/Frw2AcA4gkhY+SzzDQM\nwygBrAXwCgAfANkA5hFCLln8RgpFImiETKFQHMVNCGqyD7gEF63JEkJYQsgSQkg4ISSQEDKeOmOK\nM6EOmUKhOIqf0FKTFTIAtCZLoZiEOmQKheIoNgAYxTDMcoZhYhiGeQnAdAAfyWwXheKS/H8lB1oK\nMM8x7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19d41335a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot_surface(X, Y, W, rstride=1, cstride=1, linewidth=0,\n",
    "                cmap=plt.cm.coolwarm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeAAAAAaCAYAAABvqo9eAAAABHNCSVQICAgIfAhkiAAACUdJREFU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\n",
      "text/latex": [
       "$$\\left\\{- 2 x^{2} y - 6 x y - 2 y^{3} = 0, - 2 x^{3} + 3 x^{2} - 2 x y^{2} - 3 y^{2} = 0\\right\\}$$"
      ],
      "text/plain": [
       "   ⎛⎡     2                3           3      2        2      2    ⎤⎞\n",
       "set⎝⎣- 2⋅x ⋅y - 6⋅x⋅y - 2⋅y  = 0, - 2⋅x  + 3⋅x  - 2⋅x⋅y  - 3⋅y  = 0⎦⎠"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glg1 = Eq(f.diff(x), 0)\n",
    "glg2 = Eq(f.diff(y), 0)\n",
    "gls = {glg1, glg2}\n",
    "gls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAs4AAAAkCAYAAACZrLzhAAAABHNCSVQICAgIfAhkiAAADe5JREFU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\n",
      "text/latex": [
       "$$\\left [ \\left \\{ x : - \\frac{3}{4}, \\quad y : - \\frac{3 \\sqrt{3}}{4}\\right \\}, \\quad \\left \\{ x : - \\frac{3}{4}, \\quad y : \\frac{3 \\sqrt{3}}{4}\\right \\}, \\quad \\left \\{ x : 0, \\quad y : 0\\right \\}, \\quad \\left \\{ x : \\frac{3}{2}, \\quad y : 0\\right \\}\\right ]$$"
      ],
      "text/plain": [
       "⎡⎧            -3⋅√3 ⎫  ⎧            3⋅√3⎫                              ⎤\n",
       "⎢⎨x: -3/4, y: ──────⎬, ⎨x: -3/4, y: ────⎬, {x: 0, y: 0}, {x: 3/2, y: 0}⎥\n",
       "⎣⎩              4   ⎭  ⎩             4  ⎭                              ⎦"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Lsg = solve(gls)\n",
    "Lsg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}- 6 x^{2} + 6 x - 2 y^{2} & - 4 x y - 6 y\\\\- 4 x y - 6 y & - 2 x^{2} - 6 x - 6 y^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡     2            2                     ⎤\n",
       "⎢- 6⋅x  + 6⋅x - 2⋅y      -4⋅x⋅y - 6⋅y    ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                          2            2⎥\n",
       "⎣   -4⋅x⋅y - 6⋅y      - 2⋅x  - 6⋅x - 6⋅y ⎦"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = hessian(f, [x,y])\n",
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}- \\frac{45}{4} & \\frac{9 \\sqrt{3}}{4}\\\\\\frac{9 \\sqrt{3}}{4} & - \\frac{27}{4}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       9⋅√3 ⎤\n",
       "⎢-45/4  ──── ⎥\n",
       "⎢        4   ⎥\n",
       "⎢            ⎥\n",
       "⎢9⋅√3        ⎥\n",
       "⎢────   -27/4⎥\n",
       "⎣ 4          ⎦"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1 = H.subs(Lsg[0])\n",
    "H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACAAAAAeCAYAAABNChwpAAAABHNCSVQICAgIfAhkiAAAAWtJREFU\nSInt1j9LHEEYx/HPxYDFoRAI5J/1NRqvCwo5CEgQAmdlZaWI4EtIEUh9r8HCvIsgpLAJKRRsAiGm\nOay0sBJBEb0Us2f27nbPFLMLB/eFhdl5nuX3zMzzzD4Uzxu8QgXPsVC0YAuN1PsXdHCLH6ilnR9H\nFm9gHV9Tc228SMan/R/EDGAadfzKsA0Id3kUMYAt7GTMV7GJNexiNqLmPU3MJeN9vEvZFoUEhPf4\nLbXwGDvwEk/wM8d+ICQh/BGS8HXXGCMHloXy+pi814TtruIc3/AUV5hKfG4i6ObS9u8IZvA5ZdvG\n97TzREThGXzCEp7hAodCdawIJTovJOtlRN0Rp5Ia14Vrs5LtOsARNmIHVDr/u9phdB52GZNPzHsg\njxaucVKC1gANnOn9OfUQ83fcz7D+oJQA8vqDUgJoYk84+9IDeKg/6KGIKlhNgnibPB8wiTuhISmd\ntiFVUOQ9kNUfHBeoN2ZE+Qs3hzNIi1wFNwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\frac{45}{4}$$"
      ],
      "text/plain": [
       "-45/4"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABcAAAAeCAYAAADHJYVoAAAABHNCSVQICAgIfAhkiAAAAZlJREFU\nSInt1b9LVmEUwPGPCv2QEKKh0HcymgwiiCJKEQwJSXBIpyAw+gP6AQ1FUxEF/QVBS0NLTS21ROAW\niIsU1PLaEoGDaEU2ZMM9Vx9u99Z94bUa/MLhPuc85znPeX6dyybSlbSPYQqncR0LIUXuYhUfQh/E\niRh/GUtopgN24U6iT+Er+gqBB/EJw4ltEeejPYkvEU9nGPtxDftDf46dkVFODw7hbWHCYTxJ9G3o\nSB06Ylm5cQBrOJz4XMF2vCpknvIYNyv61nmE+4k+joPRLgt+FDfwEN25sdOvTOMjrobei92Y/00y\nr3ErvjNiz7sKTmPRcQ870MCpmOBkyJhse35gD2bxVHZLPuM25vAmDTyEC9gXMoHjJVk2bWzLEbyM\nyfLkvuNAOqAfy7JDTKUn8WnEir7hGc6E/ZzssC/FCkZLEtriL5G/yLV/msV/R/GF1qFYz9tGWT2v\npKxwVVFVz9sS/CIetOBfO/g4Xsj2uq3B69TzUurclrOq6/n7Vif8E001b0sr97wh+0+OYC9W8K7F\nxLbYZH4CR6tIdSQBVhoAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{243}{4}$$"
      ],
      "text/plain": [
       "243/4"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H1.det()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "negativ definit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}- \\frac{45}{4} & - \\frac{9 \\sqrt{3}}{4}\\\\- \\frac{9 \\sqrt{3}}{4} & - \\frac{27}{4}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡        -9⋅√3 ⎤\n",
       "⎢-45/4   ──────⎥\n",
       "⎢          4   ⎥\n",
       "⎢              ⎥\n",
       "⎢-9⋅√3         ⎥\n",
       "⎢──────  -27/4 ⎥\n",
       "⎣  4           ⎦"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H2 = H.subs(Lsg[1])\n",
    "H2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABcAAAAeCAYAAADHJYVoAAAABHNCSVQICAgIfAhkiAAAAZlJREFU\nSInt1b9LVmEUwPGPCv2QEKKh0HcymgwiiCJKEQwJSXBIpyAw+gP6AQ1FUxEF/QVBS0NLTS21ROAW\niIsU1PLaEoGDaEU2ZMM9Vx9u99Z94bUa/MLhPuc85znPeX6dyybSlbSPYQqncR0LIUXuYhUfQh/E\niRh/GUtopgN24U6iT+Er+gqBB/EJw4ltEeejPYkvEU9nGPtxDftDf46dkVFODw7hbWHCYTxJ9G3o\nSB06Ylm5cQBrOJz4XMF2vCpknvIYNyv61nmE+4k+joPRLgt+FDfwEN25sdOvTOMjrobei92Y/00y\nr3ErvjNiz7sKTmPRcQ870MCpmOBkyJhse35gD2bxVHZLPuM25vAmDTyEC9gXMoHjJVk2bWzLEbyM\nyfLkvuNAOqAfy7JDTKUn8WnEir7hGc6E/ZzssC/FCkZLEtriL5G/yLV/msV/R/GF1qFYz9tGWT2v\npKxwVVFVz9sS/CIetOBfO/g4Xsj2uq3B69TzUurclrOq6/n7Vif8E001b0sr97wh+0+OYC9W8K7F\nxLbYZH4CR6tIdSQBVhoAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{243}{4}$$"
      ],
      "text/plain": [
       "243/4"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H2.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0 & 0\\\\0 & 0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡0  0⎤\n",
       "⎢    ⎥\n",
       "⎣0  0⎦"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H3 = H.subs(Lsg[2])\n",
    "H3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}- \\frac{9}{2} & 0\\\\0 & - \\frac{27}{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-9/2    0  ⎤\n",
       "⎢           ⎥\n",
       "⎣ 0    -27/2⎦"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H4 = H.subs(Lsg[3])\n",
    "H4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIEAAAAgCAYAAAA14BsbAAAABHNCSVQICAgIfAhkiAAABqZJREFU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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( \\frac{27}{32}, \\quad 0.84375\\right )$$"
      ],
      "text/plain": [
       "⎛27         ⎞\n",
       "⎜──, 0.84375⎟\n",
       "⎝32         ⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIEAAAAgCAYAAAA14BsbAAAABHNCSVQICAgIfAhkiAAABqZJREFU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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( \\frac{27}{32}, \\quad 0.84375\\right )$$"
      ],
      "text/plain": [
       "⎛27         ⎞\n",
       "⎜──, 0.84375⎟\n",
       "⎝32         ⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD0AAAAWCAYAAABzCZQcAAAABHNCSVQICAgIfAhkiAAAAi1JREFU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\nQmCC\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(0, 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIEAAAAgCAYAAAA14BsbAAAABHNCSVQICAgIfAhkiAAABqZJREFU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\nSUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( \\frac{27}{32}, \\quad 0.84375\\right )$$"
      ],
      "text/plain": [
       "⎛27         ⎞\n",
       "⎜──, 0.84375⎟\n",
       "⎝32         ⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l in Lsg:\n",
    "    y0 = f.subs(l)\n",
    "    display((y0, y0.n()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.colors import Normalize\n",
