cylindrical_resonator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display, Math, Latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%display latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ES.<rh,ph,z> = EuclideanSpace(coordinates='cylindrical')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\rho} :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\phi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)} ;\\quad z :\\ \\left( -\\infty, +\\infty \\right)</script></html>"
      ],
      "text/plain": [
       "rh: (0, +oo); ph: [0, 2*pi] (periodic); z: (-oo, +oo)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ES.cylindrical_coordinates().coord_range()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = ES.vector_field(\n",
    "    function('H_rho')(rh,ph,z),\n",
    "    function('H_phi')(rh,ph,z),\n",
    "    function('H_z')(rh,ph,z),\n",
    "    name='H')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = ES.vector_field(\n",
    "    function('E_rho')(rh,ph,z),\n",
    "    function('E_phi')(rh,ph,z),\n",
    "    function('E_z')(rh,ph,z),\n",
    "    name='E')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}E = E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) e_{ {\\rho} } + E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) e_{ {\\phi} } + E_{z}\\left({\\rho}, {\\phi}, z\\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "E = E_rho(rh, ph, z) e_rh + E_phi(rh, ph, z) e_ph + E_z(rh, ph, z) e_z"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$rot\\,\\vec{E} = \\mu\\,\\frac{i\\,\\omega}{c}\\,\\vec{H}$\n",
    "\n",
    "$rot\\,\\vec{H} = - \\frac{i\\,\\omega}{c} \\epsilon_{\\alpha\\,\\beta} \\vec{E}$\n",
    "\n",
    "$rot\\,rot\\,\\vec{E} = \\mu\\,\\frac{i\\,\\omega}{c}rot\\,\\vec{H}$\n",
    "\n",
    "$rot\\,rot\\,\\vec{E} = \\mu\\,\\frac{i\\,\\omega}{c}\\left(- \\frac{i\\,\\omega}{c} \\epsilon_{\\alpha\\,\\beta} \\vec{E}\\right)$\n",
    "\n",
    "$rot\\,rot\\,\\vec{E} = \\mu\\,\\frac{\\omega^2}{c^2} \\epsilon_{\\alpha\\,\\beta} \\vec{E}$\n",
    "\n",
    "$rot\\,rot\\,\\vec{E} = grad\\,div\\,\\vec{E} - Laplasian\\,\\vec{E}$\n",
    "\n",
    "$Laplasian\\,\\vec{E} + \\mu\\frac{\\omega^2}{c^2}\\,\\epsilon_{\\alpha\\,\\beta}\\vec{E} - grad\\,div\\,\\vec{E} = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Laplacian of a vector field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sage.manifolds.operators import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E x H = (-E_z(rh, ph, z)*H_phi(rh, ph, z) + E_phi(rh, ph, z)*H_z(rh, ph, z)) e_rh + (E_z(rh, ph, z)*H_rho(rh, ph, z) - E_rho(rh, ph, z)*H_z(rh, ph, z)) e_ph + (E_rho(rh, ph, z)*H_phi(rh, ph, z) - E_phi(rh, ph, z)*H_rho(rh, ph, z)) e_z\n"
     ]
    }
   ],
   "source": [
    "ExH = E.cross_product(H)\n",
    "print(ExH.display())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{curl}\\left(E\\right) = \\left( -\\frac{{\\rho} \\frac{\\partial\\,E_{\\phi}}{\\partial z} - \\frac{\\partial\\,E_{z}}{\\partial {\\phi}}}{{\\rho}} \\right) e_{ {\\rho} } + \\left( \\frac{\\partial\\,E_{\\rho}}{\\partial z} - \\frac{\\partial\\,E_{z}}{\\partial {\\rho}} \\right) e_{ {\\phi} } + \\left( \\frac{{\\rho} \\frac{\\partial\\,E_{\\phi}}{\\partial {\\rho}} + E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) - \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}} \\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "curl(E) = -(rh*d(E_phi)/dz - d(E_z)/dph)/rh e_rh + (d(E_rho)/dz - d(E_z)/drh) e_ph + (rh*d(E_phi)/drh + E_phi(rh, ph, z) - d(E_rho)/dph)/rh e_z"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rot_E = curl(E)\n",
    "rot_E.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{grad}\\left(\\mathrm{div}\\left(E\\right)\\right) = \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho}\\partial z} + {\\rho} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho}\\partial {\\phi}} + {\\rho} \\frac{\\partial\\,E_{\\rho}}{\\partial {\\rho}} - E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - \\frac{\\partial\\,E_{\\phi}}{\\partial {\\phi}}}{{\\rho}^{2}} \\right) e_{ {\\rho} } + \\left( \\frac{{\\rho} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho}\\partial {\\phi}} + {\\rho} \\frac{\\partial^2\\,E_{z}}{\\partial {\\phi}\\partial z} + \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi} ^ 2} + \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}^{2}} \\right) e_{ {\\phi} } + \\left( \\frac{{\\rho} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho}\\partial z} + {\\rho} \\frac{\\partial^2\\,E_{z}}{\\partial z ^ 2} + \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi}\\partial z} + \\frac{\\partial\\,E_{\\rho}}{\\partial z}}{{\\rho}} \\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "grad(div(E)) = (rh^2*d^2(E_rho)/drh^2 + rh^2*d^2(E_z)/drhdz + rh*d^2(E_phi)/drhdph + rh*d(E_rho)/drh - E_rho(rh, ph, z) - d(E_phi)/dph)/rh^2 e_rh + (rh*d^2(E_rho)/drhdph + rh*d^2(E_z)/dphdz + d^2(E_phi)/dph^2 + d(E_rho)/dph)/rh^2 e_ph + (rh*d^2(E_rho)/drhdz + rh*d^2(E_z)/dz^2 + d^2(E_phi)/dphdz + d(E_rho)/dz)/rh e_z"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grad_div_E = grad(div(E))\n",
    "grad_div_E.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\mathrm{curl}\\left(\\mathrm{curl}\\left(E\\right)\\right) = \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial z ^ 2} - {\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho}\\partial z} - {\\rho} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho}\\partial {\\phi}} - \\frac{\\partial\\,E_{\\phi}}{\\partial {\\phi}} + \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} \\right) e_{ {\\rho} } + \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{\\phi}}{\\partial {\\rho}} - {\\rho} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho}\\partial {\\phi}} - {\\rho} \\frac{\\partial^2\\,E_{z}}{\\partial {\\phi}\\partial z} - E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}^{2}} \\right) e_{ {\\phi} } + \\left( -\\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho}\\partial z} - {\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho} ^ 2} + {\\rho} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi}\\partial z} + {\\rho} \\frac{\\partial\\,E_{\\rho}}{\\partial z} - {\\rho} \\frac{\\partial\\,E_{z}}{\\partial {\\rho}} - \\frac{\\partial^2\\,E_{z}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} \\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "-curl(curl(E)) = (rh^2*d^2(E_rho)/dz^2 - rh^2*d^2(E_z)/drhdz - rh*d^2(E_phi)/drhdph - d(E_phi)/dph + d^2(E_rho)/dph^2)/rh^2 e_rh + (rh^2*d^2(E_phi)/drh^2 + rh^2*d^2(E_phi)/dz^2 + rh*d(E_phi)/drh - rh*d^2(E_rho)/drhdph - rh*d^2(E_z)/dphdz - E_phi(rh, ph, z) + d(E_rho)/dph)/rh^2 e_ph - (rh^2*d^2(E_rho)/drhdz - rh^2*d^2(E_z)/drh^2 + rh*d^2(E_phi)/dphdz + rh*d(E_rho)/dz - rh*d(E_z)/drh - d^2(E_z)/dph^2)/rh^2 e_z"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rot_rot_E = -curl(curl(E))\n",
    "rot_rot_E.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Delta\\left(E\\right) = \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{\\rho}}{\\partial {\\rho}} - E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - 2 \\, \\frac{\\partial\\,E_{\\phi}}{\\partial {\\phi}} + \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} \\right) e_{ {\\rho} } + \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{\\phi}}{\\partial {\\rho}} - E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi} ^ 2} + 2 \\, \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}^{2}} \\right) e_{ {\\phi} } + \\left( \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{z}}{\\partial {\\rho}} + \\frac{\\partial^2\\,E_{z}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} \\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "Delta(E) = (rh^2*d^2(E_rho)/drh^2 + rh^2*d^2(E_rho)/dz^2 + rh*d(E_rho)/drh - E_rho(rh, ph, z) - 2*d(E_phi)/dph + d^2(E_rho)/dph^2)/rh^2 e_rh + (rh^2*d^2(E_phi)/drh^2 + rh^2*d^2(E_phi)/dz^2 + rh*d(E_phi)/drh - E_phi(rh, ph, z) + d^2(E_phi)/dph^2 + 2*d(E_rho)/dph)/rh^2 e_ph + (rh^2*d^2(E_z)/drh^2 + rh^2*d^2(E_z)/dz^2 + rh*d(E_z)/drh + d^2(E_z)/dph^2)/rh^2 e_z"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DE = laplacian(E)\n",
    "DE.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{\\rho}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{\\rho}}{\\partial {\\rho}} - E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - 2 \\, \\frac{\\partial\\,E_{\\phi}}{\\partial {\\phi}} + \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(rh, ph, z) |--> (rh^2*d^2(E_rho)/drh^2 + rh^2*d^2(E_rho)/dz^2 + rh*d(E_rho)/drh - E_rho(rh, ph, z) - 2*d(E_phi)/dph + d^2(E_rho)/dph^2)/rh^2\n",
      "2\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{\\phi}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{\\phi}}{\\partial {\\rho}} - E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi} ^ 2} + 2 \\, \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}^{2}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(rh, ph, z) |--> (rh^2*d^2(E_phi)/drh^2 + rh^2*d^2(E_phi)/dz^2 + rh*d(E_phi)/drh - E_phi(rh, ph, z) + d^2(E_phi)/dph^2 + 2*d(E_rho)/dph)/rh^2\n",
      "3\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$$\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{{\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho} ^ 2} + {\\rho}^{2} \\frac{\\partial^2\\,E_{z}}{\\partial z ^ 2} + {\\rho} \\frac{\\partial\\,E_{z}}{\\partial {\\rho}} + \\frac{\\partial^2\\,E_{z}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}}$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(rh, ph, z) |--> (rh^2*d^2(E_z)/drh^2 + rh^2*d^2(E_z)/dz^2 + rh*d(E_z)/drh + d^2(E_z)/dph^2)/rh^2\n"
     ]
    }
   ],
   "source": [
    "for i in ES.irange():\n",
    "    print(i)\n",
    "    display(Math(latex((DE[i].display()))))\n",
    "    print(DE[i].display())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega = var(\"omega\")\n",
    "c = var(\"c\")\n",
    "mu = var(\"mu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon_rh_rh = var(\"epsilon_rh_rh\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon_ph_ph = var(\"epsilon_ph_ph\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon_z_z = var(\"epsilon_z_z\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq_rh = (DE[1] + mu * epsilon_rh_rh * omega^2 / c^2 * E[1]).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq_ph = (DE[2] + mu * epsilon_ph_ph * omega^2 / c^2 * E[2]).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "eq_z = (DE[3] + mu * epsilon_z_z * omega^2 / c^2 * E[3]).expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{\\epsilon_{\\mathit{rh}_{\\mathit{rh}}} \\mu \\omega^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial\\,E_{\\rho}}{\\partial {\\rho}}}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial\\,E_{\\phi}}{\\partial {\\phi}}}{{\\rho}^{2}} + \\frac{\\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} + \\frac{\\partial^2\\,E_{\\rho}}{\\partial {\\rho} ^ 2} + \\frac{\\partial^2\\,E_{\\rho}}{\\partial z ^ 2}</script></html>"
      ],
      "text/plain": [
       "(rh, ph, z) |--> epsilon_rh_rh*mu*omega^2*E_rho(rh, ph, z)/c^2 + d(E_rho)/drh/rh - E_rho(rh, ph, z)/rh^2 - 2*d(E_phi)/dph/rh^2 + d^2(E_rho)/dph^2/rh^2 + d^2(E_rho)/drh^2 + d^2(E_rho)/dz^2"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{\\epsilon_{\\mathit{ph}_{\\mathit{ph}}} \\mu \\omega^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial\\,E_{\\phi}}{\\partial {\\rho}}}{{\\rho}} - \\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} + \\frac{2 \\, \\frac{\\partial\\,E_{\\rho}}{\\partial {\\phi}}}{{\\rho}^{2}} + \\frac{\\partial^2\\,E_{\\phi}}{\\partial {\\rho} ^ 2} + \\frac{\\partial^2\\,E_{\\phi}}{\\partial z ^ 2}</script></html>"
      ],
      "text/plain": [
       "(rh, ph, z) |--> epsilon_ph_ph*mu*omega^2*E_phi(rh, ph, z)/c^2 + d(E_phi)/drh/rh - E_phi(rh, ph, z)/rh^2 + d^2(E_phi)/dph^2/rh^2 + 2*d(E_rho)/dph/rh^2 + d^2(E_phi)/drh^2 + d^2(E_phi)/dz^2"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left({\\rho}, {\\phi}, z\\right) \\mapsto \\frac{\\epsilon_{z_{z}} \\mu \\omega^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial\\,E_{z}}{\\partial {\\rho}}}{{\\rho}} + \\frac{\\frac{\\partial^2\\,E_{z}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} + \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho} ^ 2} + \\frac{\\partial^2\\,E_{z}}{\\partial z ^ 2}</script></html>"
      ],
      "text/plain": [
       "(rh, ph, z) |--> epsilon_z_z*mu*omega^2*E_z(rh, ph, z)/c^2 + d(E_z)/drh/rh + d^2(E_z)/dph^2/rh^2 + d^2(E_z)/drh^2 + d^2(E_z)/dz^2"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_z.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "desolve_laplace(eq_z,E[3],ivar=rh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = var(\"k\")\n",
    "m = var(\"m\")\n",
    "# kappa_z^2 = epsilon_z_z * mu * omega^2 / c^2 - k^2\n",
    "kappa_z = var(\"kappa_z\")\n",
    "\n",
    "# kappa_rh^2 = epsilon_rh_rh * mu * omega^2 / c^2 - k^2\n",
    "kappa_rh = var(\"kappa_rh\")\n",
    "\n",
    "# kappa_ph^2 = epsilon_ph_ph * mu * omega^2 / c^2 - k^2\n",
    "kappa_ph = var(\"kappa_ph\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-k^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\epsilon_{z_{z}} \\mu \\omega^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{z}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "-k^2*E_z(rh, ph, z) + epsilon_z_z*mu*omega^2*E_z(rh, ph, z)/c^2 + diff(E_z(rh, ph, z), rh)/rh + diff(E_z(rh, ph, z), ph, ph)/rh^2 + diff(E_z(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_z_ex = eq_z.expr().subs(diff(E_z(rh, ph, z), z, z) == -k^2*E_z(rh, ph, z))\n",
    "eq_z_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{z}^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{z}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_z^2*E_z(rh, ph, z) + diff(E_z(rh, ph, z), rh)/rh + diff(E_z(rh, ph, z), ph, ph)/rh^2 + diff(E_z(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_z_ex = (eq_z_ex.subs(epsilon_z_z * mu * omega^2 * E_z(rh, ph, z) / c^2 == (kappa_z^2 + k^2) * E_z(rh, ph, z))) \\\n",
    "    .full_simplify() \\\n",
    "    .expand()\n",
    "eq_z_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{z}^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{z}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{z}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_z^2*E_z(rh, ph, z) - m^2*E_z(rh, ph, z)/rh^2 + diff(E_z(rh, ph, z), rh)/rh + diff(E_z(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_z_ex = eq_z_ex.subs(diff(E_z(rh, ph, z), ph, ph) == -m^2*E_z(rh, ph, z))\n",
    "eq_z_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_m = var(\"psi_m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "desolve(eq_z_ex == 0, E_z(rh, ph, z), ivar=rh, contrib_ode=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E_z(rh, ph, z) = E_z(rh, ph, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_sol_z(rh, ph, z) = bessel_J(m, kappa_z * rh)*sin(m * ph + psi_m) * exp(-I*k*z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}J_{m}(\\kappa_{z} {\\rho}) e^{\\left(-i \\, k z\\right)} \\sin\\left(m {\\phi} + \\psi_{m}\\right)</script></html>"
      ],
      "text/plain": [
       "bessel_J(m, kappa_z*rh)*e^(-I*k*z)*sin(m*ph + psi_m)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_sol_z(rh, ph, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "#eq_z_sol = laplacian(E_sol_z(rh, ph, z)) + mu * epsilon_z_z * omega^2 / c^2 * E_sol_z(rh, ph, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "#eq_z_sol.expr().subs(m == 0, psi_m == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "#eq_z_sol.expr().subs(m == 1, psi_m == 0).full_simplify().expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\epsilon_{\\mathit{rh}_{\\mathit{rh}}} \\mu \\omega^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\partial^{2}}{(\\partial z)^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "epsilon_rh_rh*mu*omega^2*E_rho(rh, ph, z)/c^2 + diff(E_rho(rh, ph, z), rh)/rh - E_rho(rh, ph, z)/rh^2 - 2*diff(E_phi(rh, ph, z), ph)/rh^2 + diff(E_rho(rh, ph, z), ph, ph)/rh^2 + diff(E_rho(rh, ph, z), rh, rh) + diff(E_rho(rh, ph, z), z, z)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh.expr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-k^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\epsilon_{\\mathit{rh}_{\\mathit{rh}}} \\mu \\omega^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "-k^2*E_rho(rh, ph, z) + epsilon_rh_rh*mu*omega^2*E_rho(rh, ph, z)/c^2 + diff(E_rho(rh, ph, z), rh)/rh - E_rho(rh, ph, z)/rh^2 - 2*diff(E_phi(rh, ph, z), ph)/rh^2 + diff(E_rho(rh, ph, z), ph, ph)/rh^2 + diff(E_rho(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh_ex = eq_rh.expr().subs(diff(E_rho(rh, ph, z), z, z) == -k^2*E_rho(rh, ph, z))\n",