    "norm = Normalize(-.5, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gYWFfa2VDN8JK20Tz8/P09fVx6NAhDh06xA/8wA9s2/nDMOQb3/gGv/RLv9T4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m6SzWYJBoNUVlYeaGDKe/y9wgnEsViMZDKJpmlUVFRgmmbZYLxfHrVt2/zB/5wjX4CZuRSdrSGe\nPbtFZYXIBlKpvLDCGwwxdSnN5aUssZ2sobJC2VFHCrIdz/HM2RjxRB5NwydkURndpYM01us+B6fO\n1qAvyyletdfZB8Cy/K2EupqA+0DeiuewCxLPnN0inSnQ1R7g5FDYly2CGBDz+iVLEiwtZxiZSDCz\nY813560VJSXVns6g+3dWTghiKIrCUL9JZXS3j1uctS2vZpmdS9PWYrhlTkXG178GMQC1uJxjsDdE\nbdXuPfPaEiZTghYUNmW6O/yc1+aGAJms0AI/d1GIadx+MurjHIPgB09Mp3aCrk5fV3Cn7+ovnceT\necanEvR3h6jxrKcqqrk84OGxBBJw50uiPs4xQH2NznPnBE3txKDppgWqIrnv2eSMGGa767YKn00k\ngF0QoiIDPSG37w+CNz4+neL8SJyejl2aV3uzQSJpk8naTM1mODFoIkugypI7qHV+JMFAj4Gq7vCf\n86JlcX4kvlP9EL36pRWL+QXBD3bOXRlVeexn2lw99YOi3PdfVSUe/2AnmWyBeCJPR6tBxFSojKpU\nVTplZ5CwGZ9OoGsywaBCMChjFySWVjI88e1V8oUbL2A6JW9N09yNv2mahEIhDMNA13W3N+0kCYlE\nwu1NZ7PZG6JjFQdk5xxHVbJ+MeJmyZpdT2Rn+MEwjAN5Eu/lPPF4nMrKyqsez7ZtLMsimUy6JaVQ\nKLQnfe319XX3y3M9/NEXpzg/GiccEvZ/41MJutoNJmfSVFUqpNMFKitU0hkRtLrbA8zMZzjWH0bX\nZZ49K7IXr7mDN9uojKokknmsnL2T8VSyspolbCqETZVwWCEWy5LLFzCDGksraTY2LWLbQnPZkVsE\n0fOc8QT6aFghnSmQ9bg1Fb/m5FCYi2OJHREQiZm5BIGA4uuz9ncHfUYGINTE1tazNDcajE3GkWUJ\nRYF4YndD0NSgs7QsyvWaJjHQHQJszo8WyVl6eqjifCHCpuK6JDnwlqA1TWKw18S2S8usXtnRno4A\nse08qgpXVvy84UhYeE43NQRIpfIsLmdRZKit1rlSpBB25y1RJmaSbhneuXdOD9UxlUilc0zOFA/U\nyciyRHNDgCurGdfucaAn5Gb2IErxVVGV54p665oKkbBK0w4/2KEkebPZ+lodTZW4spKlulpl2WPa\nUVcjXKKK7xPAS28N8/SZOMWPt9tPiWvL+vcq3HbS5LlzCd9DrrPV4Mpqho/8XDcvfcmNiVMU+/wW\n49tPbfB3/7zCyEScU0PCCer2U2GeOSsm4k9fiHNiwGR+KY2EaP/EE3kCARlFhvt/vJZX3lO95/Uk\nk0lkWd7Ts6IcirNppz/tRTEV63rZdCKRQNM09x4tLy9z4sQJt8/9bwA3S9Z7gTPM5ZRm0un0oQZi\n73mgfBbriL0nk0ny+TyqqhIOh/clsbnXobGxiS2GxxMYukoqnUdRJFqbDDKZAplsgZbGIBPTGXRN\nZWZOPOwqogqN9QFGJuLuZLOu7ZaAQVBhKqMqJ4ei3H5LBfW1Om3NQRrqAihK6WcxkUi4dC3btt0B\ntWy2wPyi6A1fupxie9simcq7pfCu9pCPxlQcjEH0hHN52y0N33Iiil2w0bWMe5ziLLylyXApWGsb\nFtGIysmhMD867S/dVkR2rRUty+b8qNjMnBwKMzohHvaKDMsr/uA3M5ckEtY4MRhmelZYMGoqrjiG\nc7zh0TjtrYavtA1geZY7OZtBUyVuPWGytr47CAW42uNTsylURXIzxrMX/YGrs83g6TNbhIKyuymI\nhBUfPcvhX586FnatBR04w09jU0kipsJAb5BUKu8LxiAmgnO5QGlPu08ER8F/DlDIC89jbx99eTWL\nrkvcfmuUp57xvw8raxYVUZXeziATHmqVGVIYHk/S22UwNZt2tcyjEZWL40lam4PML6bdCoSqSoKC\n1b/LlwaYmU/zH/9DDbceD7p2gDfyPLhWMLrvriqmZkX2v7Qs3tvJmRT1tRpLyxma6vUdr25R6Thz\nYZvKCo2OVoN83uaJf1nlx15aiabufX03Umq+ns2iE6T3Q8cqfnbFYjGi0ei/CnrWYeHfxLbjRpFK\npdjc3HQDcjQaPRLR9asFZEfda3tbBBlH3Wu/etd7Dchf+pvLhENCT3dhKU06nSOdsZicTXPqWJjT\nF5LEdtSaqio1XnIiwnPnkywsZRjoCbuCDv29JvFEnmP9YT743k5+4/EB/ubP7+DjH+7nJ1/bwF23\nVdHcaJQEY6cc71hf6rpOZWWl68UcCCj0dJq84p4aHnm4lQ+8p4u//KPb+L//5DY+8eF+jg9EaG/d\nnXQVsoy76OkIlJRRl1eEhObKWpbuDoM7bon4dJVBZPVeJFNCQlPTRFAL6BKNdZqr5+ygr0u4D527\nGMc0VY4NmAz1m66bkYP+HtPVkZYV0Yse7DPZ2PRPRw/2mUxfSjMykaCnM0hjncZgb4i5osGwlqYA\nT5+OU1mh0d0uhoVqqlQmPPaTubzN2GSCzS2Lzjb/QJHzriRTBS6MJuhqD9LbGSxRIRvoDXF2WATO\nE4OC311Vofom3LcTeUYnUlRXqSUylkP9JvOLGS6OJzneb6LrEmFT9s0XLCxl2NzKc2Iw7BvCA1Hq\nvjCy7ZaW3fvUK0rwM3NpjvXv/q6rPUg8UWB8Kk1XW5DAjiRma3OAZKqwI4lquD8f6jO5smoxPJba\nEWARqKvReNODNVelDlmWtafy7F6rkG99fQNtzQEWrmQ5eSzM5laexroAy6sWlRUaly5nRNa+kqGr\nPURbi8HF8TiXl4TD1798b2NP59nPmvYDZxCsnJ73XuhYgPs7y7L2zUHeD8bHx3njG99IXV0dFRUV\n3HfffXzzm9/0vWZubo4HH3wQ0zRpbGzkl3/5l0uqAGfPnuXlL385wWCQjo4OPvWpT93Qum7aLyIC\nslO+cWwJj6JEUmzxmMvl3A+jJEluv+ag9o/pdLpkUKMY/+urlxmbTDC/lObKcoaONiGs0Vhv0Nxo\nABJLyxlaGg3CYYW19SzRsCp4kYjsY3MrR0ujwYP31/Pz/7mLh1/fzFBf2Nczvtr1W5ZFIpEgk8mg\nKAq2bVNRUbGnXXAoqNDeGuS2UxW88Sca+YlX1tHZFmR5LcvSyq7tYEVUZXNr96He0yGGZRxsxHIE\ngyoBXaarPcT6ZpbqKp25y36P3+P9ES5dTpO1xIBUxFTp6QyxeCVTVCJWie1Y+6XTBdY2LKoqNCJh\n1S2Ri+G4Xau/bNYmtmURMTXMkExsZ/hJkSFXYMc5S9B0MtkCbS0Gq2t+q0fHJjGZKrARyzPUZ1IR\nVVks2owM9ZuMT6fZ3Moz2BskkcwLa8VLfhqXLImMdKDHdKsIgpMrJtXzBfH7rnbRe/ZysgF6uxzH\nKY3aGo3YVh5dl0ilC+51r6xZ1NfodLb73xOAaERhdi7F8YEwK57S+mCfyfxChuVVi8Fek9iWhSwL\nW8pkSoiGrKyJAT1Jgkvzu+/j+maO1iaDhtpd6pnzGWhvCWIGFWbnU+59XVmzONYvrBX/+89309Mp\nZGc1TXPpQI5/ujPwZFmW6xrnVcDyfqYty0JV1Wt+t1VVZqDXFP7JFRqmqaJrMnW1OrIsHLByeRtd\nk7FyBdLpArXVAeqqNbbiOdY3LO57WdWevkuOkNHz4YVcbLPo3E/vPXU2NoVCgSeeeIIf//Ef56mn\nnnKfE5lMxp3hOQzcfffdVFdX8+Uvf5kPfOADTE9P88u//Ms8+uijmKZ5FNaLcNN+cW9wdrr5fJ5Y\nLLZn7ef9wqEmhUIhcrmcy2UOBoN75jJfC7FYDFVVMU2z7O83t7L85mfG2YpbhAyZtQ2Lza0CwYBM\nU4PB6GQcXRcbkf5uk2fPbREISCiy0AxuazGoiGg8/Pom7rmjal9DLk45PpfLoaqqew+SySTV1Xvv\nfV0N8USO7z69wY9Or/Mv39sg7wlcPR0BJmd3H/4tjX4bx4qoyonBMM+cibnKTCA8fhc95eTqSo2t\n7RzVVRrVlSojE0k6W3Vm5v2ByUuHGuozWVzJ0NpYqvrl9NxlSfSbp2eFGlSxZaJT6hXKVTKTs0JJ\nqnj4rL5GJ2MVaG4IuFKXhiGhKbKvPF9ZodDZGuR0UU93sNdgZGLXGjO2laehTveVmUHolGcyBVqb\nDfc8IHjUjriHY3eIbXOuqMdbVaGSyxVobjJ8fsleHnp/d4hLCymCAYVEMufr+Xa0GlRWKpw5X9o7\nvuslUZ4qmmoHIak5OZN0J6cd3HEqwpnhbV/JX5bhTQ828J63t5QcxwsnMBdPJjtwyrqSJLkb/b08\nV77yN4t8/5lNNmOCsz59KcXxQVHef8nJCGOTSXo6xFBkMpUjFFTI5cT8wcM/2binievr9bSfbzhD\ntIZhcOnSJf7hH/6B73//+3znO98hmUy6ra3HHnuMz3/+8zd0rrW1Nerq6vj2t7/NvffeC4j7EY1G\neeKJJ3jVq151FNaLcNN+cW84SgtGL5zjJpNJLMsiFApRUVFxYBpVMa5Vsi4UCnzlr2eBPIYusbKe\no7E+SDpToKMtyLmRbQZ6RZZbVaG66k793WGSqQL93QYfel8nn/3kcX7spdV7Dsb5fN5VNLNtm3A4\nfCT2k2FT5YFX1PFLj3Xyhf/RzX/6qVqaGzTq6zSmLpUKeniRzRZ49uwWmiZz6lgEIyAx2GP6gjEI\nGlcub7O8mmVkIikmYsvIJ25u7T7dL44nyGYKaJrkV5uSd3vHhR1FJl2XUNXS++pkz1dWs0zOpjk+\nYFLuuV5XoxHbynFxPMFAT4iKqEJfl1nSK6+vDXD6gtB3NgLifLXVGhPTu9c7fSlDJptHVUo/T3U1\nGtuJPBfHExzrF6X8gZ6QT2krn4eJ6SSFAj4LSBAbou1EgdEJoSUtUaruNjaVpKpCo6PNKBnAurKS\nZXMz77p/OehsNXjquS2ODxSXtk3ODsepqdJ95fS+rhA/OrtNd2fIp7UeCir81IP1pTe4CJIkueVZ\nwzAIhUK+8qyqqr7ZlEwms6eS91vf0EhAl9mOW+i6TCiksLqWJWIqLCxmyGYLpLPCVKO6Siebtcla\neXRN4u/++Uq5pfrwYtWxBrGm7u5ufu7nfo7Xvva1vPKVryQej3P27Fm+9KUv8aY3vemGz1VTU8Pg\n4CB/8Rd/4SYJX/jCF2hoaOD2228HXhjrRbgZkIGjD8jO7s95kzRNu2EKVTlczRM5lUrx7NlFZudS\nyLKCqqkossT8YppjA2F3cMgIyKysZais0N0SoyJL/Mp/7eY3P9LOUF+45JxXg1fa82rSokdheZlK\npaiqVHn4Jxv4n5+7lV/7b/3cd1e1GwzDpsJ4kcRjb5dJKl1gO57n7PA2uqZQUaGha7vvjRGQfD1P\nEFSs8yPCGrBih/7U1x0sMbLobAvy3LltGusDdLaJkttAr1nindxUb3D6Qpz+7pC7aRjoCZUcL5HM\ns7Jq0de920evqVQZ8fR0RyeTO8G99N46PWIxxKXS2WbQUKf7rA0BOlpDnBtJCevDncBdU6X6eujD\nYwkqK1RkqfQ8vZ0hLowlMEMqLY2if11dqTIyuRt4z12M09sdoq5GLXG8siyb2fm0K3XpoK87yOx8\nmnzBprF+N8OTdjaJF0YTDPUFkcCVpQThv9xQFyCgi82Rw58enUj6etCPPNx83fbL1VBMHQqFQgSD\n4n3Sdd19eOdyOTKZjNtDTSaTpNNpLMtCkgr810fb6WwPMTyWoKPVYOFKlu6OIEsr2Z3hwSSDfSFm\n5pLML2Z26IrCh9o7aPmvBddyetI0jZMnT/LOd76TV7/61Ydyvq9//es8++yzRCIRgsEgn/3sZ/mn\nf/ont2f9Qlgvws2AXBaHFZCdYLi5uelObgOoqnoku1NvQHZoXJubm6RSKb79VJy0JcQ0UukCkbBG\nfW0AbPGAv/0Wx+fYZiNmIcvwjjc189u/Osgr761xj7mfa3b424dZBSgHR1fcsbwE3F788YEIH/ul\nfr78hy/hrW9oYqgvXGLvt7ruLzlHwipPPbtJJCxK2bIE3R2i9+pFVYW2o8ecJIRdltoAACAASURB\nVJu1OTFoUsiX3iNnCG5hKcPsvMhw40XHAtjced3YVJJ0WjhFpdKlr9M1mY1YjvGpFMf6TYKGRF2t\n5k4TO2iqNzh3McFQn+n6Ofd1+YfDVtYs4ok8iuJ35JLADWQXx5NURjRamwI01gd87QBxvxQmd7x8\nHQQCEtNzIjAsr2ZZXbcY6jNpbgy4giTe+7MRy/k4zwANdTobmznWNix6OkVQCwVl181qYzNHIpGn\nrSVAX1fIV8K/OJ6iv8dgqDfk46MLvrnBiYGwr9d+YTTByaEw3R1BXnf/blZ0mFAUxcfvNU3zqvze\nmso8990pNgn5XIGgIZPKCIW8VKZAU72OEZBJJm2OD5gsLGWYmk1i5Qp8+wfXHu56MWbIDrxr2q8X\n8l6tFwHe//7309DQwHe/+12efvpp3vjGN/LQQw+VODc937gZkPFnyIehN+0NSqlUCsMwqKysdCe3\nj6ok7gxHFAuKTM7aTM9lyWRsBnoijE4kCAZlzl3cZiNmcepYhPRO1tTRalAo2Pz+bxznvW9vR9fl\nPWWyxRsAwzCoqKhwJ6evtt7rHfdaKBQKxONxtra2KBQKhMNhQqFQ2WM21AX42Z/u4Nc/1M9/fme7\nK7rQ21Vamq7eCQzORHRDnd/cAITcpFdZLJUusBnLkUrbbhYMQr3LW8q1bSEgsrWV8xnd93X5M+tU\nukAylUfTZF+gam7QfecdHktQVy0oMV4oCq4M6cXxBAFDoafDwMqVarU31gc4O5ygsy24m5n3hrji\noW1dWc2SteyyrQpRMrUZnUwz1BdEkcV1e7nbmWyBxeU0tl16/poqjYWlLPmC7WbDNdWaq4SWSheY\nnU/veBCHfH3g7USetXWhW12M2fkMUpkn3MJShoJtU/yxPHcxzgff3YZygwIge8X1St6ve00dfd0G\n80tZ2lt05hcyqKrN4lIGVRU0w57OIJlsAU0TA2G2LfHdH26WbB5f7Cj3DNjvlPUv/dIvMTIyctV/\nFy9epLu7myeffJKvfvWr/NVf/RUve9nLuPXWW/mDP/gDgsEgX/ziF4G92SoetvUi3AzIJbiRgFwc\nlHRdp6KiwkehOkpPZGeoJJEQSlLRaJRgMMQT314nZAgHpfnFNC85GeXZs1t0tQeprFCZmE643NN7\n76rmj3/3FMcHI3u+5mw2W6IodhS0Me85HRU1by9+L4NxoaDC297YzFf+8CV88D2dVBRRnYKGzMR0\nouhnCudHkvR2BqirFq9vbwn4hElAZIoLV3azYDMklw0IuZzN5laO0ckkg70hIeRR5vmpKDKTMylS\n6bxbUq3cycp9540oTF/KcHLQxBmaHewxfWIf6xsWBVsiElZ9gShsym4Jf/pSCsuy6e8OshUvXVB9\nrc65i3GO9ZvoO3uEns6gb1r64rgYTIttl/59c4POhdEU/d2G63hVXaW6LZPNWI7VdYu+rhCNdbov\nE8/lbOYW0khlSvCtTQZjU6Kn70V3h8HZ4QQnBv2tlr7uEOdHEhwf8P/87tsrGOrfe1tmv9irAY1T\n8g4FDX7xv3SRShWIbeepqxF68031GlauQNAQ3PZcLo9kF0ilc6TTeaJRhW9+d+2q53gxZsjl1rRf\np6eamhr6+/uv+U9VVZfVUvx8cqoUIKawz507x+rqqvv7ctaL3/rWt8h7SlM3Yr0INwNyCQ4SMK8l\nc1lMKziKgJzL5dja2nKHRyKRiDs49bVvrrAdz5HL2QR02VVxkiWoiGqcvxinp9MkX7D5hf/SxXvf\n3l7C670efzoej7sbgHA4vGcqxUHkPp0Nj9MCKO7F7/WYgYDMf3xdI598fID/8ki7623r9JO9kHd4\n1BMzGdZjOU4Nmaxt+AOOGZJccQrbFiXQ2ioFpegb1tIUcEuuIPSlG+o0lxProKFOczdJyZQY4Dk5\naPpERECYOczMpbFt4SHc3BCgsU5jtag/DULI5dzFOJ2tu5lwV1vQV8KPJ/LYSNRUakWBW2F8R/p0\neCxBXW2A2hqt7H02DJl0uuD2jcX9UVz1tbGpNM0NASJhmcY63dc7TmcKrG9my7qudbUHOXuxNMCm\n03nSmQIra1naWgLuGmbnxb0S8phh9zqcDdf5kTgnd3jHisJ1p6oPihv5vne2BXnLGxqordZJpvJU\nV+pMXUrTUGcwM5ehozXE1nYBKy/oabkdTdBvPbVOIpEgnU77JC29eDEFZChdz1HxkO+++24qKyt5\n5JFHOHv2LOPj43z4wx9mZmaGBx98EHhhrBfhZkAG/B+E/QRMJzvc2tryZaXXCkqHGZDz+byvZOtQ\nGJwPTDxu8fTpTWIxi63tHJoms76ZZWI6wanjUYZHhRBJLmfzOx8d4qHXNFz1XM71Oud1hExs2/Zt\nAA6CvQgrFGfhTgvgRh8qui7zltc38+U/vJWffrjFZ5QAgiI07ZHxzOdxdaP7PSXn7g4TqyhjNk2V\n0ckUfV0G0Yj4PETM0q+crimMTCQ51me6+skiGyq6D0iwY8zgoK/b9JVw5xbEgE9N0QRyQ622mwnP\npchZNkN9oRJ3KXGNNudG4nR3BF3P5a724K7VJsK2sTJSOgshSbC8YrnmHc7gWXdH0Ecpu3Q5Q02V\nzmasdOPQUKcxMpFiqNfTk9Z3VeHOj8RdAY/eriCXFkTgTaYKrG/kaGkK0NNu+O7LuYtxTgyG6Wo3\nSKV313F+VPTYH3hFLa3Nh8NxvRoO+ll96xsaiUZUllctFAXSGZt0ukAqbSMBC1eyNNQHhCCMLRMI\nCBrUylq+rAiH4253I7rTh41ya9je3j4SHeuamhr+6Z/+iXg8zqtf/WruvPNOvve97/F3f/d3nDx5\nEti1XlQUhXvuuYdHHnnkqtaLMzMz3HHHHXz4wx++IetFuMlDBnYf+IAbZKLR6DX/xrIsUqmUy6sN\nBoN74hjG43EKhcJ1j38teB2ovDxmZ2rT4fX+zd8v8INnNkGChcU0kgS1NfrOpgDOXdymv8fko7/Y\nR3PDtR9G6+vrGIbhVgMOgz/tZPbXUiUrx1++VuC/ES65bdtcXtzmz/9ynm/9YAvbhluORXwynSD6\nvY5TVW9nQHjlyjJrHmUuXZdQFcHfBlEa7mw1GJ30Wweapkw2Y7s/q65Uqa/TmZpN+cwldA10XSGe\nEKYfJwbDXByLU1WpsbLmD2rdHUGmZsXA18SMGDgrZ9l4YtBEkiTOX4y7X+6WpoDrkQyin14RUVhb\nt0rK2EN9JmNTIqA5etJ9XYZrJwlCbOTEUJip2VSJAtfJoTCz82miYcXts5shhXyhQHonaDq61sf6\nhQWoF8f6g8QTeS5d9g/l1dVoGIbE3OVSJbbGBo2RcT9/O2wq/J+fOkZ15eFrD4B4VmQyGUzTPPB3\n5eJ4nA99XAwkNdbpLK9l6ekMMb+QFoN2eZuNWI6u9gAT00l0TebNDzXwUw82+iQt8/l8Wd3po3Rx\n2gvS6TSFQsE3A3Lffffx6U9/+tAmq18EuMlD3gu8H7zrDV05E71O4HZ4tXt9+N9IhlzOgco7wewt\n166uZ3j69AbrmxYXx+JC5GI5ixFQODu8zdZ2jq72EL/13wevG4ydL69T/jos/vS1ysve7N+5z3uR\nEz3IoJi35RAycnzofR38H795jBODYeYX/RlkTZXmWiyCKGPXVGs01um+Em9fV8gNxiDMKSRJpqcz\nSNjcrZ50thq+AL2+mUOmQF9nEG+RpbfLdAOa2EzFOTlY2u9sbtDdkvjwWIKaKo2u9qBvEAxEJru6\nlhW0o66gyxWuKOJVr29YmCGlJHusrtIYnUyQzwsO9YlBoZKVyvgf9AUbCgXbdbtyENBlpi8l2drO\nsb5pub/vbg+6wRjEsU8dC5eojwEkU7bvXjqoq1FJJApURPy/a2sJMD2boa3oWl77ipojC8aHhaG+\nMP/hVbXYNjQ3BsjnBU3RsmxChszlpQydbQZr6zmqKnS62kN866lNCoWCT9LSK06yFxena5W8DxPl\nrBePUjrzxYqbAXkH3h7k1QKEI3CRz+fdALHfDPGgPepUKkUsFnN7p+UmmL3B6O+fuEKhIFFXq9O7\n4zV8rN/kR2diNDcG0FSJ3/vEEFUVV38QOT1bhz+tKAoVFRWHzp/2wstftizLx18+CliW5Ws5OL3/\nof4on/3kCd7zjja33AziYVjsdCchcWE0QXe7QV2NuJ9bZYaaruwIimiqRG9XcMf+sbRku7yW58JY\nkpZGneqdXu9GrDQgbcVzJJN5+rp2g11VUWBZvJIlElHobg/5ft7TEXSNIsanU4SCCn3dQddz2ouN\nzZzoYQ/tbgBaGgO+3u/5kTinhkxWi7J1SYLVdcsdBnPmaPq6Q+4UdjJV4PJSmsHeEJcu+7NXEC2V\n1qbSTaOmSVwcTzHUt8sh1naMItY3c5imTGDnYxM2ZcYmk2SyBbYTOSorxH0NBGQefujarZrDwo1+\nZ9711maiEZVM1maoz8QuCNETJInB3hDZbAFJgkhEJbZtsbGZKzH6KF7PXoRNblTLe6/49+6FDDcD\ncgmKA6aTqXkFLvY60buX418L5aa2vfSpq2FhKcXEVJKCDYlEHpAImyqaJmPbYrf9ux8/RkWkfDAu\nHlJzrlXTtCNzv/JuOjKZjOs/vd8sfK8ZsvO+eg09IpFISe//J15Zz+d/u4/7X16JLO9SiRxETNkd\nVpqcTbO1neOOWyIlmXV3R9DVh96I5ZiYTvHSW6Nsxf09696ukGtKcelylkymwB23hFm84g909TUq\nk7NpEqkC49MphvqCRMNKSSYsS3B5QXg+nxwSnGpxn/z3Y2XNImQo9Hb7A3d3e5DLO3Sscxfj7lT4\n1Ezpgz6dKVBTpfo2ML2dIdfoY3gsQW9niIAulThhZbM2iiLRUO8XAQGIbedKKgJN9TrjU0Kzemwq\n4faq+3tC7oT3wpJFW3MQWRZ0PqcHvhnLYQYldA3+wysrCQXtI+2nHtYxI2GV97y9me14joUraRLJ\nPCMTcWzbZnImSSAg7DAlQFdl6mpUvvf05lXXU+57VU7YxOuJvBdhE6+m915RTtBov1PW/xZwMyAX\nwSse783UDrNMe5AhJidzu1ZAdNb1tX9ZJZ+3icctthM54UmswNRsko7WID/33k4i4fKl36tljEfJ\nn3acXbybjmvxl28EXtU0bwZ+rZZDJKzygXc18/v/23HMkD9gtzYHfApXmaxNKl2gtzPkZmGAT/XL\nwUYsR0OtTkPtbvZf/PYmUgUSSSE6onpcs+pr/YHr4niK7s4AAd1/gJ7OoCvwce5inO7OEB2thtsD\nd6AqErPzaVfO8mrrHplI0t8dQimy+RP0uRSXlyyCAdmtFBSPnoxNJTnWH2a7aHgOhOTo1GzKp0DW\n3RF0e9rnPMNc1R5udj4Ps/NC33t51b9xmZhJcXxAuGd5cXnJorcrxBt+4sbdnPaCw/osv+blNYRN\nhVQqTygko+syllWgUIB8TiibmUGZlXWLXN5mei5dNtjtd5PrLXnvRdhkvyXv4jUdxqzNv0bcDMg7\nKNe/cPq0hylzeb0MzgmIB6ESSZLE8qrFyHiclbUs4bAwAZCwXeeY3/7VQSLh0uDj7Y1DacZ4VHQt\nwHV02cum46Dwlt+9lKm9brBs2+ZYf5g/+K0hHv7JejdwrhdZJ2qqUIMan06Sy9kM9IiM0uvXC8Jg\nYWJGyB7G4kLFqrJS9XkRA0RMhfHpBOdHErQ2B6iqUHf6r/7jSRIsLFqoikRr026AzxfJak1MJ6mu\nUGio87cAertCrgb3uYtxjveb1NfqjE6VZsKLVzIEdJl6z0airdlwecNXVi2yVoHjA2ZJ4AdRaq+v\n1d2JchBT3JcXM+RyNjNzabcMrxZZd14YTXDr8bDPJxpEhh00ZBS53GdUoqcjVPLT/p4wjfURXwbo\ntEYOMwM8zO+NLEu872faaGsOcmE0QWuzwdhUis4dU5LOtgDj00li2xbhoMrySqZE8vWwcNgl72LZ\nzP1QKP+t4GZA3oFTMk0mxYc3EAhcV2nqILhaQHYmjosD4n6oRJIk8c3vbpLL2RRsODu8TduOI4+h\nK3zyVwZpqPNnVt7hKW9v/CjcrrzndPjLAIZhlC0XHwTF9/cwKFPe1+m6zLvf1sJnfmOAu26LcmXF\nn5H1dJquSlI8kWd0UvTui9WfWpsMtwebTttcHE8w2BMqCUAdbUFXanJmLk2hYHPqWJhEyh9oO1sD\nLK9ZbMRyLK9mGeozqaspNdbQVInx6STbcb8/cibj73lf2NFQLlbA6mwTusora1nS6TxtzQaqIpX0\nfmNbeVRVKhHraKjTmZxJMTufprZGc4OyNxO3LJuZ+TS3HA8zVrQhsG3I29BdJsAKK0bhtexAVSTm\nFtNcGIv76GKqIvFTrxMGEtfy8b1WBugEaScDfL7oQ72dIW47FcW2xWAXiP+VJQSVbCvPicEIw+PC\nw/r0BT9LYL8Z8n5w0JK3bYu2wcbGBk899RTLy8t7tmW9Fn7rt36Le++9F9M0r+oqd1i+x9/85je5\n/fbbMQyD/v5+V/VrP7jph7yDzc1NMpkMmqa5MoxHsTtzdoyO53I+nyeZTLobgRvxRF5ezfD/fu0K\nWQuqK3WwbdY2hHfs+9/dwalju+UfhzqVSCRcuoFpmlfV2XZoYYFAaY9vr3DKxYmEyG5CoRCWZflE\n9w8DqVTK3VA4ZTNFUQiHwweqdDg7+UAg4O7oa6sD3HNnJfFExkfzqapQS7JmbCFUEQkrPuqPV95Q\nkkQPtjKqoWmS64esKPj+JpO1CWgSrc0BX3m2vlZjbUOcN18Qg1SnjkVYWMr4isYDPSYLV7JYOdiO\nC39kRZGYL/I2VhTYjueIhlVUVXLNRpoadLfHncnaZLN5bj0RcfvoDnRdIhbLEU8KP2In+xZlZXGu\n2JbQZg6bKjPz/r8vFETwDgZkn3uWqkqkknnWNiyaGwxXJ7ytxeDSvOirtjQZbMdz2LbwUp67LPyr\nLcsmGlVJpgq86r5q7n95DdfC1Xx8vb7GhUKBXC7n80Z2Mmgvbx841E1ub1eIf/zGKtjQUBsgnsjT\n3BggnS5QXaUhKxKbsTyDvSHOj8R56DW77lXO5uEoN91eOAwQZ9OjaRq6rrt+yM5zEOA73/kOb3jD\nG/jSl74EwJkzZ5iYmCAejxOJRAiH96ek9o1vfIPbb7+d/v5+nnvuOR5//HHf7w/L93hmZoYf+7Ef\n461vfSt//Md/TH19Pe9///u5++676enpcU73Ca6DmzzkHTg8OGeY4Kg8kR11q3A47PITJUlyyzw3\nsiP80v8zx+nz6xQKCrHtPFWVGqfPb/HYu9p580PNwG7pNp0WvaVgMLinIHUjPR3nnI5knWEY7jnX\n19fd3fNhYX19HUVRyOfzyLJMKBRC07QD39tEIkEulyMajbrB2Smrx+NxRiayfPZPL5PP28S2c77p\n45bGgDsUpesSvZ0hUulCScnZ628cNmUa6wPkdjJFLxrrdJZ2BqKOD5iMTiQJGjLJdN5nLqEoEA4p\nNNYHmJlLu2pcXe1GST/1ZbdHeerZLZ8QiZdPXFWhoGsyyVSBVDpfIvPZ2ymCunei1+sJbQQkmhsN\nLi9mUBVKsvs7b4lwbiThBn0QtChVAUkWPfzFK+Kah/pM14O5IqqgqfKOcUXI59s82BtkZCJVwqtu\nbgywvpnl939jkI5WPxXroHCCr9cbOV/s9AHuUKTjkXyj2d//+sdl/vQr87Q0BFhayVIZVcnlbQxD\nIqArREwhk3rpcprP/eYgdTWiHJ9Kic+Z40L1QsPrhZzL5RgeHna1ptvb2zl9+jTb29u87W1v4y//\n8i8PdI4vfvGL/MIv/ALr6+u+nx+W7/Hjjz/OP/7jP3L27Fn32G9/+9uJxWJ89atfdX50k4e8Vzi7\nXudBe9Tlp3g8fqg96ngix9RsEtuW2IrnqIiq5PM2991VzZsfavZNTh9keOpGJEWdKfFybYDD7E07\nbQcQWcl+NK6vhWutUZIkTh0L8/n/McQr7q0qsRD00pCyWZvhsQT1tRp6kVRm0NNPjScKTE6naGwo\npXrVefq2oocYoLvTKHF66ukQ08ajk0nq6zQqoyoNdXpJMNY0ifMjcYb6TPxFmd31bcTyJFJ5+rqM\nkmBcX6MxMZNiYjpJf8/uA96reJbO2MwvpsuW2lVFYmwqKah4nrJ1b1eQRKpAPFEQWd8O/SvpqSo4\nZfHmhoDPEhJgZCLF7afCvmAMwljix++uPrRgDLuZtFOmdUrezkbTeaYc9mTyQ6+ppale3Lf+nhDR\nqEprUwBFljFDCjPzwv2ppSnA06e3Stb8YoRhGNx222309fUxNDTEt771LTY3N5mcnPSpZB0WDsv3\n+Ac/+AH333+/79gPPPAA3//+9/e1npsBeQdH7YnsBAunb+pMTh9Wj/r/++4qq+tZ4glh3D48tk06\nU+BDj3X55D1VVT3S4SkH3mnta02JH5a7ljfwgyitHyVfuhiRsMrPvrOND7y7zQ0sjpmHF7omcWZ4\nm/oandodeUsjIJfQiDRN4syFbYb6TLe/Ksv4rBNB9JWTqRwNdf5qjvey5y5nUBSJ1sbSdkNPh+AD\nD48l6O4IEtBlaqo1JoqGseKJAivrObrb/ZWM2hrxkMoXYHwqxUCPQUuj7jOcALEZWdvI+pywAHq6\nhBHF1GyK7vagOyzn5XFvxHIEdJnerhCzRde/tJwVmtll3ubteM7XN3bwinvK9xIPE94SrdNXPey+\ntKbKPPqfWjBNldn5NGFTYXQqSU21xuXFDE31BpIEs5dTjHo8qF8MUpleXMsLGYRYU3d3N/39/Yd+\n7sPyPb7aa7a2tlyp0r3gZkC+Cg4za/Nmpk4Z3OkhHwbyeZtnz24hAXOLGWYupejvCvMLP9uBXUi5\nPsH7NX/wYq+B0zucdqPn3Au8gd/ZbByF7J/zPjpTos5D05EkdPDQa+r4zCcGaGkM0NMRZDPm7yd3\nd4RIp23mFzOkM3l6O4MlOs8APZ0hUjvDXo11OlUVKj2dIV8/FaCtOcD4VIbteI7uDhF8KqJqCR95\nI2ZxeSldopiV91C2xqdSNNRrtDUHSvpTnW0GcwsZ5hfT9O5MQAuLx93es23D6GSaxvrSVk9Tg87U\nbJrl1Qytzbsbg7xHpWx0MslQr0l7i8Hcgj/wLi5nqapQUFX/+6ooMDGT9ImDAFRXKoxPp1lezbpG\nGs513Hp8b05mR4HrTSY7QdqZTHboQ6lUykcfcr6Ld91WQVO96CHLktj45PPCTSwYlBkeS9LaZLCw\nlPFZdL6YMuSrOT1dTaVrP77Hz8e6DxM3A/IOjsIT2ZnuLc5Mnd8fFr79w3XW1rNIksTxfpPVjRz3\n/3gFddU5n7znjQxOXe+elPMm3ss5D3qvvQYXcHVhj8OAU05MJpMoioKiKO5DE8QmxMu57GjV+ewn\nBzg2UDqA4r3WeKLA5EyqrPxjzkNXcswTijnQgGsfmUzZzM4L/eq2ZqOkdN7TEWJpxWJ+IeX6MFeX\noVnNXc6QSOapLLKlNIPi3FkLZubEMXq7QiU2i5omMTJRGiCrKhR3nRsxi4Y6jZoqtYQOdmEsQVOZ\nUn3QkDk7HPcZeoCYON6I5Xb0rnfP2VgvzDm243kqIqo7vf76B+p5vnG9qWbvZLI3SIdCIZc+BJSl\nD2WzWR68vwoJQVerrlSZnElSX6uzspolFJRRFYnzIwlGxuPuel6M8N6jzc3Nqwbkvfoe7wU34nss\nSdJ1XxONRvc1CHszIJfBjQZkL5dYlmVflngUJfGnntlA02Vi8RzJVJ5bj4d4+V1hn+zkUe2Ib8Sb\n+CDwSms6ymnFNK3D6ks7Qd+xtXS+XI7JhbO5cqZwvZmNXUjzyJureeThXc6yGZKZKCpNR6MqT5/e\n4ni/6WZ/QgnLH6gy2QITU3H6PUpaigKX5v1OVMNjCQKB0vuu7AQkKyfEOY4PmLQ0lWbCXe1BxqdS\nBHTJ7dsGdJnJS7vrzuUEn7ncBqG73SCRtBmdTLiBX9MkXwk7kSiQyRRobS4NvEZA4vT5bY71F0l9\ndgq3qeFRv/1izpfhJ2hvMdBU//lm5tIM9plEwwqv+rGjL1cfBq7Xl/bypZsbZO57WYRcHtpbdVJp\nm+ZGjcXlLH1dIZZXs7Q0BfjRGbF5PUra00GwX6envfoe7wWH5Xt899138+STT/qO/bWvfY277757\nT+twcDMg7+CgFoxelBPXKGeIcJiDTFOzSTa3chQKeTTFZnnV4v3vaj6Q7OS1ULzmvXgTH+S4V4NX\n2MOR1jwM5bRy8Kp55fN5N9hLkuRO0WazWSzLcisqmqaVzWze8EA1v/pfW4iYMm3NgZLhq7amALYt\nMsPWpgDRiEJHy67IhoPOtiDxpM34dNJVq+ruCJU4MDU3BnjmzPaOk5P4WSgoMzmzK6Rh2yJwa2rp\n19/htV5ZFXS52mqNnk