    "eq_rh_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{rh}}^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_rh^2*E_rho(rh, ph, z) + diff(E_rho(rh, ph, z), rh)/rh - E_rho(rh, ph, z)/rh^2 - 2*diff(E_phi(rh, ph, z), ph)/rh^2 + diff(E_rho(rh, ph, z), ph, ph)/rh^2 + diff(E_rho(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh_ex = (eq_rh_ex.subs(epsilon_rh_rh * mu * omega^2 * E_rho(rh, ph, z) / c^2 == (kappa_rh^2 + k^2) * E_rho(rh, ph, z))).full_simplify().expand()\n",
    "eq_rh_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{rh}}^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_rh^2*E_rho(rh, ph, z) - m^2*E_rho(rh, ph, z)/rh^2 + diff(E_rho(rh, ph, z), rh)/rh - E_rho(rh, ph, z)/rh^2 - 2*diff(E_phi(rh, ph, z), ph)/rh^2 + diff(E_rho(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh_ex = eq_rh_ex.subs(diff(E_rho(rh, ph, z), ph, ph) == -m^2*E_rho(rh, ph, z))\n",
    "eq_rh_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\epsilon_{\\mathit{ph}_{\\mathit{ph}}} \\mu \\omega^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\partial^{2}}{(\\partial z)^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "epsilon_ph_ph*mu*omega^2*E_phi(rh, ph, z)/c^2 + diff(E_phi(rh, ph, z), rh)/rh - E_phi(rh, ph, z)/rh^2 + diff(E_phi(rh, ph, z), ph, ph)/rh^2 + 2*diff(E_rho(rh, ph, z), ph)/rh^2 + diff(E_phi(rh, ph, z), rh, rh) + diff(E_phi(rh, ph, z), z, z)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph.expr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-k^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\epsilon_{\\mathit{ph}_{\\mathit{ph}}} \\mu \\omega^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "-k^2*E_phi(rh, ph, z) + epsilon_ph_ph*mu*omega^2*E_phi(rh, ph, z)/c^2 + diff(E_phi(rh, ph, z), rh)/rh - E_phi(rh, ph, z)/rh^2 + diff(E_phi(rh, ph, z), ph, ph)/rh^2 + 2*diff(E_rho(rh, ph, z), ph)/rh^2 + diff(E_phi(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph_ex = eq_ph.expr().subs(diff(E_phi(rh, ph, z), z, z) == -k^2*E_phi(rh, ph, z))\n",
    "eq_ph_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{ph}}^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial^{2}}{(\\partial {\\phi})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_ph^2*E_phi(rh, ph, z) + diff(E_phi(rh, ph, z), rh)/rh - E_phi(rh, ph, z)/rh^2 + diff(E_phi(rh, ph, z), ph, ph)/rh^2 + 2*diff(E_rho(rh, ph, z), ph)/rh^2 + diff(E_phi(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph_ex = (eq_ph_ex.subs(epsilon_ph_ph * mu * omega^2 * E_phi(rh, ph, z) / c^2 == (kappa_ph^2 + k^2) * E_phi(rh, ph, z))).full_simplify().expand()\n",
    "eq_ph_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{ph}}^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_ph^2*E_phi(rh, ph, z) - m^2*E_phi(rh, ph, z)/rh^2 + diff(E_phi(rh, ph, z), rh)/rh - E_phi(rh, ph, z)/rh^2 + 2*diff(E_rho(rh, ph, z), ph)/rh^2 + diff(E_phi(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph_ex = eq_ph_ex.subs(diff(E_phi(rh, ph, z), ph, ph) == -m^2*E_phi(rh, ph, z))\n",
    "eq_ph_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{rh}}^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} - \\frac{E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} - \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_rh^2*E_rho(rh, ph, z) - m^2*E_rho(rh, ph, z)/rh^2 + diff(E_rho(rh, ph, z), rh)/rh - E_rho(rh, ph, z)/rh^2 - 2*diff(E_phi(rh, ph, z), ph)/rh^2 + diff(E_rho(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\kappa_{\\mathit{ph}}^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right), -\\frac{m^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}}, \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}}, -\\frac{E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}}, \\frac{2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}}, \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)\\right]</script></html>"
      ],
      "text/plain": [
       "[kappa_ph^2*E_phi(rh, ph, z),\n",
       " -m^2*E_phi(rh, ph, z)/rh^2,\n",
       " diff(E_phi(rh, ph, z), rh)/rh,\n",
       " -E_phi(rh, ph, z)/rh^2,\n",
       " 2*diff(E_rho(rh, ph, z), ph)/rh^2,\n",
       " diff(E_phi(rh, ph, z), rh, rh)]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph_ex.operands()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{rh}}^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_rh^2*E_rho(rh, ph, z) - m^2*E_rho(rh, ph, z)/rh^2 + diff(E_rho(rh, ph, z), rh)/rh + diff(E_rho(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_rh_ex.operands()[5] + eq_rh_ex.operands()[2] + eq_rh_ex.operands()[0] + eq_rh_ex.operands()[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\kappa_{\\mathit{ph}}^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) - \\frac{m^{2} E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}^{2}} + \\frac{\\frac{\\partial}{\\partial {\\rho}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)}{{\\rho}} + \\frac{\\partial^{2}}{(\\partial {\\rho})^{2}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right)</script></html>"
      ],
      "text/plain": [
       "kappa_ph^2*E_phi(rh, ph, z) - m^2*E_phi(rh, ph, z)/rh^2 + diff(E_phi(rh, ph, z), rh)/rh + diff(E_phi(rh, ph, z), rh, rh)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_ph_ex.operands()[5] + eq_ph_ex.operands()[2] + eq_ph_ex.operands()[0] + eq_ph_ex.operands()[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bessel_J_diff(m, arg):\n",
    "    return bessel_J(m, x).diff(x).subs(x == arg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_sol_rh(rh, ph, z) = - k / kappa_rh * bessel_J_diff(m, kappa_rh * rh)*sin(m * ph + psi_m)*exp(-I*k*z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_sol_ph(rh, ph, z) = -m * k / kappa_ph^2 / rh * bessel_J(m, kappa_ph * rh)*cos(m * ph + psi_m)*exp(-I*k*z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{k {\\left(J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho}) - J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} e^{\\left(-i \\, k z\\right)} \\sin\\left(m {\\phi} + \\psi_{m}\\right)}{2 \\, \\kappa_{\\mathit{rh}}}</script></html>"
      ],
      "text/plain": [
       "1/2*k*(bessel_J(m + 1, kappa_rh*rh) - bessel_J(m - 1, kappa_rh*rh))*e^(-I*k*z)*sin(m*ph + psi_m)/kappa_rh"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_sol_rh(rh, ph, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{k m J_{m}(\\kappa_{\\mathit{ph}} {\\rho}) \\cos\\left(m {\\phi} + \\psi_{m}\\right) e^{\\left(-i \\, k z\\right)}}{\\kappa_{\\mathit{ph}}^{2} {\\rho}}</script></html>"
      ],
      "text/plain": [
       "-k*m*bessel_J(m, kappa_ph*rh)*cos(m*ph + psi_m)*e^(-I*k*z)/(kappa_ph^2*rh)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_sol_ph(rh, ph, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) - 2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) = 0</script></html>"
      ],
      "text/plain": [
       "-E_rho(rh, ph, z) - 2*diff(E_phi(rh, ph, z), ph) == 0"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((eq_rh_ex.operands()[3] + eq_rh_ex.operands()[4])*rh^2).full_simplify() == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-E_{\\phi}\\left({\\rho}, {\\phi}, z\\right) + 2 \\, \\frac{\\partial}{\\partial {\\phi}}E_{\\rho}\\left({\\rho}, {\\phi}, z\\right) = 0</script></html>"
      ],
      "text/plain": [
       "-E_phi(rh, ph, z) + 2*diff(E_rho(rh, ph, z), ph) == 0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((eq_ph_ex.operands()[3] + eq_ph_ex.operands()[4])*rh^2).full_simplify() == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho})}{2 \\, \\kappa_{\\mathit{rh}}} - \\frac{J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})}{2 \\, \\kappa_{\\mathit{rh}}} + \\frac{2 \\, m^{2} J_{m}(\\kappa_{\\mathit{ph}} {\\rho})}{\\kappa_{\\mathit{ph}}^{2} {\\rho}}</script></html>"
      ],
      "text/plain": [