6/4QNAOKxybnjbt0EAsHbKooWCKCX3dQXp6Qy6utUOtrbzbMcLrr2je53t\nQuJyZDxJd8duZrG5uUvxujAiNib1tbrP6MPKwXYix7F+s+R850fivPknG0qUzJ4vHJao0NX40j/9\ncAuqIpHN2tTVqKRSeRrqNFLp3E7FQ+H0+S1XjOfFhOv1kG8Ec3NznDlzhtnZWfL5PGfOnOHMmTMu\n9fKwfI/f9773MTU1xeOPP87o6Cif//zn+eu//mt+8Rd/cV/rvRmQy2C/AXO/4hqHFZBt2+ab371C\nKplFkW1UTeZtb6ijoe7wh5mc4znBqFjW8zC8icuhWNhjL9PhB72/xWpewWCQaDTqlsGTyaSP8uQM\n3TiiBk6Qdl7jBOm776zns58cKCtXuhXfDTQzc2k0VSJf7F4BZC1H6EQ4IJ0cCqOWqc7X7Ex1nx9J\nMNgbQlFE1msVPYfbmg2ePbftl8nUJaY8mfDqulV2Lc7fWzmYupR0e8pVFSrTHiESIWmZIqCVPma6\nO4NMzaaprtR8oiBO4C/YwhijqUGnpVFnfsnTqwYuXU7R3FB6Pzc2cyiqQVZiNwAAIABJREFUVKLV\nLUlw310vjFHBUZeIJUmitSm04wYlU1sdECp/YaFf39lqkM3mSaRyrK2LQJTNZq/al34hUM5Y4jAC\n8q//+q9z22238YlPfIJ4PM5tt93GbbfdxjPPPAMcnu9xZ2cn//AP/8ATTzzBrbfeymc+8xn+7M/+\nrGTy+nq4yUPeQbEnMogM91rw+hLvh0sci8VQVdUteR5krZZlsb6+zac+P8/ClSxZS+Leu6r5z++o\n29Pa9wtnoElV1T17E+8F17rXXi9kTdMIBoN7Ot/W1hayLO9LRMCyLJLJJPl83s0+HMGCfD5PJpMp\nS01xytXe99wrCuFAkkT28rt/dIkfPCMoKNWVpSIi1ZUK6UyB+hqdmXkR3KJhhXgy7+sLGwGZvq4Q\nw+NxN+uWJKiu1FztaoC+7iCFAr5MEnZ9hkH4Ep+7GPdxfHfXo+5cp+TzXW5tCrgexroGrc1BgobE\nhVF/Sb6qQiVr5amI6iws7QZr77kGe0KMTSWpq9W5UmQ6UVOl0dIU4Oxw3PdzRYHWZp0ry5ZvIK6h\nTuPKisWx/iDDY7vXfPupKJ/8SC8vBJzvzY2I6uwF65sWH/nkGHMLGZeXfevxsFCB6zNJpwu85fX1\nnBrS3U1mMV/a64d8WHzp6yGTyZDL5XzPw/vvv5+PfvSjPPTQQ0d67ucZN3nIe0Vxyfp6QujFvsT7\nKdfeSIbsCIvE43Geei5OriDT2myStQq8800tR6I57QQkYF8DWzdyvmIv5KM6n3c4zJkKN03TzXoL\nhQKKorhlaAeqqqKqqjt97YiteDNk7z8ATYPHP9DGT71OcB7LDS81NxokUzZzixkGdni9LU16yZBW\nR5vBuZE4PR1Bl2bV0Wr4gjHA2rqFXbDdUjTs0Kc8U8yOk5LXl9lBS6PB+qZQvXIMHZobdoMxiEGv\nhaU0Vq70O9PaLHrKqXTeDe7FJfSRySTHBkzqa0rvx1Y8RyZTKJEU7ekIMTuXpbPNPzVeUyXOcXE8\nRXvL7vFe8/KKQ7cL3Cuer55tdaXGPXdWYpoyuZyNacpsJ3LkCzYSYop9cka8784G19uXdip65fjS\njvb0QfjS10Px/bFtm1gs9u/O6QluBmQfnA/F1ZyNyvVND8IlPkjQ9AYO27aJRCL88HSSjc0cq+tZ\n/tObWqmvDRxqQC7upQKEw+FDHdjyrtfZ6Hgdtg7ihbyXe1A8HBYOhwmHw0iS5CouOdOvuVyOeDxO\nOp1G0zQikYjbu3PmBBx+qZNVOwHaG6QF5UXh3W9r5ucfbSWRKA1gjhRkPg+jkylODoVJpUuvJb+j\n0DE2laK5QSNoyD6zBgctjQGmLqVprN81c+hqDxLb8mdGs5fTPnESB+sxEeBX1y00Rbg61VSXtmLq\nanQWlrLU1/p/52wQNjZzGAEhWNHVHiRbZAM9PJoocboC4ds8OplksGhqW9p57chE0h3yUhWJuQWR\nYdu2mGI3QzJVFSovORF8XoPMC4U3P9RAW5Nw82ptNJicSdPREuTCaJyKqMLFCVFp8LJK9uLk5GzK\nj0LHu9yG5bBK1v/acDQpzr9ylBtgcnoujqaxU9I86PGvlYF74S2Ly7KMaZrous7sfArblmhqCLC4\nnOVNDzYeaC3l4GR9qVTKlddUFMXlMx82CoWCK61p2zaGYRyZ/WK5a3MyX2dgy3lIOevK5XKuFnY5\nWpXDLfVm8I6UovefM60N8PKXhamuUvjf/2CO5I56VXWlWiKoMb+QprnRvyEJGjKz87uvm53P0tqk\nsbbuL/cCbO4E+Jm5NO0tAdY2chhlBpvaWwKcG4675WsQGbxX6erKqkVzg87GplXy95VRjbmFDLom\nUVmhshnL0dwY8JWpF65k6WoPkkqXykp2dQQ5NxKnuyPI1OxuqdnpYZ8fibtynNGIwoTHdOLieJz2\nFoNgUGZ0Yvfn65s5BnpD3HYiSjQaLpG3LA4k3lKt89+HufF8PhA2Ve65o5KRiSShHapaVaXK5Kyg\niD1zdpvteJ7rqWY6n2kvHM69Iw3q3EPv35S7f3utGnrx79ELGW5myGXhBGQnEF/NH/hGj38tFJfF\ni/2Yv/vDdfIFGytn89jPdKDtDM7cSIbsFTEpHqA6KklR50t+mANiV7sHxcNhFRUVGIbhPmBs23Yf\nIul0mng87kpwmqa5L46z80BzHG+KM2lFUTgxEOQTv9TmcnTLCWo0N+pcGE0y1BfCMYzqaA2UDGlp\nmoysyEQju2usqVKZ8wT4S5cz1FarLK2UKgclkmJT4JSvAWqrSysTgYCCLOEvgUswtyRKoeubecyg\nQigoU1NVej1b8fIbgoAuUyjAylrW/btoRPH1viemxSR6e0vQN4Wez+8YdZR5z8cmkzzwSmEiUSzK\n4WSCwWBwT8pZB8mkX4jM+8HX1BEJK2zFLdqahdFGa3MAKycsKsemUgf6fl2NL+21WwQ/XzqZTF7X\nX7r4/1uWRSKRoKrqhRnCeyFxMyB7UCyf6XCJnd7iYVoEXu2LerWyuLc/XSjYDI/FSSTyNDca3H1H\n1Z6OfS14Fa/KbTwOmz/tUMS8HN+jUvTy2j06vPBQKOTrEzs7+Ww2y/b2tuvI5ZiMHBZtpThInzpe\nx6c/MUhrU8Dn6uTAcYS6OJ6krzuEqkol/WSAgC6xeCVLyJBdsZDmxlLDDk2TMAKSz1axIqow4zG7\nODcigvLicmngNkMKlxYytDYF3L5uZ3uQTc9w2uWlDI31AZbK/H1zQ4Dh8aR/uluTmN6Z7t6O5wka\nMrou0d4S9F1r1hKOWPFEaYZeKJTv054cCpdYjnrhBJm9KGc5QdorAuN8fl5MCAUV/uPr6lletTAC\nEqvrOcygwnY8T3eHMN04LHiDdDm+9NXsFr0tg+L7t7W15fa4/73hZkAuQi6XI53eHXg5ioGickGz\nODv1+vYWZ+NnhrdIpXOsrWd56xuar3vsa+H5VLyC3d6tQxFzgt1R3N/99ImdQbJ0Oo2qqkQikedF\nC1uSJFqaQnz2k8cwQ/57EDYVX2l6dDJJV5teIispSbCwJILU0opFQBdl442N0hK2ripcXrKor9Xc\nLLelUS+hUGxuZamv8We4sgRzO77HEzMp+rpDSBIlnskAdgHXXciL9Z1y9/mLcfp2OMzdHSFfn3x+\nMSPMMbZKObO6JhMIlH42W5sNRiaSPrUu4LoWi+Wwl0zQKwLjVc5yJoadTLAcx/b5wOtfW49dED38\nQEBmcTlNLm8zv5hiYiZ9pOvZa1/aCdIgnrtzc3M8+uij/Mmf/Ant7e1sbW1d50zXxvW8kM+ePcs7\n3vEO2tvbCYVCHD9+nM997nNlX/d8eCHDzYDsgxMonB2b0689Ck6v98tanJ062eLVyuLf+PYqmYzN\nK+6toa3Zv4vcaya7F8Wrgxz3anDMNYpL8EcxOe0E41gs5k7BOwItxeVp5z4kEgkkSXJ390dpvFEO\nkbDK//i1QW49sUv/6mgNllRhFUVYKgY8blHtLbpPIGR51aKmUiFe7KykSszMi0x0dj5DU4OOrksk\nU6XvaSSsiKy8aze77GgL+KQyL44nODFoMjtfmnGZpsLwWMKXCTfW7/akbWB+IUVTvU6hzGdqY9Ny\nM30vaqo1RieSHC+SJV3fGR6bvpR0TTuChsx9Lz2cPmRxJugVgfFmgpZl+YK0s7l3NoDPVwnbDCm8\n8XX11NXoRMIKDXUBwqYiNn02ZSfijxpXaxmA+FxvbGwwNjbGpz/9aSYnJ6murqa7u5s3velN/Pmf\n//m+z2dZFm95y1t47LHHyv7+mWeeoaGhga985SsMDw/zq7/6q/zKr/wKn//8593XbG9v88ADD9DV\n1cWzzz7Lpz71KT7+8Y/zp3/6p+5rZmZmeOihh3j1q1/NmTNn+Pmf/3keffRRvv71r+97zTeHujxw\nsjVFUdyM8SjgBLd8Pk8qlcKyLBRF2ZMHczqTZ3w6wZXlLL/135tLfu8NnOU2Ek5J3PEm3qsf8kED\n8mEPxF3vXI5JvG3bruOTMyXqrN05t1N2dO7DYZWmD4qgofDJj/Tzm78/yfd/tFn2oWljM30pTWdb\ngKVli3SmQNjUAH82HAjI6FqBaFhxg3Vnm+FzcZq+lGaoT0hlFmNlLY9tw8xchs42g5m5tK9v7CCZ\nytPRavj4x7IkhtFA9KQHekOMTiSpq9FZWt5dZyptU1ctsXSltLRdV6szPBanrXnXaEJUAsRrx6fi\nNDXoLF7J+jynU2mbhjqFtQ2Le++sxDCOptIj1iP5skHY5aAX+yI7n0ugZPDpKMxQAN7wQB3DY3Ge\nPbvNS06GOX0+zvGBEAtLGaZm0iWT6y8kVFXl1KlTfOtb3+LJJ5/k137t1/jIRz7Cc889x+nTpzl3\n7ty+j/mxj30M4KrZ6rvf/W7f/+/s7OR73/sef/u3f8v73/9+AL785S9jWRZ/9md/hqqqDA0N8dxz\nz/HpT3+aRx99FIAvfOELdHd38zu/8zsADAwM8J3vfIfPfOYzvOY1r9nXmm9myB4YhuHzLz2q3pAT\nGPaq7OXFU89sUlOp85MPNFARvf7rvef0uk6V8yY+bFyvLw2Hp1rm9KSdnr8kSfvqEx+l3vd+oGsy\nv/6LvfzEK2uZmvWLbKiqxOycCE4zcxmaGwMEDZmFMgEtkSywvGphhmTMkLjfilJ6nxVZ2Bp6L725\nUWdlTQROKwfLqxnamgMupci3XlVieCxJj0fmsr0l4HOlmrmUorU5wJXV0nVGIiqNDYESZa2VtSz5\nPKQyeZeu5eVZZy2QJQlNk6iu9H8PZubERuP+lz//utXF8pYOZc95thSXa4uHxw6ThhU2VW4/GQVE\n7922wS7YrG/mGZtKXOevn194v3uJRIK6ujre+c538nu/93s8+eSTfOYzn3le1hGLxXzl7efTCxlu\nBuSyOKqJYmeaOJkUD1pnYGs/weD0hS2yVoG3vL6p7O/LZbLlLAr3Oym+nwz5IH3pg95rb0/aES1x\nNjZe/u8L2SfeLxRF4r/9bCevurfW9/OOloBPlWpqNkVvV4hUUWm6Iqpyaaf3vLhsUVOlETYVn1Wi\ng+2EtePOtKtJXRzgkikbIyD5JC7FOoXdp23D5aWsOyVezGfOZG10lZJ1grALHJtMcsJTgm5pDLiZ\n9OqaRXuLGE4rNrO4vJRhoCdU4jkNooTtaH6/GPBCTHiD6KEbAZm5+fT/z96Xh0dVnu3fs6/ZSALZ\nFyCBhC0BElzQKq6frba2n9ZdRGVTUdxwX4qfoqVapVYQFVw+/RCXn7aF2qpItUVAWULIToCQnSQk\nZLbMdn5/DO+Z95w5s2ZWPPd1eV0yycy85+Scc7/P89zP/SA9TYG+E3bodVLUNhj8vzkKEDqmwcFB\nJCcnR30t//nPf/Dhhx9i0aJF7GvRnIUMiITsE+EiZFI/JR7JZNccbFRmtjjQ1mHCrBkp0OuEqw00\ncdLDLiQSCZKSkkalZPYXzdJGIsQKz1/kHyoZ0ueU1KRJnZis02AwsPXh4eFh1lA+VnXi4MBg8U1j\ncf5Z7geTRuP5N5dIgNwcNevWBbh8pum/UlvHCCYUaFk/bAK9TsZGvXVNJpSXuvQIvX0CkbBSBrVK\nyhFwFeap2SEOlhEGVqsTqckydHZ7vl+jliI9TcYx/9BppWwW4GCTAcUFLuIdw2uXamhxqbKPtnsS\nr8nsFGyvOmNWUlxstHyJusKh8Pb3jEpOkuPSeRkwmJzIz1Wht8+GwjwVmltNPt8XLQidn1jMQq6t\nrcWvfvUrPPXUU7jgggsCXne4IdaQKdBtT+FIpXqrn5LXg/38PTVDcDqAX17i3QSEHAOpTRNP53DV\nR705mPHNNiIVeZI6MRn0IFQnlsvl0Ov1HA9qArJpIHONyX/xQs7k2rBYXErY5YuKoFB24J/b+9HR\n7UlI/QM2dHSPoHSCFq1HzLA7GIxYPSNRJxgU52vRfNjIthIV5rkcnAjqmsyYNT0ZP9Zw1a0SCdDR\nbcHgkAMTi9RobbPA6QTUPLXzwKADZSVqNB/2jAr6Bx3o7rVi2mQdDpzy0M7PVaGh2VW/djqBgRNW\nJCfJ0NXjeZwWiwPJerlHa5hWLUVXr2vur4mKwOdWJ8cFIQcLQtJEQAZwDTlIXVrIkIOuTdOGHFf+\n11h8/kUvLCNOaNRSWK0M+k/YMHTSLiiciyaCnfR0//33e9R++Qh0FjJBXV0dLrzwQixevBgPP/ww\n52fRnIUMiITsFaM12LDZbDCbzWxrD52yJbXpYD//P7sHcM6ZY6DRCEe4RLAFgLWeDPcIRv738ckx\nWMGWPxEaDf6wiaSkJJaISbRAHkZE7UrEXSQrQX6X9ucm64g1SZM1O51ONmqSSCS4b3ExUpMV+PDz\nbs7vp6cpWDFT0yETykp0aOuwsD29NLp6rejrt2LqJD1qT5GwXUA0ZrM7UVKsRfNh92fk56jR1uG6\nrlqOuOqzDS1mtHd6isGkUilKx2tQ1+R+f1amgk1BH2gwonS8Bk2tZjh4XU1Dw06Ul2pQ3+z5uXI5\nIJEykMsk7AxkmQw40m6BwejAlEk6HGx0EX1BrgqFeZEd5BAsRmt0Q65JAiIeo53HaOEY4B4UkZYi\nxc/OTMPxfiuK89VwMgxKxrs2Z7NnxIc9JT9CFmpTAlyzkNPTg29l84aDBw/iggsuwC233ILf/e53\nHj8/88wz8dhjj8HhcLDnX2gW8tatWznvC2UWMiCmrDmgL4pQCZkvLhKqn4aiWLaMOPBjzUn817yx\nHj+jzUQIyZB2jHBGCfQ5oY+TmG2M1sHMG4TqxGSSk7d+YrPZzKkTkwiCGA4QIZ1er2cV1iTSN5lM\nGB4eZuvutB91JOBwONiaoUQiYddEZ2wWXJuH88/mPqRysrikU99sRHmpDvyRtzlZKvSdEmnVNhow\nvVwPlVKKw22exDd00o6Obgtyxrk/my8erG82Y/aMJJw0eJ6Prp4R1DWZUFbibsfL4PUjt3e6bDxp\ni0wCqVTKqScDgEwKHOscQUeXFaUT3GYnRXlqNmI+2GjExCLXd557RvxYLkYqtUmiYm+GHGQDSsRj\nl81LxsiI3VVvZ4D+E1Y0thhi7uEt9P3hss30Nwu5trYW559/Pi655BLcc8896OnpQU9PD/r6+tjP\niOYsZECMkL0iFIMNMl800DRxMJ//4/4hXHxeJjRq7i6ZjlDJ2MChoaGIpeucTicMBkNQx+kLvjYn\n/BYtrVbLiXRp32liNUp8p3U6nd8eZ2+RB0kL0qMXhd4z2kiabADo8Z3ezqVUKsGDd4yHZcSJHT8M\nAgAsFk9CNJocmF6mR029OxWdkabgeErX1BkwZ2YKdu4Z4rw3JVnO1mm1GidSkuQYGrajr19IxW1D\nYZ4SR9vd9eK8HBXaO12/23LYjLxsJdq7rOjnGZSYLAxSU+To7rV6zFvuPW5F/6ANudkqtme5qEDD\nWmi6pjip0NYxwqmbAy6S0ailOLsqiT2/iZi2DhV0GxYNhmEwuUSNnHGDaD48gqJ8oOe4Dcf7LTAa\njRH18PaHYFPWweCJJ57AO++8w/575syZAIBt27bh3HPPxccff4z+/n689957eO+999jfKywsRGtr\nKwD3LOQ77rgDs2fPRkZGhtdZyMuXL8crr7yCvLy8kGYhA+I8ZA5I/Q6I/EzkEydOsEMUAsHL6w/j\npqvzkJbiHpFGCIg/m3hgYIDdKYcLDMNgcHCQfcgFepz+YLfbcfLkSVaQRb5LqE4skUg45grku2lS\nI2PkwvlAESJpui4dLEmT46NT6oGeS6vNiSdeaEZdkwF2u5MTDUskLkOPk8MOzpCIwjy1hyBqymQd\nbDag6ZC7/YVOZwOuCNTugKCKOTNd4RqLKJey7lvTy5NQU+fu3yfqbiEx1sQiFRQKKSc9TfqKAVea\ne2DQDquNQXmJFnXN7hT42AwFDEYHJBK3BzfB2VVJuOd2dwdCLMkGcPk6W63WoGZzRwp7a09i5YuH\nkJwkx8AJGyYUa/D8oxM49WkCvlAqUufNarXCZrNxZiFffvnluOOOO3DVVVeF/ftiDL8nUIyQKfBT\n1v5mIpPxegCCFjIFE4E7nQyS9XKkpSg4kTiZQMQnoHD19gLuTYrJZGJrtMnJyRGrr/qqExMyJt8d\nKqkFi3BG0uTv53A4IJfLg665KxVSPHX/RKx58yj+ub2f8zO61nug3oCyUh06u0bQ1u5ptdnROQLL\niAN5OWrWxMPm4F4zR9otqK5M8SDkcZlK9Bx3EWdBrgLDRjtsNsZj2lT/CRuKCzRo67BwHMeUSgna\nOq2wWhlMLFaj5bDr89NSZOg6pY3pPm5DeakWDS0mD6vQ3j4bKqfqsbfWs3VncolL1W+z2aBUKjmT\nnQhiTdKxQsWUJBTlq1HfbMbEYg0ams0YNgDpY1wb90CmOdHnTCaTjfq8eWt7+imOXgREQvYAITNv\npMZXFIfqPBUMaTa0GHDBOWPYvkSSvvVGQOEiZBKlOhwOKJVKVkgSTjKmXctIOwdxLeNbXZJ0nN1u\nZ5XrxG842gKsUEiafi8RmoWybrVKhiU3F6C51YQjx9wRZmqyHG0d7t9rPmTEzOnJ2LWXq5rOy3a7\nXxlNdqSlyGE0OwTFYMf7R1BeqkFdk/t7xma4Cbmtw4Kpk/To6bOyAjMaA4M2TJ3sjtYBoLhAi8YW\nV2Te02tjxzUOneRugOuaTKicqsXeWs91jVidgpH/nEodu5GWyWSQy+VsScMX2UQyIowXspdIJLjw\nnBTUN5uRdkpd3dpmRvqpqV6RUHj7A7+swDAMhoeHf5KjFwGRkL2CHyF7q9dGqqeX/l6r1YqkTCks\nlsBaikZLyA6HAyaTycPS02AIvwiEfB7xkvZWJybHRFuNBlInjiaESJr0kRJiJsdBp9nlcjknkg7k\nYabXyfHsI6W4+7F61lVrkDeMwe5wmXFkj1Ohi3LzSktVsIR8YtCOvBw1ssepUNfEdW/SaqQ4eswC\nBsDEIg1aTtVx+a1HtY2umjRZB7tGrYzdMBTla9j/l8vdxzdsdGBCsRYqhVSQ0AEpdBopjGY6nera\nCOi0MsjlEtjtrmtoQpEGmely2O12SCQSj7ICIQ9CHNGICGMtmuLjzFl6vPORDGaLExljFGg9akZV\nhfdodLQKb/q8CZ07oTr/0NCQSMgiXCAPTHLDAmBbmEi9Vq/Xj5oI/JEmvQEYk+KEUqmOmAc0AV0P\nl0qlHsM1IpUKB1w+4mQOMl0nJscbqPgpnuAtkheKpOmHGXmI+SPpjDFKPPtIKe59oh5SqYRNV7s/\nB2htM0GjkSM5SY6Twy6yGTrJHV/Y3mnBnJnJkEi4I4XzspVoanV9ZvfxEWSmK2EZcXCicoITQzZO\n+hsACvI0qGtyRcYGox06rQxmswNtvGEUhw6bMGdmMnoEDEnaOkZQVKDl9EsX5mlwuM0Mg9HJid7n\nVOpgt9tZ60pCIoRAyHkn8EfS3iLCcKdtowmFQor/Oj8dO/cOI2usUlDp7g9C4jEhD2++cYmQhzf5\nPPpzwqWyTkSIbU9eQC4S4nTFMExYRzH6IjdidWkwGCCTyZCTnRZUS1GwxMl3vdJoNEhJSfFIiYeL\nkEnLFLHyBMCmxPlRsc1mw/DwMEZGRuLOd9obiPmItwlS5KFOsiz8FiySqrdYLGy71/DwMDtDln7Q\nFeZp8LsHS1CY7ykOLMjVwGhyoq/fijGpCigUEiQnyT1qygBw6LAZU3hWk/R1bjA6oVRKUJTvOYFK\nq5Hi0GETbDYH1GruQ5qgb8CG/Fw1CvM1GDZ4zn3uP2FD9jhuG1d+jsu7+mCjASXFbmtPvc4drTW1\nmjE2w5VePXNWEuvURgx5iN6CTmPTER+55ux2O8f9irQU0VOdhEYvEvcs8j38+cjxpPQmf49L543B\niUEbWo+YOBuo0YAQNLEH9TdykTiPkQ2p1WrF7t270d/fD5vNNuoasr/RizQGBgaQl5cHmUzmMfIx\nmqMXATFCFgTxlAXAWkBGggT45OYtVRwsgkmHj9bYIxgQoqLrxDKZjB3JKJfL2ciGzKUmxiqxqBMH\nC77LVjCRfKA1aaFIemKxEldcnIED9cMcskzSuz/ryDEzykt1kEgknGgTALLHKl3GISdsmFikRssR\nC2f2MUFH1whysz2V+wW5GjS0GNFz3IbyUh3qmoyQyyQeYxkbmo2orkzx6H/Wa2VoPWpGXrYaUilY\nJzFOan3IBrVaCovFyUm/2+2ARi1BcYEapRPTOW10gZw7vqiLZGd8RdIqlUowbUs6NMh7iPUl+dxg\naquRRHqaEhVTk7Dv4DC0WiksFkfEpmKRkgwN+m9DHAuPHDmCCy64ADKZDGlpabj99tsxc+ZMzJw5\nExUVFUF7W5PRi2eeeabf0Y233norKioq0NXVxXmdjF68+OKLsW7dOhw4cAC33HIL0tLS2ElPZPTi\n0qVL8f777+PLL7/EbbfdhpycnKAnPQEiIXuA7NwIwhUR80GTpr9UcSif7c/EQkjN7K8eHmqE7K+f\nWCaTedSgyPeR3XU8PMh8wZvL1mgQDEnPKFfg2l9l4P1P3aYGg0Pc81nXZER1peeDLTVFhq5e1/93\n9lgxLlMJjVrmkZqWSoG6hmFMnaznDCeQUTXhuiYjpkzSwzLixKEjnmKs7h4LxmYoOX7ZBXlq1DUZ\n0dZh4fRQkxnHgCvCnlamx+CQ3UN1fbTdikU35Xtkc0Ld4BAyDYakSbqb/g669EJMX0YjgBot6Hv3\nl5eORXunBSeG7Dh8zIyykui1ZdF/G5vNBoVCgaKiInz99dfYvn071q1bh8bGRmzevBkWiwU/+9nP\n8M033wT1Hf5GLxK89tprGBoawuOPP+7hthXt0YuASMgeoHtZIz0TmaSKQ22d8vfZQuC3TQUThYeS\nCqe9vMkIOgCch5VOp2NJm54ZS9K2Fosl4LpqtEHU4cSQZDTDOwKBL6K57tcadB+34+vvBpGkl+JY\n5wjvvUB9kwGTJmjReMhNliNW99/UZHYiJVmCVAGP44JclzCr6ZDzYUKKAAAgAElEQVQROVkqdHaP\nnGqh4hJk82EXKfORma5EW+cIigs0kEoAp8ClVNdkQM44FUasTo92qwP1BsycpsexTs/3VUzxH0EF\nStJCPeb8SNpXTVoikUChUEAqlbIaCaVSyRGOhSKAChckEgkmT9QhN1uF7TsG0dk9ElVCpkGeAUql\nErNnz4bdbsemTZvw/fffw+FwoKGhAWZz8HXuQFBXV4dnnnkGu3btQktLi8fPvY1efOGFF1jzEm+j\nF5cvXx7SmkRC5kGr1bJex0BkVJIk1UUIORKpYv66afIndc1QI89A6mJ2u52tEfH7ifntU976iYMR\nP5H2lmhGG/EiNKOJ5r4lE3C8vwkOh9NDNZ0zToGObhvaOswYmy5Hb78dKqWnGKyrZwR52Z5e0MlJ\nrseF1cbA6WCgVkmRma70iFitVtfkJ1oBDQBZY11zlg+3mVnjEhkvtW13uHyrM8ao2NnHNIwmO2Qy\ngOJMjM1QYkKR1uN3A0GgJM1PRwdC0uTffJIGICgc8yaAChdJ858JcypTsH3HIBqajbjgnPD5Qwe7\nHvq4yKQnkuqeOnVqRL7barXiuuuuw+rVq5GbmytIyN3d3R6DKujRiykpKX5HLwY7XCK+i3IxBH2T\nhRNEsEWIJRIe0HzVIvG5tlgsUKvVSE1NDclEI5DfJ17SRBxBRj6Sn5EHFPGdJoIYEq3TGQJf4ie1\nWs1+hsViYb+T+FiPZoasL5CoP16FZgq5FE/eN1FwPGfqKZc3s4U5lQmSIjdb6eF9rdfJ8MO+k5g6\nmRs10Snw7uNWTCjUIi3VM7uSma7EwUYjyku4IjHLiDuarG92RcKFeWoPt622jhGolJ73Q1qqHI2H\nLJhSyl3XGbPCq8j1J7qj522TUgzJkpCNpkQi4fybFo4RkRkhHSEBFHk/8VYnXucjIyOw2WwhXdt8\nAjy7Og1JehnawiTsChX0feNrFnI4Ry8+9NBDKC8vx7XXXgvAfW4C1d5ECmKE7AV0/SgcIC0wNpsN\ncrkcarUaFoslIulNUkMm6WJi7DHaGcD0JoVPPkIROHlw+eonJjXzQOv03iIaOpohDz4CIcesUMhz\ntC5b0UJykhy3XZ+PA/XDMFN+10aTm3l7+myYNEEHpUICgJvazhmnQFOrAw3NBuRmKdHRbUWyXuYR\nSR9sMqBymqe17LhMVyR8oN6A4gJXi5JSKcFRqiZttwNSmYSjmCZQq6Q42DSMjDEK9A24NwG5WWqc\nGDSgqdWIMakK1rIz3IQsBH/9uHQGh35g05E0DX66m3wHUSrThia0cEwokg7VdUyplOLCc9Kx7d8D\noZySUUOI2Hy1PIVz9OK2bdtQW1uLzZs3s2thGAaZmZl49NFH8eSTT0Z99CIgErIH6OgsHG0+fMEW\nsbokEXIk2iLImg0GA+RyOccnOtyg+4kZhvFaJ45kPzGJNOhjDCdJE9U9Gaih1WpDUr9HE0X5Gty3\nuAjP/NFlkq9SStDexe3zbTxkxMzpnoSqULjOo93hqi9r1FJkj1PgJK9dSaeRorHFgMx0BY73u4nT\nZjsVbcBlIqJWS1GQo0ZTK1fk1d5pwdh0z+8vyHX9btZYKfoorrCemvNsGWFQXKDEwKANWo0MM6b4\n9puPFGhhl0KhYIWSAFhCJaYZdHTKJ086OqPr1+T3CUkD8OhjD8YaVChFfOm8dHy6tTcms5G9pay9\nRcjhHL34ySefcGrTu3btwq233orvvvuOJfVoj14EREL2idEQMj9i5FtdRiIlTpM/gLC3a/HXzLfW\nJBGjvzpxuFTI/tbqj6RtNpsHSdOuWQDY9iuy2YiX1LQvkE3SjHI5rvyvMfh06wAK8jRo5hHimFQF\n9h4YxvhCDccgorvXHTH3DdhQVqKD0CHnZCnRfNiCjDESSE6Zirjandzfc7zf6pH6JsgYo0BN/TDH\nGxsApFIX8bYeHUFZiQ71zcZT4yLdn1vfbMTEYi1ys1RQyGObpSBlISKUFHLwE9JCCEXSpF4cCZIm\nIAQjkUhQkKvB1Ml6tHWYMS05uhsbIUIO16SnY8eOYWBggDN6EQAmTpwInU6H4uJizu8fP34cDMNg\n8uTJ7Ibguuuuw+9+9zssWLAAK1aswIEDB/DKK6/g5ZdfZt+3ePFivPrqq1ixYgUWLFiAr776Ch99\n9BG2bNkS0rpFQuaB3zoRSp2G9romESM/ZRVOQua3FSmVSlit1rCLjMhnCSm1fflOk35ikqqPpArZ\n3/r5JC0k3uH/TaRSKVQqVdxHxQDXHUypVGLhjcVo73LAMuJpxpE9ToWBQRsGBm3sqMWssUp093Ij\n6fpmI6aXe5KqSuU6j20dVkydpEVtowl52UocaeemwGsbDCgv9RRdZY1VoW/ABp1WxhI6APT2uYmk\nu3cEWo0UeTkazmQqABg22nFWVVZgJyZCIC5+/jZsJFKlryH+tSekvqazN/5Imu75FbIGJe8hXR0k\nWr/o3FQcaTNh6mR9zESJBMPDwygoKBj1Z/obvehvHUD0Ry8C4vhFD5DoAnClT0iaOZD3kZuTjhi9\nkY/D4cDQ0FDI5h/0WskDmKi17XY7DAYDUlJSwkp+xDULABv1k7WTG59O9ZM2JqlUyjpQxTtIloH4\nIZO0Iz/lyE93xxqkRYyYytDXnsFox+OrmnGwiWsIMqVUz742oViLw0dMmDJJjwMN3N/LyVKhb8Dl\n9kWTdUa6En2n/KtlUiAnS43UFDlnkAQAZIyRw+5gYLE4YRlxP0bo9qvJE9VoaLFwRjASTCvTg3GC\nMxoScPVFf7i+Esn66F9X9PkOp55AqAWLH0l7I2n+s5xOqQNgyzYajYZD1JYRO/7f1gFcfUWGR0o9\nku2FNpsNIyMj0Ol07HcsWLAA55xzDpYtWxaR74wxxPGLo0GgETJ/NnEgNdvRRsh0uphv7BGJmjTt\nO00EYoD/OnGipXmFXLaExDt0JB1Lkva1bgK9To47FhTg7sfr2fouAHT2uEVahw6bML1cj5ERz+sx\nPU2Bzu4RKBRSyGUS2B2Mh7mHwwnY7U4M8QZcAEDWWDVqGwyYUqrDwVOtWDIpOO1OxzpGkJIkQ3qa\nwoOQaxsMmFDoaQ06eaIu6mRMNt60d0A4M1FCkbSQHoIWhHnTQdARMh1Vk1IScR3TaBiUlTqgUql8\nTnQS8qEeDYRS1j/lSU+ASMge4Kesfams6dQtLdgK5OYMlZADsdcMZzqcT/zEWYfc5LGsE4cL/ly2\n+OIdgKuwJX3r9KjFaBiZ8NPTKpXK64NyYrEOi28qwJo3jwJwpYvpWjHgMuUozvdMLY+cElMd67Bg\nenkSauqGMY5HyIDLVKQwXckZAelap+v9B5uMrOo6L0eFo1Rq22hmUDpeAYPBs/c4a6wSds+MO6oq\novvgpk1gomnnGqhoUYikybVLWq1kMpmgunvyRE1I1qB84dhoWynDVUNOVIiELAASFXmLkGkHKSHB\nVqDfAQROmsHYa4aDkIWI35vvNL8dKJZ14mAwGpctbyQdjilO/sBPTwfaNnb5xWNRUzeM7TsGkJmu\n8CDk3Cw1BgZdNV2jycWAMpmE42l9oG4Y4ws0sNo9N6o52SocaDCgIFfNtkhJT41KJDCa7FDIJdBp\nPYmsrdOKvGylx+tpKTLUNZlROl7NTp8CgKqK4PyNQwU/CxEPKvtQSJpcr3QamxCvXifzcCjjky5t\nfEKIWoikA7UGFTIv+ilPegJEQvYJPiELCbY0Gk3IkU8gKXH+dwY6D5m8N1jQ6nBC/HQ/sS/fadpl\nK55Bzmkk2q9C9U8OhKQJMZBIPJRywPJFRWg5YoTN5kmoKUkKHG23oKxUh/pTqeX8HDXH05oBMGxy\nwHHS8/0yqQQMA9jtDOvSRew2CXr7bJg6SYshg+f7C3LVGBq2s2lxAvLM7x+wQ6GQwGZjkJIsw9h0\n19SwSGYiyMY0nB7lkQJN0mQDT6JiWnTpbcgGfd368u+WSNyuY0IkHag1qFDL5089Qo69GiUOQbcm\nkQvTarViaGgIJpMJSqUSqamp7Pze0XyPN9L09p2BbABCIWQiwiKOXhqNBsnJyWx6muyedTqdR5qc\nHMfIyAg7KjCSblmhgpzTaLpsEZIOZdQiff6IFanFYmFncoey+dFqZHjsnonoPu45e9hscf2N65uM\nKJ/kctkidpmcz1BLkZPlOfWJRNydPSMoP+Wmlaz3zDi0d43A4fAkZJVShp5eK8pL3Q5fSqXbWrN/\n0I6yia7PnT0jhRWukUyHv1GVwYBsTA0Gl5BMp9ONavMdLdDXuMPhgFarZZ3ttFotkpKSWHdA2u2O\nbPpJFi6YcZVEzKlQKFjXMa1Wy24YAXi4jpGMGl3nBnwbgwSKQEcvbty4ETNmzIBGo0FWVhbuuusu\nzs+jPXoRECNknyBpnZMnT7I1VL1eHza1sDdC5ovEwvmdQuD3E5ONhlA/Malb8uvE4TTiiATiyWXL\nWyTNV9fysxCAS1A32g3EhCItrv1VNl57+xj7mlwmQRuVmj581IyMMQoYjJ4irZRkBWrqhjGxSIuW\nUxOdMtNd7lwEBxuGkZOlxIkhT+LPHqdm69I0+gZchN582IjUZDkGT9pRmKtB82F3/3HjIQPSUuSY\nMzOV44Tk7/wFk4mga/OJkvUB3ONNybPK2wbCW7o70HGVwUTSZD4y+V1a3U2efcPDw6isrMT48eOR\nmZmJv//975