       "1/2*bessel_J(m + 1, kappa_rh*rh)/kappa_rh - 1/2*bessel_J(m - 1, kappa_rh*rh)/kappa_rh + 2*m^2*bessel_J(m, kappa_ph*rh)/(kappa_ph^2*rh)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((E_sol_rh(rh, ph, z) + 2*E_sol_ph(rh, ph, z).diff(ph))/sin(m * ph + psi_m)/exp(-I*k*z)/k).full_simplify().expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho})}{\\kappa_{\\mathit{rh}}} - \\frac{J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})}{\\kappa_{\\mathit{rh}}} + \\frac{J_{m}(\\kappa_{\\mathit{ph}} {\\rho})}{\\kappa_{\\mathit{ph}}^{2} {\\rho}}</script></html>"
      ],
      "text/plain": [
       "bessel_J(m + 1, kappa_rh*rh)/kappa_rh - bessel_J(m - 1, kappa_rh*rh)/kappa_rh + bessel_J(m, kappa_ph*rh)/(kappa_ph^2*rh)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((2*E_sol_rh(rh, ph, z).diff(ph) - E_sol_ph(rh, ph, z))/cos(m * ph + psi_m)/exp(-I*k*z)/k/m).full_simplify().expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_sol = ES.vector_field(\n",
    "    E_sol_rh(rh, ph, z),\n",
    "    E_sol_ph(rh, ph, z),\n",
    "    E_sol_z(rh, ph, z),\n",
    "    name='E_sol')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}E_sol = \\frac{k {\\left(J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho}) - J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} e^{\\left(-i \\, k z\\right)} \\sin\\left(m {\\phi} + \\psi_{m}\\right)}{2 \\, \\kappa_{\\mathit{rh}}} e_{ {\\rho} } -\\frac{k m J_{m}(\\kappa_{\\mathit{ph}} {\\rho}) \\cos\\left(m {\\phi} + \\psi_{m}\\right) e^{\\left(-i \\, k z\\right)}}{\\kappa_{\\mathit{ph}}^{2} {\\rho}} e_{ {\\phi} } + J_{m}(\\kappa_{z} {\\rho}) e^{\\left(-i \\, k z\\right)} \\sin\\left(m {\\phi} + \\psi_{m}\\right) e_{ z }</script></html>"
      ],
      "text/plain": [
       "E_sol = 1/2*k*(bessel_J(m + 1, kappa_rh*rh) - bessel_J(m - 1, kappa_rh*rh))*e^(-I*k*z)*sin(m*ph + psi_m)/kappa_rh e_rh - k*m*bessel_J(m, kappa_ph*rh)*cos(m*ph + psi_m)*e^(-I*k*z)/(kappa_ph^2*rh) e_ph + bessel_J(m, kappa_z*rh)*e^(-I*k*z)*sin(m*ph + psi_m) e_z"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_sol.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{{\\left(4 \\, k \\kappa_{\\mathit{rh}} m^{2} J_{m}(\\kappa_{\\mathit{ph}} {\\rho}) \\cos\\left(\\psi_{m}\\right) \\sin\\left(m {\\phi}\\right) + 4 \\, k \\kappa_{\\mathit{rh}} m^{2} J_{m}(\\kappa_{\\mathit{ph}} {\\rho}) \\cos\\left(m {\\phi}\\right) \\sin\\left(\\psi_{m}\\right) - {\\left({\\left(k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m + 2}(\\kappa_{\\mathit{rh}} {\\rho}) + k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m - 2}(\\kappa_{\\mathit{rh}} {\\rho}) - 2 \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m}(\\kappa_{\\mathit{rh}} {\\rho}) + 4 i \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m}(\\kappa_{z} {\\rho})\\right)} \\cos\\left(\\psi_{m}\\right) \\sin\\left(m {\\phi}\\right) + {\\left(k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m + 2}(\\kappa_{\\mathit{rh}} {\\rho}) + k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m - 2}(\\kappa_{\\mathit{rh}} {\\rho}) - 2 \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m}(\\kappa_{\\mathit{rh}} {\\rho}) + 4 i \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{m}(\\kappa_{z} {\\rho})\\right)} \\cos\\left(m {\\phi}\\right) \\sin\\left(\\psi_{m}\\right)\\right)} {\\rho}^{2} + 2 \\, {\\left({\\left(k \\kappa_{\\mathit{ph}}^{2} J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho}) - k \\kappa_{\\mathit{ph}}^{2} J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} \\cos\\left(\\psi_{m}\\right) \\sin\\left(m {\\phi}\\right) + {\\left(k \\kappa_{\\mathit{ph}}^{2} J_{m + 1}(\\kappa_{\\mathit{rh}} {\\rho}) - k \\kappa_{\\mathit{ph}}^{2} J_{m - 1}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} \\cos\\left(m {\\phi}\\right) \\sin\\left(\\psi_{m}\\right)\\right)} {\\rho}\\right)} e^{\\left(-i \\, k z\\right)}}{4 \\, \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} {\\rho}^{2}}</script></html>"
      ],
      "text/plain": [
       "1/4*(4*k*kappa_rh*m^2*bessel_J(m, kappa_ph*rh)*cos(psi_m)*sin(m*ph) + 4*k*kappa_rh*m^2*bessel_J(m, kappa_ph*rh)*cos(m*ph)*sin(psi_m) - ((k*kappa_ph^2*kappa_rh*bessel_J(m + 2, kappa_rh*rh) + k*kappa_ph^2*kappa_rh*bessel_J(m - 2, kappa_rh*rh) - 2*k*kappa_ph^2*kappa_rh*bessel_J(m, kappa_rh*rh) + 4*I*k*kappa_ph^2*kappa_rh*bessel_J(m, kappa_z*rh))*cos(psi_m)*sin(m*ph) + (k*kappa_ph^2*kappa_rh*bessel_J(m + 2, kappa_rh*rh) + k*kappa_ph^2*kappa_rh*bessel_J(m - 2, kappa_rh*rh) - 2*k*kappa_ph^2*kappa_rh*bessel_J(m, kappa_rh*rh) + 4*I*k*kappa_ph^2*kappa_rh*bessel_J(m, kappa_z*rh))*cos(m*ph)*sin(psi_m))*rh^2 + 2*((k*kappa_ph^2*bessel_J(m + 1, kappa_rh*rh) - k*kappa_ph^2*bessel_J(m - 1, kappa_rh*rh))*cos(psi_m)*sin(m*ph) + (k*kappa_ph^2*bessel_J(m + 1, kappa_rh*rh) - k*kappa_ph^2*bessel_J(m - 1, kappa_rh*rh))*cos(m*ph)*sin(psi_m))*rh)*e^(-I*k*z)/(kappa_ph^2*kappa_rh*rh^2)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div_E_sol = div(E_sol)\n",
    "div_E_sol.expr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}0</script></html>"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div_E_sol.expr().subs(m == 0, psi_m == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left({\\left(k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{3}(\\kappa_{\\mathit{rh}} {\\rho}) - 2 \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{1}(\\kappa_{\\mathit{rh}} {\\rho}) + 4 i \\, k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{1}(\\kappa_{z} {\\rho}) + k \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} J_{-1}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} {\\rho}^{2} \\sin\\left({\\phi}\\right) - 4 \\, k \\kappa_{\\mathit{rh}} J_{1}(\\kappa_{\\mathit{ph}} {\\rho}) \\sin\\left({\\phi}\\right) - 2 \\, {\\left(k \\kappa_{\\mathit{ph}}^{2} J_{2}(\\kappa_{\\mathit{rh}} {\\rho}) - k \\kappa_{\\mathit{ph}}^{2} J_{0}(\\kappa_{\\mathit{rh}} {\\rho})\\right)} {\\rho} \\sin\\left({\\phi}\\right)\\right)} e^{\\left(-i \\, k z\\right)}}{4 \\, \\kappa_{\\mathit{ph}}^{2} \\kappa_{\\mathit{rh}} {\\rho}^{2}}</script></html>"
      ],
      "text/plain": [
       "-1/4*((k*kappa_ph^2*kappa_rh*bessel_J(3, kappa_rh*rh) - 2*k*kappa_ph^2*kappa_rh*bessel_J(1, kappa_rh*rh) + 4*I*k*kappa_ph^2*kappa_rh*bessel_J(1, kappa_z*rh) + k*kappa_ph^2*kappa_rh*bessel_J(-1, kappa_rh*rh))*rh^2*sin(ph) - 4*k*kappa_rh*bessel_J(1, kappa_ph*rh)*sin(ph) - 2*(k*kappa_ph^2*bessel_J(2, kappa_rh*rh) - k*kappa_ph^2*bessel_J(0, kappa_rh*rh))*rh*sin(ph))*e^(-I*k*z)/(kappa_ph^2*kappa_rh*rh^2)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div_E_sol.expr().subs(m == 1, psi_m == 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}5.520078110286276</script></html>"
      ],
      "text/plain": [
       "5.520078110286276"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_root(bessel_J(0,x)==0,0,2*pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BXQF16gDZ2cCxY/nXORxSj+73363rFxEREZEnARXQJScnIz4+HgkJCYac31UtOgC45hoGdERERGRfARXQJSUlIS0tDampqYacv3ZtuXQV0P32myFNEhEREWkWUAGd0SpXlvlyrgK6gwcL7/NKREREZBcM6ApwOGTHiIL7uQIyhy4vDzhwwJJuEREREXnEgK6IWrWKB3TXXCOXnEdHREREdsSArghXAV1sLBAeznl0REREZE8M6IpwFdCFhAD16zOgIyIiIntiQFdErVrAkSOy3VdBXOlKREREdsWArohatWQBREZG4etZi46IiIjsigFdEbVqyaWrhRH79gG5ueb3iYiIiMgTBnRFuAvoGjQALl0CDh0yv09EREREnugW0E2bNg316tVDREQEWrdujQ0bNng8/vTp00hKSkLNmjURERGBpk2bYtWqVXp1x2+VKwPlyrkvXcJ5dERERGQ3ugR0ixYtwogRIzB27Fhs27YNnTp1QteuXZGenu7y+JycHHTu3BkHDhzAp59+ij179mDmzJmIjY3VozuaOByuV7rWqQOUKcN5dERERGQ/ZfQ4ydtvv43BgwdjyJAhAIApU6ZgzZo1mD59OiZPnlzs+Dlz5uDkyZPYtGkTypYtCwCoU6eOHl3RhauArkwZoG5dZuiIiIjIfjRn6HJycrB161YkJiYWuj4xMRGbNm1yeZ8VK1agXbt2SEpKQnR0NJo3b45JkyYh182Kg+zsbGRlZRX6MZKr7b8AmUfHgI6IiIjsRnNAd/z4ceTm5iI6OrrQ9dHR0cgoWvvjf/bt24dPP/0Uubm5WLVqFcaNG4e33noLr776qsvjJ0+ejKioqCs/cXFxWrvtkasMHcBadERERGRPui2KcDgchf6vlCp2nVNeXh5q1KiBDz74AK1bt0bfvn0xduxYTJ8+3eXxY8aMQWZm5pWfQwYvNa1VC/jjD6lHV5CzFp1ShjZPRERE5BPNc+iqVauG0NDQYtm4o0ePFsvaOdWsWRNly5ZFaGjoleuaNm2KjIwM5OTkICwsrNDx4eHhCA8P19pVr9WqJTtFHD0KXH11/vUNGgAXLshOEjExpnWHiIiIyCPNGbqwsDC0bt0aKSkpha5PSUlB+/btXd6nQ4cO+O2335BXIAX266+/ombNmsWCOSt4Ki4McNiViIiI7EWXIddRo0Zh1qxZmDNnDnbv3o2RI0ciPT0dw4YNAwAMGjQIY8aMuXL88OHDceLECTzzzDP49ddf8cUXX2DSpElISkrSozuaOQO6oiO79epJWRMGdERERGQnupQt6dOnD06cOIGJEyfiyJEjaN68OVatWnWlFEl6ejpCQvJjx7i4OKxduxYjR45Ey5YtERsbi2eeeQbPP/+8Ht3RrFo1ICyseIYuIkJWwLIWHREREdmJQ6nAm+KflZWFqKgoZGZmIjIy0pA2GjQAevcGXnut8PW33QZUrw4sWmRIs0REREQ+416ubngqXbJ3r/n9ISIiInKHAZ0b7gK6Bg2A/fvN7w8RERGROwzo3HAX0NWrB5w+DZw6ZX6fiIiIiFxhQOeGM6ArOsOwfn25ZJaOiIiI7IIBnRu1agE5OcDx44Wvr1dPLvftM79PRERERK4woHPDXXHhKlWAyEhm6IiIiMg+GNC54S6gczgkS8cMHREREdkFAzo3atQAypRxvTCifn1m6IiIiMg+GNC5ERoKxMS4X+nKDB0RERHZRUAFdMnJyYiPj0dCQoIp7bkrXVK/PnDwIJCba0o3iIiIiDwKqIAuKSkJaWlpSE1NNaU9T7XocnKAP/80pRtEREREHgVUQGc2Txk6gPPoiIiIyB4Y0HlQqxZw6FDx4sJ168ol59ERERGRHTCg8yA2FrhwQbb6KigiQhZMMENHREREdsCAzoPYWLn844/it3GlKxEREdkFAzoPPAV0rEVHREREdsGAzoOYGLlkho6IiIjsjAGdB2FhQPXq7gO6I0dkjh0RERGRlRjQlSA21v2QKwAcOGBqd4iIiIiKYUBXAncBXb16csl5dERERGQ1BnQlcBfQxcTIkCzn0REREZHVGNCVIDbW9RZfoaFAnTrM0BEREZH1GNCVIDYWOHoUuHSp+G0sXUJERER2wICuBDExsvXXkSPFb2PpEiIiIrKDgArokpOTER8fj4SEBNPadBYXdjXs6szQFd3rlYiIiMhMARXQJSUlIS0tDampqaa16Swu7Cqgq1cPyMoCTp40rTtERERExQRUQGeFqlVlNaunWnScR0dERERWYkBXAodDsnTuMnQA59ERERGRtRjQecFdQFe5MlCpEjN0REREZC0GdF5wV1wY4EpXIiIish4DOi+4y9ABrEVHRERE1mNA5wVPAR0zdERERGQ1BnReiIkBMjOBc+eK31a/PnDwIJCba36/iIiIiAAGdF7xVFy4Xj3g8mXg8GFz+0RERETkxIDOC56KC7MWHREREVmNAZ0XPAV0depIrTrOoyMiIiKrMKDzQsWK8uOqdEl4uAzJMkNHREREVmFA5yWudCUiIiK7YkDnJdaiIyIiIrsKqIAuOTkZ8fHxSEhIML1t7hZBREREdhVQAV1SUhLS0tKQmppqetslZej++gs4f97cPhEREREBARbQWckZ0ClV/LZ69eSSw65ERERkBQZ0XoqJAS5eBE6fLn4ba9ERERGRlRjQecm5W4SreXRXXy3lSziPjoiIiKzAgM5LnooLh4QAdesCBw6Y2SMiIiIiwYDOSzVryqW7hREM6IiIiMgqDOi8FB4OVKvmuXQJ59ARERGRFRjQ+cBT6RJm6IiIiMgqDOh8UNL2X6dPu14FS0RERGQkBnQ+8LRbRN26csksHREREZlNt4Bu2rRpqFevHiIiItC6dWts2LDBq/stXLgQDocDPXv21KsrhikpQwdwHh0RERGZT5eAbtGiRRgxYgTGjh2Lbdu2oVOnTujatSvS09M93u/gwYP429/+hk6dOunRDcPFxAAZGUBubvHbqlUDypdnQEdERETm0yWge/vttzF48GAMGTIETZs2xZQpUxAXF4fp06e7vU9ubi769++Pl156CfWdWy3YXEyMBHPHjhW/zeGQLB2HXImIiMhsmgO6nJwcbN26FYmJiYWuT0xMxKZNm9zeb+LEiahevToGDx5cYhvZ2dnIysoq9GMFT7tFADKPjhk6IiIiMpvmgO748ePIzc1FdHR0oeujo6ORkZHh8j4bN27E7NmzMXPmTK/amDx5MqKioq78xMXFae22XzztFgEwQ0dERETW0G1RhMPhKPR/pVSx6wDgzJkzGDBgAGbOnIlq1ap5de4xY8YgMzPzys+hQ4d06bOvatQAQkM916Lbvx9QytRuERERUSlXRusJqlWrhtDQ0GLZuKNHjxbL2gHA77//jgMHDqB79+5XrsvLy5POlCmDPXv2oEGDBoXuEx4ejvDwcK1d1Sw0FLj6as+7RZw7B5w4IYskiIiIiMygOUMXFhaG1q1bIyUlpdD1KSkpaN++fbHjmzRpgp07d2L79u1Xfnr06IFbb70V27dvt2w41Vsl7RYBcB4dERERmUtzhg4ARo0ahYEDB+KGG25Au3bt8MEHHyA9PR3Dhg0DAAwaNAixsbGYPHkyIiIi0Lx580L3r1SpEgAUu96OvKlFd+AAkJBgWpeIiIiolNMloOvTpw9OnDiBiRMn4siRI2jevDlWrVqFOnXqAADS09MREhIcm1LExgIbN7q+rVIlIDKSGToiIiIyl0OpwJvCn5WVhaioKGRmZiIyMtLUtl99FZgyxXUtOgC47jqgfXtg2jRTu0VERESlWHCkzUwUEwMcPw5kZ7u+nbXoiIiIyGwM6HzkrEXnpsQea9ERERGR6RjQ+cib3SIOHGAtOiIiIjIPAzofebNbxMWLwF9/mdcnIiIiKt0Y0PmocmUgPJy16IiIiMg+GND5yOGQYVdPQ64A59ERERGReRjQ+cFTceHISKBKFWboiIiIyDwM6PzgKaADuNKViIiIzBVQAV1ycjLi4+ORYPG+WrGxngM61qIjIiIiMwVUQJeUlIS0tDSkpqZa2o+YGPdz6ADJ0DGgIyIiIrMEVEBnFzExwJkz8uNK3bpAejqQm2tqt4iIiKiUYkDnB2ctuiNHXN9erx5w6ZLnYVkiIiIivTCg84M3u0UAXBhBRERE5mBA54eaNeWSxYWJiIjIDhjQ+eGqq6TenLuArnx5oEYNZuiIiIjIHAzo/FRS6RKudCUiIiKzMKDzkzelS5ihIyIiIjMwoPNTSbtFsLgwERERmYUBnZ+8GXI9fBi4fNm8PhEREVHpxIDOT84MnVKub69bVwoLHzpkareIiIioFGJA56eYGCA7Gzh50vXt9erJJefRERERkdEY0PnJuVuEu2HX2rUBh4Pz6IiIiMh4DOj8VNJuEeHhEvQxQ6ePv/4CLlywpu2sLGmfiIjIrhjQ+enqq+WSK12N9eGHQPPm8niXLw+0agWsWWN8uwcPAk89Je1GRcllbCzw6KPAvn3Gt09EROSLgArokpOTER8fj4SEBKu7grAwoHr1kle6MkPnn+xsYMgQ4JFHgCZNgAULgH/9C6hQAbjzTmDcOPcLUrRQCpgzB2jaVNocNAiYPx/497+BgQOB1aulP5MnG9M+ERGRPxxKBd7HUlZWFqKiopCZmYnIyEjL+nH99UC7dsC0aa5vHz9egpDDh83tVzB47DFg7lxgxgzg4Yfzr1cKePNN4LnngLFjgVde0a9NpYDRo4HXX5dg8p13ZJu3gs6fB15+GfjHP4B+/YCPPgLKlNGvD0RERP7gR5EG3uwW8eefkm0KDzevX4Fu9mxg5kzJlBUM5gBZaPLss1ISZswY4Lbb5EcPkyZJMPfOO8CIEa6PKV9esnOtWgEPPgiULStBe0hA5bqJiCjY8GNIA292i1AKSE83rUsB7+BB4MkngaFDZbjVneeeA265RY7JzNTe7sKFMow7caL7YK6g++8H5s2Tn5de0t4+ERGRFgzoNPBmtwiA8+h8MX68LEJ4+23Px4WESGbs1Clg1ChtbR44ADz+ONC3rwR13urbV4K5l18G1q3T1gciIiItGNBpEBMDZGS4396rVi0JPLjS1Ts7dgAffwy8+GLxuWuu1K0rQ6Rz5gA//eRfm3l5wIABQJUqwPvvy5CuL/7+d+DWW4H+/YFjx/zrAxERkVYM6DSIiZGA4OhR17eXLQvExTGg89bzzwMNGwKDB3t/n8GDgfr1JUvmj48/BjZulAUYUVG+3z80VM6RnS39JyIisgIDOg1K2i0CkCwSh1xLtnmz1JebNEkCYW+VLStZsk8/BXbt8q3NCxdkpWzv3sBNN/l234Jq1pSFEv/6lwSHREREZmNAp4Fzt4iS5tExQ1ey6dPlserVy/f7DhwoW629+qpv95syRXaAmDzZ9zaLGjwYSEgAkpLcD8ETEREZhQGdBtWry5Cbp9IlzNCV7MQJYPFiWZjgT/mPsDApYbJoEbB3r3f3OXZMArknngCuucb3NosKDZV6hDt2yMpXIiIiMzGg0yAkRIbbSsrQ/fWXFKQl1+bOlbmIjz7q/zkefhioXFkWNnhj4kT5+40f73+bRd1wgwzfTpwI5OTod14iIqKSMKDTqKTSJXXryuXBg6Z0J+Dk5UkQ1ru3ZDz9FREhw55z5gAXL3o+9vhxKVz87LNA1ar+t+nKiy/K33rOHH3PS0RE5AkDOo282S0C4Dw6d775RoZJhw/Xfq7Bg4HTp4EVKzwfN3u2XD7+uPY2i2rWTOrTvfIKs3RERGQeBnQalbRbREyMrMTkPDrXFiwAGjQAOnbUfq7GjYG2bWUI153cXJnr1q8fUK2a9jZdGTdOgvzFi405PxERUVEM6DQqacg1NFRWYDJDV9zly8DSpbKNlq8Ffd156CEpf5KR4fr2zz+XrdiefFKf9lyJjwc6dwb++U/Z+o2IiMhoARXQJScnIz4+HgkJCVZ35YqYGFml6WneFle6uvbNN/LY9e6t3zn79AHKlAHmz3d9+9SpQLt2QOvW+rXpyjPPAD/8AHz3nbHtEBERAQEW0CUlJSEtLQ2pqalWd+UKZ3HhI0fcH8NadK59+qkEu61a6XfOypWB7t2BTz4pftvu3cBXXxmbnXPq2lXKobxT7yRyAAAgAElEQVT7rvFtERERBVRAZ0fcLcI/ubnAkiX6Drc6PfAA8OOPxYPoqVOB6Gh9M4LuhIQATz0lQaunRTNERER6YECnkbe7RZw4AZw5Y06fAsGGDVLc14jgqmtXKWPy2Wf512VmymKJxx+XQsRmePhhoFw5WYRBRERkJAZ0GkVFyYd2SbtFAMzSFbR8OVCrlmyXpberrpKg7tNP869bsEDmORpRqsSdyEjgkUeAGTNk31giIiKjMKDTyOEouXQJa9EVt2qVBF16D7c63Xcf8P33wKFD8v/582XlqXOI3CxPPSXZ2YLBJRERkd4Y0OmgpNIl0dFAeDgzdE779gG//ioBnVHuvluGVpculZ0b/vtfoH9/49pz55prgJtv5v6uRERkrDJWdyAYlLRbREiIDLsyQye+/FJKi9x+u3FtREVJIPXFF8C5czIs3rOnce15MnAgMHSoPEeccy6JiIj0xAydDkoacgW40rWgL7+UnSEiI41t5667pNbdxx8D99wjc+us0Lu3ZGjd1cYLdocPA2vXyhB4ZqbVvTHW8ePyu65bB/z2GwtLE5F5GNDpoKQhV4C16Jyys+XDzsjhVqdu3WQ/1bQ0a4ZbnaKiJDv40Uel6wN+3TpZ9BIXB3TpItuy1awp2Urn3MZgcPiw1DZs1AioXl1+19tuAxo2BJo0AV56CcjKsrqXRBTsdAvopk2bhnr16iEiIgKtW7fGhg0b3B47c+ZMdOrUCZUrV0blypVxxx13YMuWLXp1xXQxMcDZs57LkjBDJzZvBs6fBxITjW+rYUMpNBwWZk57ngwaBPz8M7B9u7X9MINSwIQJEtSUKSN72v7+u/zuf/87sHIl0LKlFHkOZHl5wKuvyvNs4UIJ5ObPB/bulZ+VK4EOHYDXX5dgr7QF9ERkMqWDhQsXqrJly6qZM2eqtLQ09cwzz6gKFSqogwcPujz+wQcfVMnJyWrbtm1q9+7d6pFHHlFRUVHq8OHDXrWXmZmpAKjMzEw9uq/Zt98qBSi1e7f7YxYtkmNOnjSvX3Y0frxSVasqlZtrTnuVKytVvrxSeXnmtOfOpUtKRUcrNWKEtf0wWm6uUk8/Lc/1SZNcP+4nTiiVmCh/lw0bzO+jHk6eVKpLF6UcDqWef14pT29Fhw4p1bevPCYPPaRUTo5p3SSiUkSXgO7GG29Uw4YNK3RdkyZN1OjRo726/+XLl1XFihXV3LlzvTrebgHd3r3yZv3VV+6P+f57OWbrVvP6ZUcdOyp1773mtLV7tzzmgFI7dpjTpicjRypVo0Zwf6C/+KIEOdOnez7u/Hmlbr1VqYoVldqyxZy+6eXUKaVat1aqShWlVq/2/n4ff6xU2bLy/M/ONq5/RFQ6aR5yzcnJwdatW5FYZEwrMTERmzZt8uoc58+fx6VLl1ClShWt3bGEN9t/OWvRleZh13PnZGL8bbeZ097SpbK6tUIFqXtntUGDgKNHgTVrrO6JMb77Dnj5ZeCFF4BhwzwfW64csGIF0KwZ0KMHcPKkOX3UKisLuPNOKb3z9dcyzOqt/v1l95KVK2WhTHa2cf0kotJHc0B3/Phx5ObmIjo6utD10dHRyMjI8Ooco0ePRmxsLO644w6Xt2dnZyMrK6vQj52ULw9UquS5dEm1anJcaV4YsXEjcOkScOut5rS3dKksjLj5ZuA//zGnTU+uvVYCmEWLrO6J/s6eBQYMAG64ARg3zrv7XHWVBDgXL0oBZrvLywMefBD45RcgJUX+nr7q3l12SVmzBnjmGf37SESll26LIhxFSv4rpYpd58rrr7+OBQsWYMmSJYiIiHB5zOTJkxEVFXXlJy4uTpc+66mk0iUOh2TpSnOG7uuvpchy06bGt3XoEJCaCvTqJfXuNm6UwMFKDofsYPH557L6NpiMHAlkZEgB5TI+VLeMiQHeew/45BNgyRLj+qeHSZMk07tgAdC6tf/nufNOIDlZtoSbPVu//hFR6aY5oKtWrRpCQ0OLZeOOHj1aLGtX1JtvvolJkyZh7dq1aNmypdvjxowZg8zMzCs/h2xY88Cb0iWlvbjwt98Ct9xi3HZfBS1fDpQtKxm622+XYM7LGQCGuu8+qcX29ddW90Q/qanArFnAm2/Kik9f9e8vZV2GD/e8UtxKX30lQ8kvvKBPyZ0hQ4DHHgOeeEIePyIirTQHdGFhYWjdujVSUlIKXZ+SkoL27du7vd8bb7yBl19+GatXr8YNN9zgsY3w8HBERkYW+rGbknaLAEp3hu7CBWDrVikobIaVK2WoNSoKaNFChrztUCajRQvZDuyzz6zuiX7Gj5es69Ch/t3f4QD++U8JdN9+W9++6eHsWeDRR2Xu5/jx+p333Xdl2HbQIM6nIyLtdBlyHTVqFGbNmoU5c+Zg9+7dGDlyJNLT0zHsfzOjBw0ahDFjxlw5/vXXX8e4ceMwZ84c1K1bFxkZGcjIyMDZs2f16I4lvNktwllcuDTWokpNlflzZgR0587JDhHdusn/Q0Lkw9gOAZ3DAdx7L7BsGXD5stW90W7DBpkPNnEiEBrq/3lq15bivG++KQtH7GT8eODYMeCDD7T9jkWFhwNz5kiNvsmT9TsvEZVOugR0ffr0wZQpUzBx4kRcd911WL9+PVatWoU6deoAANLT03HkyJErx0+bNg05OTno3bs3ataseeXnzTff1KM7lnAOuXoK1urWlaK6x4+b1i3b2LgRqFhRMlRG+/pryXjcdVf+dbffLkGlHbaeuu8+eQ78979W90QbpYCxY4HrrpMgVasxYyT4fvVV7efSS2qqZNImTgTq19f//M2bA88/L/Pz0tL0Pz8RlR4OpQIvX5SVlYWoqChkZmbaZvh16VL5UDt2TIb3XNm2DWjVSkp33Hijuf2z2t13y0KAtWuNb2vYMMnG7d2bf93vv8tQ5/LlUibDSkoBderI/rLvvWdtX7RISZEdOFauzM+GajVpEvDii/L3snrt0+XLsmo3JATYssW3xR6+uHhRhl6rVwfWr5f27ODsWZkakJoqWdPGjWX7tttuk7Iz5B+lZNeUVatkms7Jk7KvdePGUganWTNz5hlT8LHJW0fgc9ai8zSPrm5duSxt8+jy8mRBQocOxrelFPDFF8UDjPr1JYiy07DrkiXy2ASqV1+VLyYFM6FaPfWU1A185x39zumvOXOAHTtkqNWoYA4AIiKkjY0bgZkzjWvHW0oB778v72kPPyzTF44dk1W5d98t8yU//bR0Th3RIi9PnlPXXCNf7N94Q7ZCPHZM5he/8IKMYLRuLV+WiHzFgE4n3hQXrlxZJumXtpWuv/wCnDplTkC3c6dsll40oHM4ZNjVDgEdIAHdn39KtjYQ/fSTrFr+v//TN5tQsSKQlCQBjpXFhs+elQ9YZ209o918syy8GD0aOH3a+PbcOX5cMtjDhwP9+smXz127gHXrgL/+kn+3aAHcfz/Qt6/1pYACRWqqfPkZPBhISJB5p8eOyajNV19JQHfypHwZLV9eMt9duhQeZSAqCQM6nVx9tXyweVO6pLRl6DZulGGkNm2Mb2vNGhkOuumm4rfddhvw88/yRmq1Dh2AGjXsX3vNnalTZd5or176n/upp2QBzZw5+p/bW2+9JYHVK6+Y1+Yrr8jczzfeMK/Ngk6dAu64Q3b8WLFCMnL/mwYNQN7fmjWTOoqLF8sxd95p31IzdrFoEdCpk2Q0N24EFi6UgK1s2cLHhYdLtnvDBpnCs2+fBH922OWGAgMDOp2ULSsf0N6ULiltGbqNG2WOUMWKxre1dq3UugsPL36bM8izw2KE0FAJhj77LPCGrk6eBD7+WOYqFv1Q0kN0NNCnjxTfzc3V//wlycqSId8nnigc0BitZk3ZPWLKFCnSbKazZyWYOHRIsnHdu3s+/v77ZfeVH3+UTF0wrNjWm1LAa6/J43P//TLtxEMlryscDqnLuHWrvGfdfbc9piCQ/TGg05E3pUtKY4bOrPlzFy7It9si2wpfERcnH9AbNhjfF2/06iXB/c6dVvfENx9+KIHWY48Z18aTT8rrxIrsxPTp8lz629/Mb/u554CwMHNX+iolwfmuXZLhbt7cu/t16CBz6dasAUaNMraPgUYpmY4werSUvfnoI9dfMj2JjJTyRs8+K4/vlCnG9JWCBwM6HXmzW4SzuHAgT4b3xcmTMg+kbVvj29qwQYas3AV0gAx9rF9vfF+8ccstsgDgiy+s7olvPvxQMgg1ahjXxo03ys/Uqca14cqFC1Lc+OGH8+fFmqlyZQnqZswwL5M/dy4wf7606et8wcREKevy3nuB9zw20htvSFYtOVlK3vg7zzQkBPjHP+Q5MXKkLFYhcocBnY68zdBlZ8sE49LAua2RGWVa1q6Vv4GnvWJvukkmItth3k94uMxZCqQPwh07JKM4cKDxbQ0fLn9TMzPac+bIwoDnnjOvzaKefhqoUgV46SXj2/rtN1mE8sgjwIMP+neO4cNlO7QhQ4ATJ/TtXyBasEBqC44fL8P2WjkcEtQ99ZSc7/PPvbvfrl2S1XvxRWDCBMk8l/T5RIGNAZ2OvN3+Cyg98+hSU4FKlWSpvtHWrpWMgadvw506SXZ082bj++ONbt2kL4HyQfjxx1JnsUsX49u6/37gqqskI2iGS5eA11+XOU8NGpjTpisVKgB//7s81kYGs0rJ0Hb16trqITocspdvdracrzTbtUtWsg4YoG9A7nBIcHbPPRJ4//67+2O/+w7o3FlWI48ZI6VwZs+WLwq1aslr95df9Osb2QcDOh3FxkrmzdME4dJWi27LFlmpZXShzCNHJHPkabgVkOKdzgKudnDXXRJgrlljdU9KlpsLfPKJBDxGLIYoqkIFaetf/zJnccQnnwDp6TLvyWqDB8sXISP3tnXOf3vvPXmstYiJkeHFhQu9zyAFm7Nn5UtIgwYyfK33e15IiMzFi46WgLHo58zly5KN69BBVvIvWiQrl//4Q0o5HT0qGeh9+2SR2qRJgbcgi0qgAsjUqVNV06ZNVaNGjRQAlZmZaXWXCvniC6UApQ4f9nxc1apKvfKKOX2yUl6eUtHRSo0da3xbn3wij31GRsnH3nuvUjfdZHyfvHXddUo9+KDVvShZSoo8xt9/b16bmzdLm2vXGtvO5ctKNW6sVI8exrbjixdfVKpcOaWOHdP/3OfPK1Wrlr6/b16eUnfcoVSjRkplZ+t33kDxyCNKVaig1O7dxrazebNSoaFKTZiQf93ly0r166dUSIhSL70k/3fn/HmlRo+W19WTT8rfjYJDQAV0TpmZmbYM6LZt8+4Dr3VrpYYMMadPVjp4UB6P5cuNb2voUKXi4707dsoUpcLDlbp40dg+eWvsWKWqVPH8JmwHgwbJh7WZHwB5eUo1aaLUgAHGtrNihTxXN20yth1fHD+uVPnyhT+49fLmm0qVKaPU3r36nnfHDgkqpkzR97x2t3q1PH9mzTKnvQkTJKjbtEleI0OHyuP+7397f44ZM6TPjz+uVG6uYV0lE3HIVUfe7BYBlJ5adM4FEQkJxre1bp2sGvVGp04y38fZP6t16yargb/7zuqeuHfunNTMGzDA3H0mHQ6ZM7RsmaxANcr06bLlUrt2xrXhq6pVZaHBe+/J46+XzEwZbhsyRP+5rS1bynDxSy/JcF9pcPYs8PjjshPNo4+a0+a4cfK+2r+/zI1zzpPr3dv7czz2mAzBfvAB5z4GCwZ0OqpWTeYWebPStTQEdFu2yCTcmjWNbefwYVmtd+ut3h3vLHJsl3p0N94ozx07r3ZdvlyCiv79zW+7b1/50DTq8dm/H1i9WlZr2s2oURKAzZ2r3znfeUeC4/Hj9TtnQRMnyvn/+U9jzm8348bJ/LQPPjDvy06ZMrJo5s8/pbTPu+9KqR1fPfKIlEKZPl3mqlJgY0Cno5AQCV68Wemanm5NFXwzbdliTrmSb76Ry5tv9u740FCp2G6HHSMA6c+dd9o7oFu4UB6z+vXNb7thQ8meLVhgzPk/+ECKuPbta8z5tahTR2r+JSfrM4H9zBn58H/8cePq7F19tZx/yhQJRoPZ99/L4/nyy+a/NrKz8+uZXnut/+d57DHJLD7xhJQlosDFgE5n3taiu3y55MAvkOXlAT/8YF5A17y5rF71Vrt2MsRpl1Ve3brJhveHDlndk+LOnQNSUozZt9Vb/fpJwJuVpe95s7NlqOqhh7Sv9DRKUhKQlgZ8+632c82YIdnO//s/7efy5LnngIsXJdgJVnl5Mtx57bWyZZuZLl6U10TDhjL0mpQkZXf8NXUq0KSJfKnJztavn2QuBnQ683a3CCC4S5fs3SsfHK1bG9+WL/PnnNq1y9/Fwg66dJFMnR034k5JkQ+Qe+6xrg8PPCAfNMuW6XveJUukxMOwYfqeV0+33CLFspOTtZ0nOxt46y1g0CCZCmGkmBjJ/Lzzjj2KeBth4UIZhXjnHRkCNdOkSVJLbsECGTL9+Wdtz49y5YB586S+nZnbzpG+GNDpzJsMnXPD72CeR7dtm1xef72x7aSnS10lb+fPOTkzh3YpMFy5sgxp2nHYdcUKCSgaNrSuD3FxsphF72HX99/PD5jsyuGQ4bClS7Vl9T/9FMjIMG+P2meflYxqMM7NunBB6hX27On7l0mt9u4FXntNsqAtWwKtWsn8zxdekC8n/mreXApaT54sowUUeBjQ6cyb3SLKl5fikMGcofvxR/kQrlrV2Hac8+duusm3+1WqBMTH2yegA2TY9auvJBtmF7m5wMqVQI8eVvdEhphSUmRrLj38/LMUmLbjYoiiBg0CIiJkvp+/pk2TlZhNmujXL0/i4iSzOmVK8M0XfvttCY5ff93cdpWSLcBq1pRdIJxeekkC/0mTtJ1/zBgpvj58uH2mo5D3GNDpLDZWluuXVGIh2Fe6btsm3xyN9s038i21WjXf7+ucR2cX3boB58/rM1dKL5s3y7d+K4dbnZwlGZYs0ed8M2bIF6uePfU5n5EiI2X/3A8+8G+u1PbtwKZN+uwt6otRo+R9bvlyc9s10okTkiF74gnzs9affy67e7z7riQGnKpVk4zotGnAwYP+nz88XIaQN22SzDwFFgZ0OnOuHDtyxPNx9eoFb4ZOKQnojB5uBfybP+fUtq1sF2aXOT7NmskXgpQUq3uSb/lyCXratLG6J7Lo5aabZOhRq5wc2erroYeAsDDt5zNDUpJkhfz5/adNk+eW2ZnWG24AOnY0dgszs73+uiyI+PvfzW03Lw8YO1aml3TvXvz2kSNl6sYLL2hrp3Nn4I475PfztI0l+eavv4xvgwGdzpwBXUnDrsGcoTt8WL7FGh3QHTggP77On3Nq107eJO1SYNjhkDfTtWut7olQSgK67t2lJI8d9Oolw9Jay2GsWSPP0YED9emXGZo3l4DW18nvp08D8+dLKRGzJ+8DwIgRwMaNwTEvKyNDCj2PHAnUqGFu24sXA7t2Aa+84rreXYUKEszNmydfVLX4xz9kZfVHH2k7D4nTp4HrrpNFSUayydt08PBlt4jDh7UtNberH3+US6MDuvXr5dLX+XNOTZsCUVH2GnZNTJQ345IyvGb45ReZgG2H4Vannj3lNaN18ci8eVJuonlzffpllqQked778oH90UeSkRwyxLh+edKjhwQ/s2db076e/vlPCYpHjTK33cuXgRdfBO66SxZPuTN0qNTD05o9bN0a6NNHAkQjd2gpLcaNk6oPffoY2w4DOp1FRso3JW9q0eXl2bPumFbbtsmcDqNLI2zcKAsbqlTx7/4hITKUaKeFEXfcIZd2GHZdvlzm6dx+u9U9yRcXJ3W3tMyjO31a5gcFUnbOqVcvGQKfOdO745WS4db77jN+xxZ3ypaVoe2PP7bXgh9fZWbKYzl8uAxtmmn+fGDPHtmFw5OyZSWDt3Kl9p1wXnlFhgmnTtV2ntIuNVWeNxMnGv+ZyIBOZw6Hd6VLnFXF9+0zvk9mc86fM3obnI0bgQ4dtJ2jbVt7FRiuXl0Wk9gloEtMlBpVdtKrF/Dll/5nDj77TLJ8/frp2y8z+BocrVsngYDZiyGKGjxY6j7qXUfQTO+/L4/5iBHmtpuTI6tY773Xu7qeDzwg778TJmhr95prpJbgpEmlZ19eveXmSo3Lli0lgZOWZmx7ARXQJScnIz4+Hglm7PaugTelS2rXlgxRMAd0Rjp1SspOaA3o2rWTMhi//65Pv/SQmCgBnXNbHytkZMi2RnYabnXq1UtWA/s713DePMk6GrX1ldEeeUSe/96sHP3Xv4BGjaSGn5UaN5bFEYE67Hrxoqz+fPhh8zOd8+fLfOuXXvLu+JAQWTyxbp28hrUYP14CytKyL6/epk2Tz8P/+z+p/7hxo7HtBVRAl5SUhLS0NKTaZRa7G97sFhEWJkGdnQIJPRw/LsPIRgd0zmFSrQGdc/WmnYZdO3eWoQ6tE5u1WLNGLrt1s64P7jRpIgGCP2UV0tOlLEwgDrc6NWkiz/uSgqMzZ2Ro+qGHzNs03pMhQ4D//CcwF4PNnSvle5591tx2lZKJ9N27+zbfs1cveY1Mnqyt/auvluzq1KnyJYq8d+yYzJ177DEpiN6woXwZM1JABXSBwpshVwBo0CD4AjrnDhFG16DbuFEmWjdooO08lSvLB6SdAroOHWSY08rVrmvXyt/Ql/1xzdS9uyyM8DWLOX++zAu0cl9aPQweLMGRp5pjn30mw9IDBpjXL0969wYqVgy8nSMuX5ZSJb17yzCkmdaskZEIX3f3CAmRnSSWL5f7azFqlMw7DbS/m9VeeUUuu3WTKSIvv2z8KnMGdAZwDrmWNC+rfv3gG3Ldtg246irj3/ic8+f0yDzYrcBweLjU1rMqoMvLkyHfzp2tad8b3btLFnPrVu/vo5QMt/bqJc/RQHb//bL46sMP3R8zd66U9Kld27RueVShAvDggxIYBNLOEZ9+Ku/Tzz9vfttvvSW1/PwZMh8wQCbhv/aatj7UrSvPt7feYl06b+3bB0yfLkH1a69JyZL77ze+XQZ0BoiNlfR0Vpbn45wZOrtMyNfDtm1SDsLIumWXLsmm2FqHW53atZMaWefO6XM+PSQmyio1K0oG/PSTDBckJprftrfat5fs6uefe3+fbduA3bsDe7jV6aqrpATC3Lmu3z8OHJBdVB56yOyeeTZ4sJRrskutxZIoJTXZEhPN2fmmoO3bJQv7t7/598U1LEzmbn3yibbdIwAZat6/X79dWoLd2LEyutG0qSQfJk82p5YnAzoDeFuLrkEDCfpOnDC+T2YxY0HE9u0S6OgV0LVtKxkDO03NTEwEsrO1lx7wx9q1Mizpqd6V1cqUAbp2lfIM3po3T0p+2KkMixYDB8qH7KZNxW+bP18yYvfea36/PLnhBlnxN2uW1T3xzpo1wI4dwOjR5rf99ttAnTpScsZfQ4fKvtVvvqmtL61aSUml118PrgSEEX74AVi4UFYZT5wodVK7dDGnbQZ0BvB2twjn/K9gmUd37hzw66/GB3QbN8qwpF7txMfL3B47zaNr2lSeR1ZkMlJSgJtvlsfYzu6+W75AlPQ6A2SoaMECGfKzYrcEI3TqJMOpH39c/LaFC2WFst2Glh0OydKtWAEcPWp1b0r22mvAjTf6v72gv44eBRYtAp58UtvztUIF4OmnJYDW+ng/+6xMcVi3Ttt5gplSMjTftKl8Kd6xQ7JzZi1KYkBnAOey9tJWiy4tTZ7QLVsa287GjVJcVq+AIzRUVrvaaR6dwyFZOrMDuvPnJSto5+FWpzvvlL+dN1m6r7+WOXd2WSCgh5AQoH9/+eDPzs6/Pi1Ntogyuiq9vwYMkL/bvHlW98SzHTtk2NrfIU8t5syRv68eqyKdQaHW0iOdOwMtWsjWZ+TamjXyXvPKK7Kzx913mzvSwYDOAOXKye4FJQV0UVFA1arBk6HbtUve+Jo2Na4NpfQpKFxU27aSobPTcIIV24Bt2CDBQSAEdJUrS20zbwK6xYulbIDR2WOzDRggNem+/DL/usWLZccas4Z5fFWligwFz55tr9dbUcnJMh+6Z09z283NBWbMAPr2lc8HrapUkX18k5NLntfticMhu2R8/rnMg6TC8vIkO9exo4xW/f67rGw1EwM6g5TG0iW7dknWsUIF49o4cEACHL0DunbtZCGAnbKlzm3A/vMf89pMSZHnrpFBuZ7uvlseH081si5dApYulVVmdqjHpqf4eAlSncOuSknGrmdPew+ZDxokC1R27LC6J66dOiWP6bBhsjuHmVavlve54cP1O+eoUTLvePp0becZMEASFoFaINpI//63LCj7xz9kqL5bN1ndaiYGdAbxZrcIQAI6OwURWuzcafxm585K23qnsZ0Fhu007OrcBszMYde1ayU7FyiBT/fuUsX/66/dH/P117Lt1AMPmNcvMw0cKFmTU6fkNfjLL/YdbnW6/XbZ7/mTT6zuiWtz5kim7LHHzG972jTZ4kvPDZFiYuR58u678gXHXxUryjD/zJksYVJQXp4Ms3bpkr+LkRULaRjQGcSb3SIAyWgFU4auRQtj29i0SQoB6zEUUVDVqrJFkp0WRgAyb8WsbcCOHJGAwM7154pq1EhqHnoadl28WI4zem6nVfr2lQ/XTz+V7FzlyvnZXbsqW1YC7AULrN3izpXcXAmqHnhAipeb6eBBGT4fPlz/L1XPPCOfSZ99pu08w4ZJssKXFebBbtky+fwbP14ydB06yNCr2RjQGcSXIdc//rCm3pieTpyQgMCMDJ3ew61Obdtq3/tQb4mJ5m0D5hzatXswUJDDAdx1l3wIupqPlZMTvMOtTjVryt9s3jwJXnv1khpkdvfggzIXy+j9LX21erWMmjz5pPltz5snqyONyLC2aCGFpt99V9t5rrtO3ivff1+ffgU6pSQ7d9ttMs1h40bfd/bQCwM6gzgDupK+fTpLlwTi/oYFObeXMTKgy8yUwMaogK5Nm/wad3Zh5jZga9pgiX8AACAASURBVNfKfCyzsxJade0qe7Tu3l38tq++kiGQYB1udRo4UBa0/Pab/Ydbndq1k7Irdht2nTpV6uXdeKO57SoFfPSR1J0zqtzMM8/IKITWmpvDhsmKzmAZXdLiiy+kfNL48bICuG5dmQpiBQZ0BomNlWGQ48c9HxcspUt27pRhlEaNjGvju+/kTc/IDN3ly/n70dqBcxuwlBRj21HK/tt9uXPzzUBEROGVnk6LF8sm5UZPBbBaz55SmqJ8eckUBIKQEKBfP5lMrmVel55+/VUydE89ZX5Gd/NmYO9eY3f3uPtuoF497SVMHnhAChZ/8IE+/QpUSknx4I4dZSHZwoVAUpKU5bFCQAV0ycnJiI+PR4Kes0UN4u1uETEx8qEd6N90du2SuW1GrgjbuFEmUjdsaMz5W7SQwMCOw67r1xubOdy5U4Z2A6FcSVHlyslQUtGA7tIl2Zy8d+/gHW51qlBB3kfCwqz7MPFHv34yXcPoLyzemj5d3mOsyOjOnSsZSyOLGIeGylDy4sXayiGVKwc8/LAsHilYA7G0WbtWsp0vvCALRcqUkcLZVgmogC4pKQlpaWlItdMeTW54G9CFhATHwohdu8yZP9e+vXEfzmXLyuoyuwV0nTsbvw1YSoq8SRuV/TRa167y+Jw9m3/dt9/KcKvdtr8yQmqq1L46fRr48Uere+O9li2l9Iodhl0vXpQhz0cekS92ZrpwQRa0DBxo/J6fjz4qgb/WOXDDhskIVGnd31UpqTPXpo2MEkybJn+/ypWt61NABXSBJDpaXpiloXSJUsYHdJcvS6BldMDRtq29SpcA8oFn9DZga9fKnoNmf5DppWtXWQBRsHzJ0qWyF2awFRN2ZckSKXNTo4brrcDsyuGQLN2yZZ5rCZphyRIpbzNkiPltf/65zBEeOND4tipVkmHd99/Xll1r3Fgy41pr2wWqb76RJMP