g7dy4mT54c0nMvkNGLL774Il566SWsXr0a1dXVMBqNOHLkCPvzWIxeBMS2J0GQlKzB\nYGDTtJGoG/HbqvjzgkeTSh0YGGB3qd5A14nlcjm0Wi0r+iA3GLmxQqkTCz0k6RuXNuEIl4E+H3yX\nLTLJK95B1y0B9+ZQSLgTyiaHYRg8+lwTftjv8hwnYisaE4o0ONZhgdXGvfVLirVoPmxyEbbJAYvF\n6TGSEQAKchXo6rHBxuN08rvlpXrUnWq7oq0wAaB8kh51jQZ2CAXn/ZP0ePrBEiT5UVj7u/74JC2R\nSFivaG8GH/EIb0r7cHyur0lY3mrFZBMv1M9P16bJSEq73Y7XX38de/fuxVdffcWOv9VoNPjFL36B\nDz/8MKT1v/3221i+fDkGBrjWoIODg8jNzcXf/vY3nHfeeYLvfe211/D444+ju7ub3RQ8/PDD+Oyz\nz1BXVwcAWLFiBbZu3Yqamhr2fddeey2Ghoa8GYOIbU+hwGQysRcLgKC8loMB3VLjy9VrNJ8tBP5Y\nw2B8p4PZmAjtxH0ZcYSzfYhuT0kkly2AG83z1bzhykRIJBLcv3Q8Ft1fi6FhO5IEhlFIIMHkiXrU\n1LvHkNKRdN+AjSVXh8PzWlMp5ZhcovIg1N5T6fLOHgu0GilMZidrUkJQ12hAUb6G7XPmnB8n45eM\nyTH6Ez4JZSJkMhkUCgV7b8bzNUNfK+GucY9GE0ELyMj76Eia/D8JdpYvX462tjZ8++23aG9vR01N\nDX788ceIbIj++c9/gmEYHDt2DOXl5RgeHsZZZ52FP/zhD8jLywMQm9GLgEjIgiC7Y7lcHtGZyIDr\nhhocHAyLSIyGECELCcRI2k+on5jedYeL0AJxLKLbh8hDNRjRDp1yjGZ7ymhB6vgkmhfaCPojGSKo\noUnaWyZiTKoC9y4uwpO/b4HR7Jma1mplqG8a5rh35fFEXqRHmD+7GADUGjlaWo1ITZFjcMj1+Rlj\nFOg9RbKDQ3Y2AhbaPMrlErS1exLyzOmhi374549O8xIyITVpgmi0sAULOioOdkDLaBAoSfMV23S6\nm/h7A2CtdgHgwIEDAICUlBSce+65Xh21RovW1lY4HA4899xzeOWVV5CcnIxHH30UF110EQ4cOAC5\nXB6T0YuASMiCIG5XdCN9uGGz2VjBiT9Xr1DAJ+Rg68R0X66v/tZwgE/SoSqTQ20HijVGG83TJENv\nsALJRMyeocflF2fii219Hp9rMNphswNqlQxSCeBkhEVerrKAZ014cMgGs8WJogINS8jjTtllEhxs\nNCA3WyVI6CqlFJNLdB5znSunjr7dyV8rU6A1abLZiaYmIpJRcSgIlKTpTSIA7NmzB99++y0qKyvR\n0NCAP/zhDzjzzDMFsxIPP/wwnn/+eZ9rqK+vR2lpqd/1EiX4mjVrcMEFFwAAPvjgA2RlZWHbtm0+\n67+RFqjG/9MqhghHPy8fdN2WRCqBWHOGAvJQoevEycnJ7C6VbDhIeolfJyY15WgjkBuc31pBb0BU\nKhWUSmVCRMW+0tOjQSCZCELSv70iGbv3DaK7130+FQp3avrIMTMbyZpMng4dGrUUkyZocaDBTZw6\nrQztp/qP65tcgyBaDpvAOLn3ktMJJOvl6Oji9kQDLm/r3j4r2+pEvotWYYeCQAgtlHR3pIWLdLte\nNKPiUMC/h+n2MTIJq6WlBevWrcPg4CAAICMjAwqFAk8//TR++9vfory8nP28cI5ezM7OBgCUlZWx\nr2VkZCAjIwNtbW0AvI9VlEgiN3oREAnZJ8JJyEJjGEkrQKRgt9sxNDTEfh+5eYXqxHSqVKvVQi6X\nxzwtR8MbSRPBFv03Ig+tWCu7fSGQ9HS4IZSJYBgGWocDd9+Wj0eeawU5jTnjFDhKpYsbWwzIzVJx\nlNgETkaKpmYjssep0NXjup7zctRobHET9LDB1UPc2e15vcvlEkyeqENDCzcS7uqx4ASV1gaA6eVJ\nkIc43Wm0hBaoGUekZ3HHQ1QcKLyl1p1OJzQalx3q3XffjTlz5qC2thZ79uzBa6+9hoqKCg4hh3P0\n4tlnnw0AaGxsRE5ODgCXCLavrw9FRUUAYjN6ERAJWRB0HzLAVbYGC/Lgpb1vyc1E123DBfLQIdFv\noHViIDSjiViB1PmIyxZJ+fMfkHQ9NZyisVDBT0/Hsq2GVrzOmpGOX11qxKdbXTv+JL0CgJtYrDYg\nSSdBZ4/n9drRbYHd4YpeCZQK7vH0HLdi1vQk/FjjqcmwWhmcGLKxZiIA19rz8FET9FoZDCYHZk4L\nLV0dqVamSJN0IkXFfHjbRPT09GDZsmWor6/HZ599hnPOOYdz/EIK7WDgb/RiSUkJrrjiCtx9991Y\nt24dkpKS8PDDD6O8vJxVXcdi9CIgErJfEDeaYEF2hvxJTDQB0BF4OB4OZACE0+lkb3K1Wh0XdeJw\nwZ/LViyV3f4QT73QQrjl2lzs3DuIzu4RmC2e17xUJsGkCa6pTATjMhXoOe5K27YeNaO81FXzpRXT\nBDYbg/Q0BfpPULVYCdDeZYbR5OREwrS1p4H6WeW04ARddCZCJgvOHjVUhIukieAs0fqhvUXFDMPg\n008/xfLly/Gb3/wG77//PpKSPGcwj7b9MZDRi++++y6WL1+OX/ziF5BKpTjvvPOwdetW9tqIxehF\nQOxDFgS5oACXlZtcLodOF3jdij+QwVst1mq1wmAwIDU1dVQPZqF+YhI9EvEW3U9MfpZIvtPhjCzJ\n5oR+OAr1V4ZLVcuPcuK5F7q2YRgrnmmEROKKXGlMKFKju9cKuVzKTnWaMkmHg41U7VgnhU4j5cw0\nJigrcd1D9c3u38/PUeNYp4vg9VopIJHAYHRg8gQtGg65DUHkcqAoX4s/r5oS8LEEOqs4VvDXJ01A\nZnHHU8nFG2jVOh0VDwwM4L777sN//vMfrF+/HpdcckncH0sEIPYhjxa++nn5IBEQ2Y37m3U82hq1\nUF2a7MpJStxgMLC1Q/IAIKrSeKsTe0O4I0s6VRvJwRDE8pKQQiJEOVMnJ+G6K7Px9oednNelEqCz\n2wqzxYnyUg1LyDyNFoxGJ0qLtejt4/YeA0BHlxknDU4U5rknPaWlKFhCJpHwwQaDh+rabncTuj/Q\nM63jMRNBIBRJ05sI/jhTIPaOd95ANsxms5mjWmcYBn//+99x1113Yd68eaipqUFaWlqslxu3EAnZ\nDwIhZP70J1+TmPifDQRPyHQ/MSBcJ1YoFJDL5Syx0PNNyftJ/TWebmwafJetSE7ZCUXZ7evhyM9E\nxCspCOGXl2Zi69fH0dvnPtacLDVLknVNRtati4i4aNgdDPJz1TjWIZzadjgYSCQuFbXRzE1t1zUa\nUFaqx8FGT0IvHe+bkPmkEO5ZxZEEP7VOt0HGuy0tvQGiLTtPnjyJRx99FH/961/x2muv4corr0yI\nv0UsIRKyAOiLhkSaQuAbbQRr7BEsIZMHDl1XIt/HrxMTSzoyB5V4IPNTtfwbmzaRiBWBxIvLljeS\n9vdwBMAR1REv33gH2Vg67DYsvCELz/zR7XWdlipHe5f7dwdP2pGXrUK7QLvS4EkH5FLu3yozXcUS\ncnuXFWUlWjQeMnmorh1OQKEQvt+mT/Eu6IpU+1g0QAvOhK71WKq7fYG+TwFwouJ//etfWLJkCSor\nK1FTU+NhoCFCGCIhewGJjL05XtHESIw2gn0ABEPIQgMnfPUT+5rzK3RjkzqqN8ETIepIk2K8u2z5\nejharVYPG0baqCTWGx1v4D9YNRoNzjkjGT8704jtO1w+wET9THC834qqymQPQtaopWjvtIBhwAq8\nAMDJy213H7eiOF+DQ0c926gMRidys5To6HYTTGa6AqlJTjaCJASTyCrk0QjOYk3StAkPfZ+aTCY8\n9dRT+OCDD/Dyyy/juuuui7vrPZ6RGFduDMEn5HBOYgqEkH3VicPRT+xPlUx6pUkNK1I2gonqsgVw\nSwBEKEeyFoEou2NZy/cVWS6dX4Afa4ZgMDoEU9NmsxNjM5To7XM/9HOz1Wg5NZ2pq3cEKqUUI1Yn\nunq57z8xaEdJsdaDkEmtOjdbDbrtaupkrUcLG529isfNmy+Q50g4M0DRImlSFgDcGSCGYbB7924s\nXLgQRUVF2LdvH/Lz80d1PD9FJMYTLwbgR8j0JCZCjOGqTwkRMr9/WavVcsaYCfUTj4yMhOUGD9bK\ncjQ7b76FYaLV/egWLP4GSMiEg85G0KYw0fZLDiSyTEtVYMG1efi//9fFIV2C3v4RpCYrOD/TatwR\n3olBO6aXJ6GrZ4QzmpHAYHQgOUmOk8NufQOpVTe3mjgTqGbNGIPk5GTW9pDMiiYgOolY95n7g69a\ncSQQTpJmGPegGVoXMTIyglWrVuH111/Hs88+i0WLFsXdeU8UiIQcABiGweDgIPvQDaepAPl8+ruC\nqROTVGMkU7yh1lL91aPptSeS+xAQ/NpHq+wmdoPhOD/02v0pv39+YSYamo34x3au13Vykhy9x23o\nPW5D6XgtmlpdUbGRNz+5odmAqZOTPAhZIgHa2s0oLtDiADW2ka5V00uaUe7qVyXlGHrjyb8WY9Vn\n7g/x0oYVCkmTvmjANSt43LhxkEgkOHDgABYuXIjU1FT88MMPmDBhQtSP53SCSMheQCIIEqEKGXuE\nA/QNSafDFQoFkpKS2Bsh2DpxpOHrpvZXjyYbCWJLF+21jwa0onS0a/en7CbnMVzZCH5ZIJC1SyQS\n/Prn4/Dlt32gtY3Z41RsZDs0bIdcJgEkYFuYCKw2BnKBr8gep0Jn9wjqWwzIGKNgB07YbO4vaT1q\nRkmxFsNGBzLTFWyvPT+yFNro8AmGP0EsmtoIb5FlPMHb/UxKVnQ24uabb0ZNTQ0mTJiAxsZG/OY3\nv8EjjzyColO2kyJCh2gM4gUDAwMYGRmBXC6H3W5HSkpKREhjcHCQfZCQ9CGtVnQ6nZw6MQA25UVS\nvPHcT8yvR9M3NnkIRCtNOxrwU+vE3CMa6/VnICFELvS6wrH2V986is++6GX/TbtqkX8PGxyc0YwE\n4zIVUCplnDaoaZP1bGRMzEUkEkCvlWHY6L5GCnJVmDRBh0U3ZgJAyOddKBsRSTMYAjoqTqRyDCBc\n5waATz75BB988AGOHTuGkydPsgMZdDodGhsbkZubG8tlxzNEY5BQQcQKpJ8u3J7TgHsnT9cgyUVP\n0tOAcJ04EUwmAHDqT7QAh1aIR3NiTiigld+xSK0Hko3w5tktkUjY1rfRlDRu/m0uvtkxwBqCGAzc\nqU8th40oK9HjyDHu+5L0MvQct2FiEbd/3EGprusajcgZ5+qj7+SJx9o6RvCby9JYsVyokWUgfebh\nMIMhoLMR8RoVewO/zk06SBwOB9atW4dnnnkG9957Lz777DMoFAoMDg5iz5492LdvHzusQURoECNk\nL6AfdkNDQ35dt4IBv04slUqRnJwc0zpxpBCIy1YgEWAs+qP5Kd5IC3BGCz650GYw4UjTbv3qOF56\n/QgUCsmpdCb359WVydi19yTntUkTdezUJ2ImArhqxScG3R8waYIWCoUUtQ2ehiBvvliG/NzIjCjl\nIxyRNK1CjmYmJRzw1hN99OhRLF68GAMDA9i4cSNmzpyZMMcURxAj5NEiVDctb+DXiQm5EFIiRBwP\ndeLRIBiXrdHUoyNRA0xU5Te5bgCw0bJSqYRMJuPUUkNtYbvk/Axs+eo4RqxOwdR0Y4sROVkqjtmH\nipr6ZLY4IZEA6WnumjH73kMmTCvzJN2MMYqokTEQWl1fKpWyZSPy80SMiumxpbTPwTvvvINHHnkE\nCxcuxFNPPcWOTRQRfoiE7AXkwRQuQqbbpmQyl8+1XC6HwWBgd6WEYACwnthC7TTxjHC5bMWqPzrW\n6enRIBAP50DTtGSjQ5cMpFIJ7lhQgDf+l5eXBth+5LGZ3MHsw1Rqu73LgvJSPSBhPAgZABgBR7yp\nkz2nAUUbNEmTkhI/q2Oz2Ty6JeiZ3PFQevEGh8MhOFWqq6sLd911F1paWvDXv/4VZ511VtweQ2dn\nJ1asWIGtW7fCZDKhpKQEGzZsYCc9JQpEQvaD0RIyqcfQput0nZgM66ZbDAjkcjlUKlVci51oRNpl\nK5L90aEokOMF/Ije1wbOVwRIojtf57GkWIOCXA1q6rip5Ywxrn7k5lYTJhZp0XLEBIVCgmNd3Ei6\nt28E2eO4pA0AY1LlqG00oSBXhbYOd4Q9dXL0ouNgQDaMUqkUdrsdDMNALpezYsx49Jzmg9+LTq55\nhmGwefNm3Hfffbjmmmvw4YcfQq+Pz78D4BLGnn322bjggqqO+7YAACAASURBVAvwxRdfICMjA83N\nzQk5xEIk5ADAd+sKBOQhSddjaAcnUidWKBRQKpUcNSZRydrtdrYOGKs6aiCIlctWOPqjiegp0dLT\nBOGI6IM9j7+4UI9/bu/DCDWeUUp5V1usrtR0bpbaI7XdN2BDXrYnIWemKzAwaIdKxd0ExUOELAT+\nIAtvJZlgTDjIJioa1x6t7aCj4r6+Ptx7773YvXs3PvjgA1x44YVxfy+sWrUKBQUFeOONN9jXCgsL\nY7ii0CESshfQFyFt0RcI/PUT+6oTq9VqlswCqaPyySWaiMdaa7D1aAKSjoz1+gMF3yY13JsgX32p\nKpUDV1ycjs1/dZuFnBh0R7XtnRaUleggl3ueR61GhqPtZigVElht7r+BQuEi4uZWEwpy1WjrsECv\nk6EoP/7qlfzpRr4yQf5KL74U8vR9Ha5rkr5n6euGYRj87W9/w7Jly3DJJZdg//79SE1NDct3Rhp/\n+ctfcOmll+Lqq6/G9u3bkZubi6VLl+K2226L9dKChkjIAYDMEvYHb3ViQgikn5jcvHSdWIjM+Dez\nkP0iMS4h6+RH0ZEil0Ry2eKfR/qBSh52JGIwm81Rt7EMBuGq0YcCiUQChUIBhUKBG64qwJffDuLE\nkB0qpQRdvdyacM9xC9LTPB8vOVkqtBw2oaxEg/pmd/Q8OORWXKvVrvujvFTPibxjjUCjYn/gl14A\nT5KOhNsYHRXT9+zQ0BBWrFiBf/7zn1i7di2uuOKKuLneA0Fraytee+013HfffXj00Uexa9cuLFu2\nDCqVCjfeeGOslxcUREL2Aj4x+iJkf3Vifj8x/UANpp+YkIe3OipJcUdypGIiK79JdCDk+R1Jv+5w\nIRDRVrSgUctw41W5eOWNo8jNVqOVNyRiYNCBvGw1AG5fsVLhuhc6uqxQKSUYsTJQq6Xo6HZvLJsO\nmZCfq8aUSfFTtySbbYfDwZn5Gy4I6SPCZQnqKyretm0bli5dijPOOAM1NTXIzMwM2zFFC06nE9XV\n1Vi5ciUAYMaMGaitrcXatWtFQj4d4S1lHWidmJ5PHG7Rky8FaDhT3fxBCvGQng4GdrvdNevXITwv\nNxz16EiRo9AQi3D1xI8G/3VBJj77ew/0Ws/HSMYYBY60W6BWSWEZcd875P9PGhwoL9GgrtmM7LEK\nHG7jErdWI8O0stjXj4UEc9E499423/Q1SToN6Pfwr0mGYdiNBB0VG41GPPHEE9i8eTPWrFmDa665\nJmHuZT6ys7NRVlbGea2srAyffPJJjFYUOkRC9gESOQlFyHa7HUajkX3A+6oTk901iSojLXoKJdXt\nrdWFnyJNFIcwAn4/dDDnPh76o+O5DUsmleC26/Px3sedHj/LzFCivsmIKZO0ONjoMgORSICe4+6s\nw7EuK1QqKWdCFEHrERPyc6Qe84+jCW8p3ljBX4aM/Eff2wStra0YHh5GRUUF6urqsGjRIpSWlmL/\n/v0Jb3V59tlno7GxkfNaY2NjQgq7REIOADQhk5vUW52Yn562WCwxjyoDSXULpWiJ6MzpdMY8RRos\nIlVrjVZ/dKK0Yc2ZmYpPt/Z4vC47dZkcOWaGRi2F2eJE1lgVZ67ysMGBaWV6mC2e2afxhWpIJU7W\n8QoQVshH4l7yluKNRwhlduiNBNnIbNy4EW+88Qb7+1VVVbjkkkvQ1taGMWPGJLTZx/Lly3H22Wfj\nueeew9VXX42dO3fijTfewPr162O9tKAhWmf6gM1mY+t2ZrMZarVaMHVFzycmD4hEjCrJpsJms3kY\nHcSDqjtQ0A+kWFiN+rNf9FWPjqVoK1TUNRlwz+P1nNfyc5Q41ulK75NBFFMn6z2sMZP1MshkEpwY\n4vpw/vrn47D4pgLB8xhusRONeIuKgwF97QBgAwCGYbBnzx48/vjj0Gq1SEtLQ1NTE/bv3w+bzYa3\n334bN910U4xXPzps2bIFDz30EFpaWlBcXIz77rsPCxYsiPWy+BCtM0cLQlKAK9pVq9XsbjJadeJo\nwul0smRMWrBo04hAU92xQKRbgQJFqPVoOiORSNdOeakec2amYOeeIQCATAZ097qPreWwCXqdTHBL\nr9fLkZ6mwIkhLlGXlbgEXaEokkOZIMY3yYjnqFgIdEaFvnZsNhtWr16NP/3pT3jqqadw5513stfl\nyMgIamtrEzK1y8dll12Gyy67LNbLGDUS54qLAex2O4aHh1lCTk5OhkwmY0ci8uvEZOZpNM0xwgVf\nGwmZTBZUqptP0pFGIkSV/urRJCtBwLdTjeeMhNPpxDW/zMCuvUNgGJchSBs1atFscWJamR59A55u\ndGNSFWjvskAul8BudzN2WYnO6/cF69jmr2zgzToyUUAPsyBT6gCgvr4eixYtglwux44dOzB58mTO\n+1QqFWbNmhX19YrwjsRhjBiATv2QCz5e68ShIliXLV+qbppc+EYHkUp1xzo9PRrQ5Q1CBgqFgrPh\niYRfd7hAb4Tyc+SYW52Cb3cOISVZDnRwf/dYpwVOh0CIzAAnBu2cdHbGGAXGZni6eXmDLztQfyRN\nzE4kEknCbaIZhmGDAFrj4XA48Oqrr2LVqlW4//778dBDDyXUcf2UIf6VfECv13PsK00mE0suJB2U\naHVignC6bNHRn0rlepDyo+hwp7r56el4aQUKFL5EW94yEvHUHy20EZp/TT7+vXsITofn76enKaHT\nSj08sE8MuY7leP8IpBLAybjT1aOBv7IB2TjSP7NYLDHvNQ8UtNUufe+2trZiyZIlOHnyJLZt24aK\nioq4PQYaq1atwiOPPIJ77rkHL774YqyXEzOIhOwDhIABQKFQCPb+SaVSNrJJhAsfiI7Llq+04mhS\n3YnehsV3e/K3EYq3/mhffbn5ORpcdG4G9h4c8nifViNFy2ETtBoZTGYXY6vVUnZUY89xG8pKdKhv\nNqKsNDKGIORckk22VCrl6EH4NpYABOvRsc5KkI0oHRU7nU689dZbeOKJJ7BkyRI88cQTUKvVMVtn\nMNi9ezdef/11zJgxI9ZLiTlEQvaByspKyOVyzJ49G1VVVSguLsb7778PrVaLVatWsTeCxWJhH1Dx\nrESOpctWOFLd5FzHg1NVKAhXej1W/dF0rdXbRu7Gq3Lw9Xf9Hu+12ZwwmZ2YXp6EmrphAEDuOBUO\nUQ5fhlOjGssjRMi0ToK/kfPlNR0JG8tQ128ymTx0Eh0dHbjzzjtx5MgRbNmyBWeccUZcPXd8wWAw\n4IYbbsAbb7zBOm39lCESsg8cOHAAe/fuxb/+9S+sX78eDQ0NSEtLw1lnnYXnnnsOc+bMQVVVFbKy\nsjjRH52ejVVKkUa8umz5SnULnUsCpVIZd6ItX4iGgjeS/dHBqNfHZqhw4bnp2Pp1H+f1nj7XRuvw\nURPr3qXlOXwd63INpZhYrA35PPhbfyAb0UBsLPkOWaEou0Ndv1arZYOBTZs24YEHHsANN9yATz75\nBDqddzFcPOKOO+7A5Zdfjnnz5omEDJGQfUKn02HSpEn47W9/i/7+fqxYsQLz589HbW0tvv/+e6xd\nuxYLFy5EWloaZs+ejerqalRVVaGiogJKpVIwpcjfYXubWxsOJGJ6l34Y0uld8jMAsFqt7PkUivzi\n6fjoWl+0z3845keTqD4YBfI1V+bgH9v74Tgl4kpNkePEoEuHMWx0sH3JVptnsVmvlUGpCF/ESUfF\noarvA3XICkbZPdr19/b24p577sH+/fvx4YcfYt68eXF13QeC//u//8O+ffvwww8/xHopcQORkP0g\nMzMTd999N6666ioUFxcDACZNmoTf/OY3LGEcOHAA33//Pb7//nu8/fbbOHz4MKZMmYKqqipUVVWh\nuroaxcXFnBuYToPRNy8RjI325qLTo4ma3qXT02q1mo1qAkl1x7pdiD8Igl5/rBBKPZq8T61WB5xV\nyR6rwry5Y/DP7a7U9bgMFWeaU3unBQqFBD3HPdugcrLDU/cMNioOFoEou/nCsWCyZXRWhV4/wzD4\ny1/+gmXLluHyyy/Hvn37kJKSErbjihba29txzz334Msvv0woMWakITp1hRkMw2BgYAA7d+7E999/\nj507d2L37t2QSqUsQc+ePRuzZ8+GXq/32GUThCrM4Xs3kwdpokAovR5IFoH/IKTPZTQNTPiip2CI\nLB5Arx9wjx4Nth7d3mnBbfcegJMBppfrPdTVM6clY8+Bkx7ve/DOYlx4TsaojsFbrTUW4G94iPEL\ngRBJE+97flbixIkTePDBB/HNN99g3bp1+PnPf54w1xUfn332GX7961+zmwzAtQkn1xe5/08z+D0g\nkZCjAIfDgcbGRuzcuZP9r66uDhMmTOBE0ZMmTQIAjjNWoA5EiWCO4Q+0+nu06V2haEXoQRjOVHci\n2y4Cvsc7BrLh4V+bz71yCNv+PYCJxVq0HDZxvmtKqQ71LUbwh6i9+dJU5OeE5qvMj4o1Gk3MsxJC\nEMpKCD2HDx06hHHjxiEnJwdfffUVli5dinPPPRdr1qxBenp6DFYePhiNRhw9epTz2vz581FWVoaH\nHnrIY3rTaQKRkOMRDMPAaDTihx9+wI4dO7Bz507s2rULw8PDmDlzJkvQVVVVyMjI4BC0kCeyRCJh\nU+CJZo4BRC+9y091e/NFDjbVzRc9kag+UeCtJ93fe/z5dXd023D34y3QqKUwmrjMO71MD5udQX2z\nkX1Nr5Ph4zcrQ9rE0LX6RNyM0rVikpW4+OKLceDAAWRkZODkyZO48sorsWDBAlRVVSEtLS3WSw47\nzj//fFRWVp7OfcgiIScKGIZBW1sbduzYge+//x67du3C3r17kZWVxUbRVVVVmD59OuRyORwOB2vr\nSfcb0lF0JAVj4UCo6elwItDIT6i2T1yeEpkIwhnVC6Vn177ThX/+y7MveUKRBg47gyPtbhV95bRk\nPP/YpKC/U8itKlHAnyxF7gGn04ktW7Zg7dq1sFqtkEgkqKmpwcmTrjT//v37MX369BivPryYN28e\nKioqREIOECIhRxGErPbt28emuXft2oX29nZMmzYNqamp2LFjB/Lz8/Htt9+yxiWEWAjibQAEQTTM\nSUJBoKlu4tSWqKI5fitWpKL6liNGLF1R5/G6ViOBycygIFeFtg5XC9Fvf5mFW6/LD/izvblVJQq8\nbYbMZjNWrlyJd955B3/4wx9w8803s7Xl5uZm7N69G1dffTXbzy8iYSAS8ukEhmGwadMm3H///ejs\n7MTcuXNx6NAhOBwOTi26srISGo2G0xvNJ5VIOTn5A52ejuc6Hw1+qpve8ADurES8D4Eg8GWQEQk8\n9D+N2FPjFnCNzVCi91Rfcsl4NZpbXVHyA0tycMasZL/tQrTtaKJuhoSiYoZhsHfvXixcuBA5OTl4\n8803T4tJTCJYiOMXTycMDAzgtttuQ1VVFbZu3YqpU6fC4XCgrq6Obbv68MMP0dTUhLKyMlbRXVVV\nhZKSEjb6I60tox1ZFwzC6Z0dbZDzA4BtCVIoFJzRlN5MN8LVxhYORLoVyBuuujyLQ8jpaQqWkFta\nLSxBT5mcCrlc6rM/mhxDol1DBERBzY+KrVYrfv/73+PPf/4zVq5ciaVLlybUJkNEeCBGyAmGxsZG\nlJaW+uxfHBoawu7du9m2q127dsFms2HWrFmc1qu0tDS/gjG6Fh3qg4+OyOIpPR0oAlHvBprqDsf5\nDAWxFj0tWXEQh464lNbEGIRg6mQ9unpG8MHaCva1QNqFYpXlCQXePMwBoK6uDgsXLoRGo8GGDRtQ\nWloa49V6x3PPPYdPP/0UDQ0N0Gg0OOuss/D888/H9ZrjCGLKWoRrV97a2soKxnbv3o2amhrk5+dz\nUt1Tpkxh3Zn4D8FQVMj8iUaJkJ6mMdpWMl/tLdEyMPHVyhRNfP1dP1ataQUAjC/UoJXysFYqJThn\nzhisuHO8x/uE3OYA9zCIaJ/PUED/DRQKBTQaDSQSCex2O/70pz/hhRdewMMPP4z77rsv7tX5l112\nGa699lrMnj0bdrsdDz/8MGpra1FfX88O6hDhFSIhi/AEUabu2bOHE0X39fWhsrISs2bNQnV1Naqr\nqzk+3YEKxhLdHAPwdAoLF5HxW4WEzmc4Ut38iCzWfwOHg8H8u2vQ22eFWiWB2cJ9nCy8MQ///Yts\nzmt8IhNq5wulPzpaoDcTADhRcUtLC5YsWQKz2YwNGzYk7KSjvr4+jB07Fv/6178wd+7cWC8n3iES\nsojAwDAMOjs72Vr0zp07sWfPHo5P9+zZs1FRUQGVSuVVMEbUoAA40UCiwNsgjkh+X7hT3eGaKhVu\nfLqlG59u7UF3r6dl5rMPl2J2hcsC0ld61x8C6Y8O1L5yNKCzQ/TfwOl04o033sDTTz+Nu+66C489\n9lhCq6VbWlowadIkHDhwAOXl5bFeTrxDJGQRoUHIp3v37t1efbr7+/uxbds2zJs3j/OAiYZgLFyI\nl1p3oKlufq95tFqZQoXZ4sDv/tCCH2s8LTM3r69ASrLCa3p3NIh2PZoeiELKHABw7NgxLF26FF1d\nXdiwYQOqq6vj9l4IBAzD4PLLL8fw8DC2b98e6+UkAkRCFhE+CPl0E8EY4IqIn332WVxxxRVITk4O\nKEqJhcCJj0SodftLdZPaP3Fri9fMxHsfdeCdzZ2c1zLTlXjv1elBu4WNBvz50eGoR3szKXE6nXj/\n/ffx0EMPYf78+XjmmWeg1YZ3xGQssGTJEnzxxRf497//jezsbP9vECESsojIYdeuXViyZAn27NmD\n888/H6WlpYI+3VVVVZg8eTIkEknYBGPhAF8wlEhtNPwWNjriA+Jv00PQN2DFjXfWgIxmBICzZqfi\n/iXZbIo9VpuJ0dSjvZmU9PT0YNmyZairq8Nbb72Fc889Ny7+DqPFnXfeib/85S/49ttvUVBQEOvl\nJArEPmQRkcPevXvBMAx27NiBM844A4CnT/dXX32FZ5991qdPN3kICvXyRsphLF7rrIFCIpGwk72I\nAlyhUHDOp7exlLG0Vc0Yo8Tc6lRs33GCfS0/Rwan0wmdThfTFHso86NJBOxwOCCTyaDValkv6k8/\n/RTLly/HlVdeiffffx9JSUmxOrSw4s4778Rnn32G7du3i2QcZogRsoiQ4XQ6wTCM3/SuL59uYlxS\nXV3N+nTTvdF05MevRYdCoPFeZw0EwaTYo6XqDgYHG4ax/MkG9t+PLy/E3DmZCRE5+nJte++99/D5\n559jxowZqKurQ319Pd566y1ceumlCXFsgWDp0qX44IMP8Pnnn3N6j1NSUjie+iIEIaasRcQfSFvU\nvn37OLXo9vZ2zJgxgzUuqa6uRn5+PjvEgV/rC7atJZzjHWMBfhtNKK1MwaiQI5HqJn/7ux9vROtR\nVzZk07oKpKUm1sxuvlEMwzD4/PPPsWHDBtTU1KCvrw8AkJOTg+rqatx22234+c9/HuOVjx7eNm0b\nNmzATTfdFIMVJRTElHWw+Nvf/oaVK1eipqYGarUa5513Hj755JNYL+u0gkQigUqlwpw5czBnzhwA\nrodcb28vq+h+9913cffdd0Oj0Xj4dOt0Op9pRD6hkAcoiSijZRkZTgTSkxsI6NQ1AV+FHKlUN10m\nuPyiDLz8RgfS0xQJRca0Ep82ihkeHsa2bdtQW1uLtWvXYs6cOdi9ezd2796NXbt2ob+/P9ZLDwv4\nWgUR4YUYIVP4+OOPsXDhQqxatQrz5s2DzWZDbW0t/vu//zvWS/vJgZAE7dO9a9cuNDU1YfLkyRzB\nGO3T7Wvgu1KphEqlSqhacSizisOBQFPdgWQmhMoETkaKG+7Yj0kTdFi5Iv5tF+ljoMsEDMPg22+/\nxZIlS1BRUYHXXnsNWVlZsV6uiPiEmLIOFA6HA0VFRVi5ciXmz58f6+WIEEAgPt2kJt3Z2YlNmzZh\n8eLFSElJ4RC0VCr16DuNx9R1OGcVjxahprodDgdMJpNgmWDjpnZIpRLcdFVuTI4pUHg7BpPJhKef\nfhrvv/8+XnrpJdxwww0JtdkTEXWIKetAsWfPHnR2uvojZ86cie7ublRUVOD3v/89pkyZEuPViQBc\n6dPU1FRcdNFFuOiiiwBwfbp37tyJZ599Fvv27QMAFBUVISMjA+eddx7r000EY6RdiCAcgrFwgR9R\nxlp9DASW6qbPKSFkp9MJiUQCrVbrEdlfftFYtLaZEa/g/x1IqYNhGOzevRuLFi1CYWEh9u3bh/z8\nwOc4xwqvvvoqVq9eje7ubsyYMQNr1qxBVVVVrJclgoIYIZ/Cpk2bcO2116KwsBAvvfQSCgsLsXr1\navzjH/9Ac3MzUlNTY71EEX7w5Zdf4tZbb0Vvby9uvvlmjB8/nq3hHT9+HJWVlaxYrLq6GtnZ2R7T\nroQEY9FUIEd7VnG44XQ6YbVa2fY1GkKpbgBxeXx0doL+O4yMjGDVqlV4/fXX8eyzz2LRokUJERVv\n2rQJN998M15//XVUV1fjpZdewubNm9HU1ISMjIxYL++nAjFl/fDDD+P555/3+nOJRIL6+nr8+OOP\nuP7667F+/XrceuutAFyzb/Py8vA///M/uP3226O1ZBEhYsuWLVizZg1effVVjB/vnhzkz6eb1KIr\nKiqgVqv9pmXp3uhwgXZ5ile3MH/gR5SkJzcevKWDOQZSs6fb4hiGwcGDB3H77bcjJSUFb731FiZO\nnBizdQaLM844A3PmzMHLL78MwHWc+fn5WLZsGR588MEYr+4nA5GQ+/v7/Socx48fj++++w7z5s3D\nd999h7POOov92RlnnIGLLroIK1eujPRSRYQBDMP4faDzfbpJLdqbTze/95RvsUinu4MlE9LSFctZ\nxeFAMJG9L29pvqo7muUDbzV7u92OP/7xj3jxxRfx2GOPYfny5Qm1WbLZbNBqtfj4449xxRVXsK/P\nnz8fQ0ND+PTTT2O4up8UxBpyeno60tPT/f7erFmzoFKp0NjYyBKyzWbDkSNHUFhYGOlliggTAiEy\niUQCpVKJWbNmYdasWbjjjjs8fLo3b96MBx98EFKplBNFz5o1C8nJyRxFN+kLBoITjMXLrOLRgN+T\nG0hLGRk4QtfF+VG01WoNud88lGOgo2K6Zt/U1IRFixbB6XTiu+++w9SpU8P2vdFCX18fHA4Hxo0b\nx3l93LhxaGxsjNGqRAjhtCfkQJGUlITFixfjySefRF5eHgoLC/HCCy9AIpHgqquuitm6rFYrqqur\nUVNTg3379mH69OkxW8vpDIlEgvT0dFx22WW47LLLALgipsbGRuzcuRM7d+7Ek08+iYMHD2LixIkc\nhzHi0y0kGBPq4wXAaWXSarUxs7IcDbz15IaCUGwrw5HqdjqdMJlMHlGxw+HAunXr8Mwzz2D58uV4\n5JFHotJuJuKnDZGQKaxevRoKhQI33XQTzGYz5syZg6+//hopKSkxW9ODDz6IvLw8HDhwIGZr+KlC\nJpOhvLwc5eXluOWWWzx8ur/++ms899xzHJ9uQtKZmZleIz4CUqOM55GUQgglKg4Woai6g0l182cu\n0yrwo0ePYsmSJejr68OXX36JWbNmJdTfh4+MjAzIZDL09PRwXu/p6RF7puMMp30NOZGxdetW3H//\n/fj4449RXl4uRshxiEB9uidNmoSNGzdCpVLh2muvZcVOBJEUjIUTdrsdJpMpburdQoIxf6lubzOX\nnU4n3n33XTzyyCO4/fbb8fTTT0Oj0cTs2MIJIVFXQUEBli1bhgceeCDGq/vJQKwhJyp6enqwcOFC\nfP7556fNQ+F0hEQiQWFhIQoLC3HNNdcI+nS/8sorOH78OJxOJ6644gqkp6ejqqqK9en2ZVk5GsFY\nOMFXgRMFdawRbKqbWKkCrrJBUlISJBIJurq6cNddd6G5uRmff/455s6dm9BRMR/33nsv5s+fj1mz\nZrFtTyaTSTRBijOIhBynuOWWW7B06VJUVlbi6NGjsV6OiABB+3TPnDkTLS0t6OzsxIwZM7BgwQJ0\ndnbinXfewbJlyzg+3VVVVZg5cyZ0Oh2nN5oWjMWqRcjbrN94hLdUNxHf0VmJ+fPnY//+/SgrK8Pe\nvXsxb948fPnll6eliPPqq69GX18fnnjiCfT09KCiogJffPEFMjMzY700ERTElHUUEWhP9N///nd8\n9NFH+OabbyCVSnHkyBGMHz9eTFknGBiGwTXXXIMzzzwTd911F0sSwfp0AwioRSjcwjB6zGOiqsAB\n94YCAJtmdzqd2LJlC/73f/8XjY2N6OrqwsmTJwEAEyZMwPr163H++efHctkiTj+IfcjxhEB6oouL\ni3H11Vfjr3/9K+d1h8MBuVyO66+/Hhs2bIjkMkWEEYH0RZPf8+bTTQvGqqqqMGbMmIDqpqNxGEuk\nqNgb6DQ7vaFgGAZbtmzBsmXLcMkll+CPf/wjUlJS0Nrayp73O+64g90MiRARJoiEnIhob29nd+sA\n0NnZiUsuuQQff/wxqqurkZOTE8PViYgW+D7du3btwv79+1FQUMCZGT1lyhTIZDJObzRfMMbvjfb1\nnadTVMzfUAwNDWHFihX4xz/+gbVr1+KXv/xlwm00RCQsREI+HXD06FEUFxfHLGV99OhRrFy5El9/\n/TW6u7uRm5uL66+/Ho8++qjYmxlFkIhvz549nCia79NdVVWFnJwcDkHTUTQx5uB7SttsNrZmrVar\nEzYqJi1Z/Kj4m2++wdKlS1FdXY0///nPCVU/Fe/B0wKiyvp0QSwfjA0NDWAYBuvXr8eECRNQW1uL\n2267DSaTCS+88ELM1vVTA+mXnTt3LubOnQvA06d73bp1WLRoEVJTUzkEXVlZCZVKxRGM0epjgkTt\njQa8t2QZjUY8+eST+PDDD/Hyyy/juuuuS7hjE+/BnwbECFlESFi9ejXWrl2LlpaWWC9FBIVAfLoJ\nURcVFWHLli0YHh7G5ZdfzmkJogVjJJqOVxLjG5WQliyGYbBz504sWrQIJSUlWL9+PXJz43v2cjAQ\n78GEgxghi4gMBgcHMWbMmFgvQwQPgfh0f/TRR3jgL+x0JAAACWNJREFUgQdgs9lgMplw4YUXIisr\ny8On2+FwsNObALdgjDYviTVJe7PvtFgsePbZZ/Hmm2/i+eefx2233ZaQtXBfEO/B0w9ihCwiaLS0\ntGD27Nl48cUXsWDBglgvR0QQYBgGb775Ju677z6oVCrcdNNNMBgM2LlzJw4ePIgJEyZwLEBpn+7R\nCsbCfRxks0CPq2QYBjU1NVi4cCHGjBmDDRs2cEZxni4Q78GEhCjqEuEdgfZFl5aWsq91dHTgvPPO\nw7x587Bu3bpoLFNEmHH11VdDr9fjxRdfRGpqKgB4+HTv2rULO3fuZH266Xr02LFjgxKMhTuKdjgc\nMJlMHqMebTYbVq9ejTVr1uDJJ5/EsmXL4n5MongP/qQgErII7wh0VjSZUNTZ2Ynzzz8fZ511ltgL\nncAg4x79IVCf7mnTprFmG4SgHQ4H+zlC5iWhkDQdFUulUmi1WpZwGxoasHDhQshkMmzYsAHl5eVB\nf34sIN6DPymIhCwiPOjo6MC8efNQVVWFd999N+a1QxHRh5BP965du9De3o7p06dzUt18n25vDmOB\nCsYcDgfMZjMcDgcnKnY4HPjzn/+M5557Dvfffz8eeuihgDYbiQjxHkx4iIQsYvTo7OzEz372MxQX\nF2Pjxo2cNCB/6Hmk8Oqrr2L16tXo7u7GjBkzsGbNGlRVVUXlu0V4B8Mw6O3t5ViA/vDDD9BoNJwo\neubMmdBqtRzBmN1uZz/Hm2CMbAIsFgvbkkUI9/Dhw1iyZAmGhoawceNGVFRUnLYkFQ/3oIhRQyRk\nEaPH22+/7SEcIZaQdGoyUti0aRNuvvlmvP766+ykms2bN6OpqQkZGRkR/34RgSNQn+7Zs2ezdVFf\ngjGn0wmGYSCTyaDT6ViB2caNG/H4449j8eLFePLJJ6FWq2N1yFFBrO9BEWGBSMgiEh9Cs1zz8/Ox\nbNkyPPjggzFenQh/8ObTbbVaMWvWLA5Jp6enw2azYceOHSgpKYFerwcArF27Fm+//TZmzJiBtrY2\n9Pf3491338W555572kbFIk47iIQsIrFhs9mg1Wrx8ccf44orrmBfnz9/PoaGhvDpp5/GcHUiQoU3\nn+7s7Gyo1Wo0NjZixYoVePDBB6FQKPDdd99h48aNqKmpQXNzM1tLrqysxC233IKFCxfG+pBEiPAH\n0RhERGKjr68PDofDo042btw4NDY2xmhVIkYLqVSKiRMnYuLEibjxxhvhdDqxbt06PPDAA1AoFLjm\nmmvwwQcf4JVXXsG0adMwMDAA6/9v7/5Dqt7vOI4/3+fkHyVkRPRTKhV28Z+Q1TT6wUhYQsM/kqYw\nu+HYRfphP3CsOv80tgb6RxSLsRsUCQ0jNoSMfkxCmpljW41r0TjNP244XOMLjkVZ5Klvn/2h9yy5\nVtb1nM85ntcDvn+cDwqvA+L7+/mdSHD27FnWr1/P3bt3kwedJBIJ319HZFqoIIuIdw8fPmT//v3U\n19dz4sQJ5s2blzyn+9atW5w6dYqLFy9SUFAAQEVFBRUVFezbt89zcpHpM7POkpMZZ8GCBUSjUYIg\nmNAeBAGLFy/2lEqmW0lJCfF4nLa2tuRhJWbGsmXLqKur48aNG8linG0SiQRlZWVEIhHu3bvnO45k\nMBVkyWh5eXmsXr2a7u7uZJtzju7ubtatW+cxmUy3kpIS3xFS4uDBgxQWFmrxmbyXCrJkvObmZk6f\nPs25c+d48OABO3fu5Pnz5zQ0NKQ9S0tLC+Xl5cydO5dFixaxdetWBgYG0p5DssO1a9e4fv06x44d\n4wMW0EqO0hyyZLza2lqGh4c5cuQIQRBQVlZGV1eXlwvme3t72bt3L2vWrOHVq1fEYjE2b95MPB5n\n9uzZac8jmSsIAhobG7l06ZL+NmRKtO1J5BsYHh5m4cKF3Lx5kw0bNviOIxlky5YtbNy4kVgsxuDg\nIEVFRfT397Nq1Srf0cSP985ZaMha5Bt4/PgxZqZ7aXNELBYjEom89YlGowwMDHDy5ElGRkY4dOgQ\ngIarZUrUQxb5SM45qqurefr0KT09Pb7jSBpM5XamoqIiamtruXz58oT2MAyZNWsW9fX1uqkpN+mk\nLpFU2bVrF11dXfT19bFkyRLfcSSDDA0N8eTJk+TnR48eUVVVRUdHB+Xl5SxdutRjOvFEJ3WJpEJT\nUxNXr16lt7dXxVi+prCwcMLn/Px8nHMUFxerGMtbqSCLfKCmpiY6Ozvp6elh+fLlvuNIltA+ZHkf\nLeoS+QC7d++mvb2d8+fPk5+fTxAEBEHAixcvfEdLam1tJRKJ0Nzc7DuKjFuxYgVhGGqFtbyT5pBF\nPkAkEpm0p9PW1saOHTs8JJro9u3b1NXVUVBQwKZNmzh+/LjvSCIyRtueRKbT69evCcPwa08mFOOR\nkRG2b9/OmTNnkudBi0j2UEEWmSH27NlDdXU1lZWVvqOIyEfQoi6RGeDChQv09/dz584d31FE5COp\nhyyS5YaGhjhw4ADt7e3k5eX5jpPVrly5wtq1a5kzZw7z58+npqbGdyTJIVrUJZLlOjs7qampIRqN\nJo9oDMMQMyMajTI6OqotN1PQ0dFBY2Mjra2tVFZW8vLlS+7fv8+2bdt8R5OZQSd1icx0z549Y3Bw\ncEJbQ0MDpaWlHD58mNLSUk/JskcYhqxcuZKjR496udZTcsK0FmQRyRJmdgP4wjmnzchTYGbfAf4M\n/BjYBywG+oGfOuf+7jOb5A7NIYvMTBnxpm1mS83st2Y2bGbPzeyumX3bd65JFDPWg/kZ8Avg+8B/\ngT+amfaQSVqoIIvMQM65St+94/FC1geMAlVAKfATxgpdujK0mNnrdzyhmX2L//8v/KVz7qJz7gvg\nR4y92PwgXXklt2nbk4ikymHgn865z95oG3zbD6fIMeB9dx1+CXx140P8q0bnXMLMvgR0YLmkhQqy\niKRKNfAHM/sd8F3gX8BvnHNn0hXAOfcf4N0XGANm9jfGevKfAH8ab8sDVpL+lwjJURqyFpFUKQZ2\nAf8ANgOfAyfN7FOvqSbhnHsKnAJ+bmbfGx/G/pyxIevfew0nOUOrrEUkJcxsFPirc27jG22/AtY4\n59b7SzY5M4sCLcCnwGzgL8AB51z8nb8oMk3UQxaRVPk3b8zJjouToXOyzrnQOXfQObfEOTfPOVel\nYizppIIsIqnSx9ic7Js+QXOyIpNSQRaRVDkBrDWzmJmVmNkPgc+AX3vOJZKR/gfwfi99jQbKZgAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19d430c0d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot_surface(X, Y, W, rstride=1, cstride=1, linewidth=0,\n",
    "                cmap=plt.cm.coolwarm, norm=norm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARwAAAAWCAYAAAASGCMyAAAABHNCSVQICAgIfAhkiAAACC5JREFU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\ngg==\n",
      "text/latex": [
       "$$\\left ( -0.75, \\quad -1.29903810567666\\right )$$"
      ],
      "text/plain": [
       "(-0.75, -1.29903810567666)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQUAAAAWCAYAAADJo4kQAAAABHNCSVQICAgIfAhkiAAACBtJREFU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\njvzXkRkZGRkZGRkZGRkZGTH8DePK7FiAr6pIAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( -0.75, \\quad 1.29903810567666\\right )$$"
      ],
      "text/plain": [
       "(-0.75, 1.29903810567666)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD0AAAAWCAYAAABzCZQcAAAABHNCSVQICAgIfAhkiAAAAi1JREFU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\nQmCC\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(0, 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAWCAYAAABXEBvcAAAABHNCSVQICAgIfAhkiAAAAuRJREFU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\npkvKAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 1.5, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(1.5, 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l in Lsg:\n",
    "    display((x.subs(l).n(), y.subs(l).n()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-1.5, 2, 100)\n",
    "yn = np.linspace(-1.8, 1.8, 100)\n",
    "X, Y = np.meshgrid(xn, yn)\n",
    "W = np.maximum(fn(X, Y), -.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DFRIrJVIpyEH0X45MGGFViJACm+cILFYI7MY5xOrlU5/vXtdit/KQ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19d413d4240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot_surface(X, Y, W, rstride=1, cstride=1, linewidth=0,\n",
    "                cmap=plt.cm.coolwarm);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAAbCAYAAABlVEF+AAAABHNCSVQICAgIfAhkiAAAAzdJREFU\naIHt2V2oFVUUwPFfaZlmJRUl2oeKgkEhalwvpiF9PGT1kgVRokRFERFRPSSKSUZQBBGCUFKdMChI\nFPog6iG0yAjKIgWhCDQoLIKKTMjKelhzudN0PefMzJmZe+n84cDstWfvtdbZe6+99h76jDrGNW1A\nwhP4Hd80bUhNLMVlWIQH8DMONGlQlqX4HstytLmhGlNq40esTp5vwm+YPFR5YhMWpTgd87A/R5u5\nWFWNObWxDNtS5ZNxwlCh6UG5E1tytrkFr2RkA9iOt7EXz2N6aeuqY59YHcSq34hfmzNnmOtxcfK8\nU/fhaw8mpsoL8C6mJOXJeB8/YEYBu04q0KYIA1iHFzCpJp1tmebfIWin7gZlAFszsrcwOyObj7/x\nagHbtqh3ld2NT6X2lKa4DWvwcPL7Ds/h2g7tnsE1GdlhkbWdk5H/JDbUvLQUW2HdMigSm5lJea6Y\nQDdWqLMQB3ReKePwBcZn5HtFOj0zIz9kOG7noaXaQbkU72FCUl6Oo5gz9ELWwTIsxEox6jNwB+4S\nsX46HsHXmTbn4T5MxYNiCb95nP6vwAf4MyMfxGliEIaYhnNFWKyLbv3/ROwj9+IYluA6fNVrg+Zg\nk+G0roUvsVgcko6JP70MLyZ9dcPj+CvRn5eW/CulDv9zsxmnpsqv4ePk+Xw8hbNK9H8KPpfK5dsw\nS6SXjxXU1ZJ/UHrqf9rJeYlB3TgOn4kNGy7EwVTdt0lfa7s1pAMrRCxe0+G9CdiF3eL6oh0vCZ+z\nXCBC4dER6m4XmVKWqv0vzUUirl7Vwz63GT7TtGMrHi2pq6XcRl/a/ypO9FeKWbY7JZtVor8zxOzd\n1+G9DSKOr0/JmriOKe1/LwZlIp7EJUn5apG6HknpeKhE/yvEFUo7ViZ6NmbkS0ro7Zae+9+LlHh5\nonQP/hCz4pdU/Vr/PYXn4WZxR3Y8LsfTeAcvp+TjRRipmp7734tB2SXi8MLkNyiykWfFMn4dHxXs\ne6rYvA+2eWcHzsStI9QVzcDyUKX/o5L7cU/NOluqPdGPeT7E2TXrXKC+m+Ixx2xxA/y/o+mPXO0Y\n6WNWn4Z5wyj4xtCnT58+ffqMZf4BW/mi4+AF40MAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- \\frac{x^{4}}{2} + x^{3}$$"
      ],
      "text/plain": [
       "   4     \n",
       "  x     3\n",
       "- ── + x \n",
       "  2      "
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs(y, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also Sattel in $(0,0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "anaconda-cloud": {},
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   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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   },
   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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