48fLcOXLEmoU0BTGgM0iZMhLUlYbSJX/8IZkBIwO6n36SDITRAV2bNlI64K+/jG3HFw5HfvkSI+TkAP/9b2BvWn/NNfLjHHbNy5MgoVev4B9uBeR37dFDaoQtWBBYNcL69ZPX9uefW9uPWbMk02LkPGB35s6VL5ONG5vT3tNP5+8Xq8WwYZIZdy6KK00mTZIvi3fdJSuHb7vN+FGqkjCgM5AvpUv277dfPSZv7doll0ZOPN+yRYLkVq2MawPILzBsx2HXn34yJtDcskWyI7feqv+5zdS1a375ktRUee316mV1r4y3ezewZ48sjBgwQJ4jZu4uolWDBrKi1Mph199+k03nrcjOZWTIilEjF0MU1bix7IX87rvatl/r2VMSFzNm6Ne3QLBtm7zGnn8e2LpVFrQ8/bTVvWJAZyhfdovIzvbuWDvatUsmZdepY1wb338v823KlTOuDQCIiwOuvtp+w65GbgO2bp3sKxzoQ5Ndu0p2dfduGW6tXj1w5wT6Ytkyef3dcYf8DZs2DaxhV0CydF9+KZl+K8yaJUOR991nftvz58tiBbPLzTz9tAQjmzb5f46wMFkEMHeuZFlLizfflPIk992XX6rk7rut7hUDOkPFxnof0AGBO49u1y6gWTNjJ/N+/31+9sxIDoc9CwxHR0tAa8Sw67p1Mn8ukFZHunLLLTIHcNUqmdPSo0fg/07eWLpUgtmICHn+Dhwo1xVcIGJ3998vw8TLlpnf9qVLwIcfyuNm9BfGopSSYKhHD/Mn03fpIsPLWkuYDB0KnDkjK2dLg4MHZah61ChZoW11qZKCGNAZKC4OOHSo5OPq1pU34kCdR2f0Hq6ZmbI/pRkBHSDtpKbKFkB24pxHp2WIpKiLF+UbeqAPtwLyYXzLLbK10d69pWO49fBhea727Jl/3YMPyhD60qXW9ctXsbFSy0vrnC5/rFwpw9RWDLfu2CHvn2YOtzqFhEiWbskS7z6n3KlbV7LDs2fr1jVbmzIFiIyU1dAffGB9qZKCGNAZqHZtieBLWr0VESFvaIEY0OXmAmlpxs6f++EHCWLMqtzepo184/zlF3Pa81bnzjIvzNWOCP767jsZ7g+GgA6QTFVqqgxBBvIiD28tXy4fKN265V9Xp45kXANt2LVPH5lScOKEue3OnCnvLVbs9Tt3rqxM7tLF/LYBYNAgea1Mm6btPEOGyIpPu71n6u3UKXm+PPGEDDdPn259qZKCGNAZKC5OLr359hOopUv27ZMsj5EZuu+/l29EZq0Au+EG+fZqt3l0nTrJm4iew67r1smbUbBsXN+1q3zJuO66wC3B4otlyyQYr1Sp8PUDB0pwpKV4rNl695aFYWbWNUtPl50hhg41r02nS5dk/lz//sYWZPekYkXJLn3wgbbC5ffcA1StKoWGg9mMGTI14Kmn7FOqpCAGdAaqXVsu09NLPjZQS5c4V7gaGdBt2QIkJBhfcNOpYkWZE2i3eXTly8uwlJ4B3TffSKkGsx5bozk3pTd7LpQVTp2Sv5+roeXevSVzt2CB6d3yW3S0DJmbOew6Z45kqPr2Na9Np9WrgWPHrBluLeiJJ+S5pOVxDw+XFdZz59pnGze9ZWfLfMNBg+S5On26vHdaXaqkoCB5G7en2FiZG+dthi5QA7qqVeUJbgSlzFsQUVCbNvYL6AAZdv3mG6kdp9WFC5KFDJbhVkAyViEhsiennnMN7eiLLyRb0KNH8dsqVZINwufPN79fWvTpI1ljM+pA5uZKQNevH3DVVca3V9TcuZIZv/Za89su6JprJLP93nvaXjODB0ttu5Ur9eubncyfLyVmRo2SaUbr1wPDh1vdq8IY0BkoLExKYHiToWvQQKqUW7Vs3187d8r8OaOKtx4+LC8iKwK6Xbvst1Kwc2cpD6DHcPCmTRIYBlNAt3SplO5ITw/++TzLlsnzNDbW9e39+8s2YHrOuTTavfdKQP7ZZ8a3tXatfNm2YjHEyZNSSNnq7JzTk0/Kc0XL+0qLFjKSEoyLI/LypFRJjx6yZ/mMGVIWyW4LrxjQGczbla6BWrrE6C2/nFkysxZEOLVtKy/iH34wt92SXH+9ZET1GHZdt042Im/WTPu57ODYMala//DDMgTk3DUiGF24IL9fwdWtRd11l2TqAilLV62arJg0Y9h15kzJkCUkGN9WUYsWSYawf3/z23alSxf5DJo6Vdt5Bg+W52Wg1lR158sv5YvRs8/KIse5c+V3dU7xsAsGdAarXdv7OXRAYA27ZmfL0JbRAV3t2pLpNFPTpjIMY7dh15AQWb2pV0B3yy3BM3/u889lyOj++yXrGMwB3X/+Ix8sngK68HCZS/fJJ4E1/NynjwTm3uyy46+MDHm+DB1qzdZwc+fKTg1GTVXxVUiI1FL797/lsfFX377yvJs7V7++2cEbb8iX/A4dJBjPygIee8zqXhVXxuoOOCmlcObMGZe3ZWdnI7vALsLO47KyskzpmxY1agDbt8sTwJMyZaRa/65d1i1h99WuXfIts169kn8/f23aJNt9WfGnvv56+WCx2zyJjh3ljffgQf+Xy589K8Hqa69Z89gaYfFiGYIsV04CunHjJCiwYn6U0RYvBho2lN1oPP39evaUXRD+8x/zpy3467bb5P1w3jzjXnszZkgh2O7dzX/+790rr71//cter7177wXGjpW5dM8/7985HI7859wTTwTHl8WtW4Fvv5Xn45kzksW8/XYZKTH671exYkU4fPjG4VDKHt/dsrKyEBUVZXU3iIiIiCyXmZmJyMhIr4+3TUDnS4buyJEjuPHGG5GWloZYdzOCNUhISEBqaqou51q+XJY5798PdOni+bxDh0rWZe1a39rQs79OWVlZiIuLw6FDh9w+oV58UTIFaWm+ndvb/u7cKdmoL78E2rfX99ze+OILqbr/889Ar17WPMbuXH+9LJmfMsX17SU9DhMmyFDcr7/6NuRkxHNNj/MuXSpz53bskMr1gNSi69gxB/PmVffrMS6JVY/Fxo0yP+6rr6RmYkleeAH46COgWrV2+OGHzTr2VNtz2JNFi2RIa9eu/Hqeelm/XjJzq1bpv9dvSX+7vDyZs9qli/vXblFGPcZA8f7+/LO81374of8T/pUCqlc/gF696mLmTH366WTUa87dY7x/v7zXvvmmLJ55+mmZ7rJzp2SRje6zrxk62wy5OhwOn5+sFStW1P0JDgChoaG6nbdJE7k8dark8zZrJvOafG1az/4WFRkZ6fbce/fKpGKj+puWJsMinTpJrSg9z+0N5+pP6Yc1j7E7d94pdazc3a2k/m7aJENbvibFjXoctJ539WoJ4AoWSO7WDVixIg+Af49xSax6LNaulaFWb+c/Pvqo1M+qUOEmWz2HPenbF3j88Yv48ssI/O1vup0WgHyRCQvbjzvvrKf7/LmS/nZffSXTAIYO9f1904zncLt28kVxzhxtK3ArVUrBihX/hxkzihe91sLI92Gg+GM8a5YMrQ4fLvX1Pv0UeO45oEoV789pdJ8LCoIRbv0lJSXpdq6Cu0WUdN6GDWWlnq+lS/Tsry/8XeHqbX+//17O720w58u5vXH11bIg47vvrHuM3encWVZEu1sV7am/WVkyL8SfciVGPQ5azpudLdnUohmFrl2B9PQQAMZsMWLFY6GUlCvp2dP7+UktW8rrKDp6pE49NF7FikDLln/ovtr1xAkpiXLXXUcMWQxR0nNi7lx5n2/bVv+2/eGqv08+KVnMn37y/7wjR1bBpUsSPOvJzPfhEycksH3ySZmXO2+e7Irk676tpn52qAB06NAhBUAdOnTI6q6UKDdXqbJllXrvvZKP/eEHpQCltmwxvl8lyczMVABUZmamy9uzsqSvH31kXB9atFDqsceMO783HnhAqY4djTl3SY+xJ6dPKxUaqtT77/ve7sqV8rf79Vff72tHq1bJ7/PTT4WvP3dOqfDwPAWM8OsxtqNt2+R3XbvWt/tNnqxUuXLyutWTludwSRYtkt/1t9/0O+eUKfJ+/Ndf+p3TW1lZSpUvr9TLL/t2PyMfY1dycpSKjVVq6FBt5+nRQ6lWrfTpk9FcPcYTJyoVEaHU0aNK5eUpFR+v1H33WdhJLwRkhi48PLzQpZ2FhHhfi65hQ7ncu9fYPnkjPDwcEyZMcPsY//yzXBpVsuTsWWnD7PpzRbVpI9ksI7azKekx9iQqSh4bf8qXrFsnxWivucb3+9rR0qVSQ6voc7F8eeCmmxTq138yIN4rvLFsmfztb77Zt/v16ye165Yt07c/Wp7DJenWTf6Gixfrcz6lpPbcPfdI9QGzffaZlJoZONC3+xn5GLtStiwwbBjw8ccyVchfQ4ZIseJt2/Trm1GKPsYXLshq30cekQLCGzbI1Bu7VTwoxuqI0h9mf2PR6uablerb17tjo6OVmjDByN7oY+ZMpUJClDp/3pjzr1sn38537jTm/N7673+lH1u3WtsPVyZMUKpyZaUuX/btfq1aKTVggCFdMt3ly0rVqKHU3/7m+vYpU5QKC1Pq7Flz+2WUa69Vqn9//+7bqZNSXbro2x+j9ekjv7MeNm2S1/Lq1fqcz1e33io/gSAjQ143r7/u/zkuXVKqZk2lkpL065dZ3n9fKYdDqb175f99+ijVqJFk6uwsIDN0gaZ2be8ydIBk6eyQoSvJrl2S4TFqE/QtW6R+WNOmxpzfW61ayWomuxUYBmQe3alTkkH01smT8o35ttuM65eZNm+W/SPdrcjr2lW2N1u3ztx+GWH/flnF66mYsCf9+0tG14x9UvXSp4/8znps4zZrFlCnjrxuzHbwoDwH7bLVV0mio2WF/3vvyX7B/ihTRn7f+fMl4xUo8vKAt96SunzXXCOvlyVLJDtnRRFqXzCgM0FcnHe7RQBAo0ZSSsLunHu4GuX776UkQ2iocW14o1w52TzbjgHdjTfK5HFfhl3Xr5ehp2DZv3XpUlm84m6SecOGsgtLMOwasWyZVOG/807/7n///fJ6WrhQ334ZqWtXeY5rXRyRlSW/9+DB1hS7nTdPho/vvdf8tv01YoQkIrTsq/voo7LIb+lS/fpltBUrJKny7LPy/9mz84NTu2NAZ4LatWWpujffdJwZOntUB3TPjD1c7VLZvk0bewZ0ZctKYOZLQLdundRpc9ZqC2RKyQfFPfe4/5B2OCQo+PJL+7+mSrJ0qWSX/N35okoVqV8XSHu7RkTI33fRIm1/vwULZIXiI4/o1zdvKSV1AO+7T4LTQHHttZLJf/tt/x/7hg2Bm26SoChQvPGG1D9t00Z2QpoxQ8ro+Lsrj5kY0JkgLk6eGEeOlHxso0ZAZqaUL7HC5MmTkZCQgIoVK6JGjRro2bMn9uzZU+iYo0flx6iA7o8/5MfqBRFObdrIkI+WCcLuTJ48GQ6HAyNGjPDr/p07S025s2e9O37duuDJzv30kwxDuhpu/eOPPzBgwABUrVoVM2fei/37gSVLdpnfSZ0cPSoFhf0t9urUvz+QmgoUeUn77PLlyxg3bhzq1auHcuXKoX79+pg4cSLy8vK0ndiFPn1kY/RdGv58M2dKYF+rln798tbmzfIlvaQMz/r169G9e3fExMTA4XBgWZEVLEopvPjii4iJiUG5cuVwyy234Gfn6jSDjBwp0182a6hHPXgw8PXX1u9T7unxvXTpEp5//nk0aDAAmzYBP//8MAYNGoR58078f3tnHh7T2f7xbxLEFlG1hNorGrG0tmqT2ImWopZSe3VBJV6KWtq+XV5v7XQRtZZSW1sEpS1REltpNEIspUUpv8bSkoSQ9fn98X0niCTmzJwzZya5P9c11yRnzvM898ycOec+94rz59nGzBUQhc4BVK3KZ1fIdI2KikJISAj279+PiIgIpKenIzg4GDdv3szax+gM159/5rOzWOgs7jy9C5RHR0dj4cKFaHB3NVyNBAczAzcy8sH7XrlCV3l+UejCw5nxmf39XLt2DYGBgShcuDC+//57xMZ+hMKFM3DokI85gurApk18fu45++bp3JmFXr/4wr55pk2bhvnz5yMsLAwnTpzA9OnTMWPGDMyZM8e+iXMgOJgy2+oq/uUXPoYO1Vcua1m+nDf1D/rd3bx5E48//jjCwsJyfH369OmYPXs2wsLCEB0dDR8fH7Rv3z7XDkt60LEjjQwffWT7HD170ro1f75+ctlCXp9vcnIyYmJiUKbMNNSsmYLNm4fh1KlTGDnyVzRpYl1HFqfA7KwMW3C1LNfr15ldtXr1g/dNTua+S5YYL5c1XL58WQFQUVFRWds+/VQpT09mMRnBhAmsg+QsZGYym/Q//9FvzqSkJOXr66siIiJUy5Yt1ciRI22WrUYNpUJDH7zv11/z2HKB8o1W0aCBUn373r99/PjxKihb8cDgYKXat3eQYAbwzDNKtWqlz1zDhytVqZJ9v99OnTqpl19++Z5t3bt3V/0NSp8eMkSpqlVZ11MrQ4fyfGLU+Sovbt1SqnRppSZO1DYOgAoPD8/6PzMzU/n4+KipU6dmbbt9+7by9vZW820pRqmBuXNZ0eDsWdvnGDNGqTJljKuKoJXsn69SSh09yvPj0qX8Pzz8sAIy1IwZVx0voI2Ihc4BeHuzzYs1FrpixXg35yyZrgkJCQCAMnf1OomLY/aptb3stHLggPO4WwHGYT35JDtG6EVISAg6deqEdu3a2TWPm9udNmAPYudOWoDNcDvpzZkzdLnm5ILctGkTmjRpghdeeAHly5dHw4YNUabMPkRGMjje1bh2Ddi+nZYOPRg8mDG9WntG301QUBB+/PFHnPpfBtfhw4exZ88edOzYUR8hszFwIBPLdu3SNu7GDcYMvvKKceervNi0iUkB9gbUnz17FvHx8QgODs7a5unpiZYtW2Lfvn12Spk3gwbxGmaP8XXYMGbY6935Q0+mTeO5sW9f/r96dSkACejfv7CpcmlBFDoH4YqZrkopjB49GkFBQah3l3/VyISIjAy6Np3F3WohIIBxJHqECK1ZswYxMTGYMmWK/ZOBCt3vv/ORF/kpfi48PPeMzzNnzmDevHnw9fXF1q1bMWzYMKxfPxhpafYpMWaxaRN/F/bGz1lo3JgZ6kuX2j7H+PHj0adPH/j5+aFw4cJo2LAhRo0ahT59+ugjZDYCApitvHy5tnFr1gA3b2pv16QXy5bxXPaYnd3n4uPjAQAVKlS4Z3uFChWyXjOKEiWAIUNY9sVW726tWkCHDsBnn+krm16cO8c2ZWPHAkWKAFev3sa6dQ+jTp298PFxTB9WPXAphW7u3Lnw9/dH06ZNzRZFM65Yiy40NBRHjhzB6tWrs7YpZaxC9+uvvKt2RoXu2jX762H9+eefGDlyJFasWIGiRYvqIlvr1sx4zctK99dflD2/KHTr1vECkVPGZ2ZmJho1aoTJkyejYcOGGDp0KIYO7YBixU5j82bHy2ov69bx+KtUSZ/53Nxopdu4Ebh61bY5vvrqK6xYsQKrVq1CTEwMli1bhpkzZ2LZsmX6CJkNNzda6b75ht0WrGXhQiZDWOKYHUl8PLB1q77lLtyyFUJTSt23zQhCQ/m5L1li+xwhIbxZ1zsWWQ9mzmSc5quvMkGiTZsvkZFRDGvXamzJYjZm+3xtwdVi6JRiDIi1fe1mz2bfRVviRfQiNDRUVa5cWZ05c+ae7efOMc5gyxZj1v38c1bo1rvnpL0kJjKOZNEi++YJDw9XAJSHh0fWA4Byc3NTHh4eKl1r24f/0bq1Up065f76ypX83uLjbRTcibh4ke9l2bKcX69atap65ZVX7tn22WefqZIlP1Vly2rvrGEmCQms2P/RR/rOe/myUoUKKfXJJ7aNr1y5sgoLC7tn26RJk9Rjjz2mg3Q5c/o0v/eVK63bPyaG+2/YYJhIeTJtGmON//5b+1hki/E6ffq0AqBiYmLu2a9Lly5q4MCB9opqFX36MF7X1t9PerpS1aop9dJLuoplE3d/vpcusWfrBx8olZqaqrp27a6KFDmnunW7bbKU2nEpC50rU7Wq9S5XX19W1r540ViZckIphdDQUKxfvx47duxAjRo17nk9Lo7PRlnoDhwA6tZ1vnpNXl6sy7R3r33ztG3bFnFxcYiNjc16NGnSBP369UNsbCw8bKyk/OyzdKnevp3z6zt3Av7+rADv6oSHMx6qc+ecXw8MDLyv1M6pU6dQvXocrl51zpqCubF5Mztd6F2Qtlw5Zsza6nZNTk6Ge7bifx4eHoaULbFQsybrg1nrdl20iFbNTp0MEylXlKKLskcP1v+zlxo1asDHxwcRdxWdTE1NRVRUFAICAuxfwAreeINlgiwZ11rx8GAs3Zo1wN9/6yubPXz6KWUbOjQNvXr1QkzMI0hNrYoJE1yw/7PZGqUtuKKFbtky3i1ak+Vz8iT3/fFH4+XKzuuvv668vb1VZGSk+uuvv7Ieyf8TfOpUpUqVMq6n3RNPKJUtec5pCAlRytdX/3ntyXK1cOQIj5mIiJxff/RR1+ypmBOtWzNrNTd+/vlnVahQIfXhhx+q3377Ta1cuVIVL15cLV++UpUtqz3j0Ey6d1fqySeNmXvTJh4z2Yw+VjFo0CD1yCOPqM2bN6uzZ8+q9evXq7Jly6px48bpL+hdLFxIS/nFi3nvl5SklJeXUv/+t6Hi5EpUFD/bHTusH5OUlKQOHTqkDh06pACo2bNnq0OHDqlz584ppZSaOnWq8vb2VuvXr1dxcXGqT58+qmLFiirRge6MwEClsiWQa+LSJVqcZ8zQTyZryenz3b37sCpVKkONGpWhunTpoipXrqwaN05STZumZF37UlJSHC+sjYhC5yB27OAP/OTJB++bmqqUh4dS8+YZL1d2AOT4WPq/XO7+/ZUKCDBm7Zs3+b4XLDBmfntZtYrf4aVL+s6rh0KXmclSFKNH3/+axU2+dq1dSzgFV67wgv6gY+Tbb79V9erVU56ensrPz08tXLhQKaXUwIFK1avnAEF1ICmJriB7GqTnRVqaUhUqKDVihPaxiYmJauTIkapq1aqqaNGiqmbNmurtt982/OJ37RrdmA9SCBYvZujGH38YKk6uDBjAmygtYTM7d+7M8dw7aNAgpRRLl7z33nvKx8dHeXp6qhYtWqi4uDhj3kAuhIfzXLJrl+1z9OunVM2ajg8pyvnzfVO5u6epffvO/+//xor21W5Z++zcudOxgtqBKHQO4vff+UPYvt26/WvVyvnibDZPPMF4QCPYvZufUWysMfPbi0UxMism50G8/LJS/v73b//iC8p91XXKKeWK5UJtq1K9di0/i9On9ZXLCCx1A42UdexY1ge77ULhQr16USnPy0vQtClr95nBtWtUxCdPNmd9I8nIUKp+fftqOv70k3OcR2/cUKps2XuvZ3372hcnaDYSQ+cgLLW/tMTROUPpkrtJT2cLHiPj54oXZwydM1K1Kr9He+PojOKZZ4Djx+8/xnbuZPzfww+bI5eerFsHNG8OlC9v2/gOHVjuxBWaha9bBzRsyNgxoxg8mPXBvv3WuDX0ZuBAZtofPpzz6z//zEzKkBDHymVh9Wp2b3GFZu5acXcH3nmH/aNtjUV96ikgMBCYPl1f2bTy2WesEfjWW/z/wgXg66+BkSMZU+eKiELnIDw9GZBubemS2rWdo3TJ3fz+O5CSYqxC17ixOQVArSUgwHkVuvbt+dlt2XJnm1L5p/5cQgIL7PboYfscJUtSqXN2he7WLSZE6FVMODf8/VkiyJ5yFI4mOJgKfW7JEWFhQI0aTBQyg8WLmYihV5kZZ6NHDxaWnzTJ9jnGj2cP6j179JNLCzdvAjNm8IamWjVuCwujQeHll82RSQ9EoXMgVauygKE1+PqymXF6urEyacHSHNvIHq7OVn8uO4GBwMGDVGydjdKlab2629py9iwtdvlBodu8mZYPewvsduvGi4nB9VjtYutWXnTsUV6tZfBgrmdGVr0tFC7Mav4rV/J4uJvLl9mNYPhwc6wsMTF8vPqq49d2FB4ewNtv88YxJsa2Uz7/pAAAIABJREFUOTp14s3EtGn6ymYt8+axrqjFOpeQACxYALz2mvNVWNCCKHQOpFo16xW62rWpzFm7vyM4epRWxnLl9J/70iW+V2dq+ZUTgYEsI/HLL2ZLkjOdOwM7dlAZAGidc3cHWrQwVy49WLeOx0eVKvbN07kzP5ONG/WRywjWruWNk70dBqzhxRdZHf/LL41fSy8GD6bylr1Q9OLF/G7NsrIsXEjLnFnWQUfRuze7P9hqpXN3B8aN4/dnMRQ4Cot17qWXgOrVue3jj1nyacwYx8qiN6LQOZAaNWgxsQZfXz47UxxdXJyx1jnA+S10DRrQLO+sbtfOnWk9tJSr2rEDaNSI1jtX5uZNdsLQw2L18MNAy5bA+vX2z2UEKSm0shrtbrXg7c3PdckSuuhdgQYNeK5YsODOtvR0Wl769dOn9ptWrl+nUjxkiHOHjehBoUK00m3YwJ7KttCnD2OSZ8zQV7YH8dFH/K7efpv///MPMHs2rboVKzpWFr0Rhc6B1KhB91dGxoP3rVKFcXfOpNAZ2fLrwAFa/+y1vhhN4cIM6t2922xJcqZWLcDPjwpBfoqf++EHxpXpVWC3e3cqu9ev6zOfnmzfDiQmOsbdauGVVxizGxXluDXtZehQ9ua13CRv2sTAdrOSIZYto/V+yBBz1nc0/frRwvXhh7aNL1IEGD2aPVStjS23lytXmIwREnLHOjd7Nm8Gxo1zjAxGIgqdA6lenQeONbEqHh68ODuLQnfrFpMi6tc3Zv4DB3jH7YC2hHbTogWDeQ0sim8XnTszvuXXX9nDNT8odOvW0SpTq5Y+8z3/PH+LdyeQOAtr19LV6shs71ateCMwd67j1rSXXr0Y77RoEf8PC2NIRMOGjpclM5NZk927u76Vx1oKFwYmTmR/3RMnbJvDErPmqFi6//6X1xhL7NzVq8Ann7BXbX7ooiMKnQOxdNGy1u1ap47tPxS9+fVXnrSMsNBlZrLMgLO7Wy20bMmAWkfHflhLly6MSfziC94YBAWZLZF9pKQw1kZPi9Ujj/B4W7dOvzn14PZtuoJ79XLszY2bG11O4eGukxxRogRLgyxezOD8nTt5YTaDbdt4822WddAsBg2i29TWWLqSJYEJE+g6N9p4ceYMXfLjxwNly3LbzJl8fvNNY9d2FKLQORBLerQrKnQW5cXfX/+5T51ilpGzJ0RYaNaM7gJndU89/TTjxDZupKyunLUF0AWZlKR/P9OePYHvv6d701nYvJny9Ovn+LUHDgSKFmVgv6swYgTdaCNH0jKm9zFiLdOnA02aMMu8IOHpCbz7Lmvv2ZrxOmIEvzuL1cwo/v1vKnKjRvH/S5eAOXOAf/3rjoLn6riUQjd37lz4+/ujadOmZotiE8WKAT4+wB9/WLe/nx9LKzhDnE9cHF3GRigHBw7QQuAqX2uxYlQ+d+0yW5Kc8fBgkeHffmPNNVfn66+NcUH27k2LmK3Nxo1gxQr+DhyR3Zodb29gwAAqdKmpjl/fFnx9gbZtGQLxxhu80XI00dG0Do4f7xohI3rz0ks0Prz5pm1JNcWKMQ5v3TqWEzKCQ4cYq/fBB0xqA+jm9fBw/czWu3EphS4kJATHjx9HdHS02aLYjJZM1zp1+Pzrr8bJYy1HjxoXP/fzz1Revb2Nmd8IWrSgQuesWYF+fnRlN2hgtiT2cfs23YAvvqj/xbJKFbqj16zRd15b+ecf4LvvzLHOWQgJ4U2ksxdevhvLecOsDjPTpzO20976iK5KoULA1KlMMtq61bY5+vUDnnjCdqUwL5RiwoOfH8vdAPQKhYVxPTMyoo3CpRS6/ED16tZb6GrX5rOzKHRGZri6irvVQosWrIN18qTZkuTMjRt8trbVnLPyww90t/bubcz8L77Ii9A//xgzvxa++YZK+IsvmidDvXqMEf3kE/Nk0MLff/MYKVfOHFfx77/TsjR2rOu2i9KDzp3pbh43zrZi+O7uLF+yb5/+NxPr1jFsY/r0O+VkRo9mHO3YsfquZTai0DkYLRa6EiUYd2d2HF1CAtPKjVDobt1iT0ZXSYiwEBDAE7izxtFFRbE9kjNmcWrhq69oZbRYq/WmZ08qUc5Qk27FCrZvMzvbbswY4KefjHN/6cmcObTAvPUWXeeOPlfOnEllcuBAx67rbLi5AbNm8cbf1kzpdu0YKjJhwv0dQGwlKYkxc126UOkEGKe6ZQu/u2LF9FnHWRCFzsFUr85aSdbGqDhDYoSRLb9iYnhH99RT+s9tJF5eLNjrjArdtWt0Y7dpA0RG8qTmity8yYu0UdY5gMpTmzZsI2Umv/3GOLABA8yVA2Bbpsceu5MB6KzcuEGF7rXXmKH7yCPAlCmOW9+SST5yZP5TDGyhaVNg2DDgnXdsz5SePp0tL2fN0kemDz6g9f3TT/n/9euUsUMH8xJojEQUOgdTowbvKK0tpOjnZ77L9ehRmqr9/PSfe/9+ngyNis8zktatGQztbHF0P/5Iq9OIEbxx+O47syWyjS1bgORkYxU6gNaVyEjrQyGMYMkSdvNwhjgsd3da6TZsoEvRWVm0iBnBY8YwGeLNNxn4fuaMY9afPZvnxddfd8x6rsDkyUw6sGSSaqV+fbpB33vP/rJQR46wpde7796pMDFmDI+ZRYvyZwKLKHQOxpZadKdPm9sM/uhRxvMZkUF24ADv7FyxVU7btgwgP37cbEnuZetWHjcBAbQiOlutNWv56iuWgnj0UWPX6d6d9bCWLzd2ndxIT6elp39/57H0DBhAV+JHH5ktSc6kpNCK068fULUqt736KgPcp041fv0//mCc4ZgxwEMPGb+eq1C6NI+ZtWttv5H84AMmmQwcaLvrNTOTVtvatRkvBzDWcskSHjfO3pHIVkShczBVqvDOQItCl5lp7p2ykQkR+/e7nrvVQlAQldwffzRbkjsoxSKnwcH8v0cPnlhv3TJXLq0kJlJuo61zAGNVe/WiUmVG94/vvuONwSuvOH7t3ChalEV6ly5lNX1nY+VKuvXGj7+zrXhxBuUvWWJ8kdq33qIil18K0upJnz682Q0NpYVdK0WL8ubqyBHg/fdtk2HWLPbbnjeP5+jz53mTEhxMxT+/IgqdgylShJW1tdSiA8yLo1OKNeiMUOguXqTr2dUSIiwUL04r2PbtZktyh5MnefKy1J/r2ZOxaLaWEzCLtWtphXFUxuegQbzJ2rPHMevdzeefA40bs2yDMzF8ON2vs2ebLcm9ZGSwhtjzz9+fLBMaClSqdKfxuhEcOMBCuv/9Ly27wr24ubEN2sWLtn8PjRvz8508WXt868GDVLjffJMZ27duMZShRAnOlR9drRZEoTOB6tWtt9CVK8eq/2YpdJcusTSAETFuBw7w2VUtdAAzsyIjbUvVN4Jt23jT0KIF/69dm8r42rXmyqWV5ct5l1+5smPWCwoCatakdceRXLzIWEFnss5ZePhhKkhz5vAc4CyEh9MCN3Hi/a8VLco2VGvX3jm/6IlSdOE1aMCCukLO1K5N1/fHHwPffmvbHOPH80br5ZeB3butG3PjBtC3L/D441QI09M5/sQJxoTml44QuSEKnQnUqKEtANvMxAgjM1z376cLulIl/ed2FG3bMovUWWpdb93KelAlStzZ1qMHT6pmxmFq4dw5Zg87MuPT3Z2umK++cqzy8tln/K7693fcmloYM4ZuaGeJpUtLYxZl+/a5167s358K14gRtObpiaWbwaxZBbvunDVYyoUMGmRbPUw3N9YWDAigNfbIkQeP+de/gP/7P1pQMzOBF15gfcfly53PAm4EotCZgJZadADdCmYF3h89ykBtSzKHnrhy/JyFJk2AUqWcw+168yartXfseO/2F15gTNoPP5gjl1ZWrKA729FlBV59lReBpUsds15yMjB/Pq1zztpvt1w5do/49FPnKL68cCGtczNm5L6Phwdjpw4epMKsF7du0WrUsSMt80LeuLnxt+TlxdAJWxIcihShEl21KhW7vBK8Vq/memFhLEf07LM8523cyNCTgoAodCZQvTqDoK0NVK9blxY6ve82rSEuDvD31/9uND2dJ1xXV+gKFQJatXKOxIht29gqq2vXe7fXrUsXxIoV5silBaWAL7+8k3nqSMqVY3LEvHmOSY5YsYJ1sUaMMH4texg7lp+HI7JH8+L6dZazGDyYx3NeBASwnMhbb1lfIupBWOqr6VUjrSBQpgyt3tHR/C5snWPPHtZH7NmTrvbExHv32bOHx0W/fsyQffppIDYWiIjguIKCKHQmYLF2nTtn3f716vFC7aj6SndjVA/XuDgqtK6u0AG8W9+3jxYyM9m4kcpbTmU++ven2zUhwfFyaSE6mokdZhXYDQnh78xoa6ZSjC/q2tUY67eelC/PAPNPP7X+nGUEkyfznDFpkvX7lyoFDBliv4IeGUm386RJxtTjzM889RQLBs+cabvFtEQJ9lyePJnzVK7McIBdu+gd6diRMbDx8Qw5KVmSSl5QkL7vxelRLkhCQoICoBISEswWxSb++EMpQKnvvrNu///7P+4fHm6sXNnJyFCqRAmlZs7Uf+7PPlOqUCGlkpP1n9vRnDzJ72fjRvNkSEtT6uGHlZo4MefXL1xQys1Nqc8/d6xcWgkNVapiRaXS081ZPzNTqUaNlAoONnadrVt5zERFGbuOXiQlKeXjo1T//uasf+aMUkWKKPX++9rGff89j3ut4+7m7FmlypZVqk0b845LVyczU6k33uB3sWqVfXNduKDUhAlKlS7N39Ddj6AgpZYvL7jfk0spdGFhYapOnTqqdu3aLq3QpadTmZk717r9MzOVeughpf77X2Plys6ZM/yR/PCD/nMPHKhUkyb6z2sWtWopNWSIeetHRfG72r8/933atFGqdWvHyaSVlBReOMeONVeO1av5WUZHG7dG+/ZKNWzI37arsGABP5eDBx2/dq9eSlWqpNSNG9rHTppEub/9VvvYpCSlGjRQqmZNpa5e1T5euENGhlKDBvHat3y5/fMdP65U5cpKlSvHm+lLl+yf09VxKYXOgqtb6JRS6tFHlRozxvr9g4KUevFF4+TJiU2beCK8cEH/uWvXpjUmvzByJE8uZl2gR4+mZSsjI/d9lizhHfKffzpOLi18/TWPt7g4c+VIT1fK11ep5583Zv49e/g+v/rKmPmNIi1Nqfr1lWra1LEWkN27+XktXWrb+IwMpbp2VapkSaUiIqwfd/OmUp06cZzZx2R+IS1NqcGD+X2+/77t58vt25WqUIHXkT/+0FdGV0Zi6EzC11db94d69YBjx4yTJyfi4lgNXe+yIn//zUy1/BA/Z6FTJ+DCBetS6/VGKcbPde7M8hu50b07s8ZWr3acbFqYP58xL0Z1JbEWDw8GcG/YwN+A3rz3HstquFrmXaFC/I6io/nsCJKTWUesWTPb4yrd3ZmA0rw5Mx+tSQ66fBlo04a9mteuNf+YzC8UKsRC2h9+yC4QHTtqq/iQlsZixe3bM7Z79+47fVoFSYowjVq1gN9+s37/unUZLO7IAraWll96V9b++Wc+5yeFrkULBu5u2eL4tY8fZ7/f7Nmt2fH2Zl0oZ8x2PXmSJVeGDTNbEtKvHy8UkyfrO29UFDOiP/ggb+XbWQkIYJLBxIms92U0EycyS3XZMvsy7UuW5E3PgAF8vPkmcOXK/fspxVZsTz3FBJBdu+50XRH0wc2NN0ybN9NIUbcuFbycvg8LV64AU6bwujltGn+XW7cyYUe4C7NNhLaQH1yuH3+slKdn3i6yu9mxg2bqEyeMletu6tdX6vXX9Z/3vfcYK+VK8UPW0K2bUk8/7fh1P/yQySu3bj143w0beBwdOWK8XFoYPZpJHda8B0cxbx5d1DEx+syXkcHjo1Ej1z72//lHqfLllXruOWPfx86dPFZnz9ZvzsxMpSZPVqp4caWKFeP5belS/i4mTVIqIIBrtmzJZAjBWJKSGHpUqJBSHh5Kdeyo1KxZSq1Zo9SWLYzb7N+fCTFFi9JdGxtrttTOiyh0JrF5M08c589bt/+lS9x/7Vpj5bKQmqpU4cLWJ25ooUMHxqbkNxYvpgJw5Ypj133ySaW6d7du35QUpcqUUWrcOGNl0kJyMmUyOxkiO6mpStWty4u8tTdeebF0KX/DO3faP5fZfPst38unnxozf2KiUtWrK9W8uT6ffXauXlXqgw+YaGHJkPT2VuqZZ1h9wJUVblfkyhVeawIDqWhbvhN3d6X8/FhpQZJSHowodCZhKXWxY4f1Y8qVsy/9XgtHjxpTViEjg+nmkybpO68zYCkvo0cGl9Y1ly2zfkxoKC0sKSnGyaWF5cv5Hk6dMluS+7FYibR8vjlx7Rp/v3366CKWU/Cvf9FycuiQvvNmZirVuzetzr//ru/cOXH7tlIXLxqjOAraycxU6vp1GjtSU82WxrVwwSiO/EH16oyh0ZIYUb++MUHaOXH48J019eTUKVZ8z0/xcxYqVmR/yfXrHbfmN98AhQsDzz1n/ZihQxn0vXGjcXJpYf58Fmf29TVbkvtp1Ypti8aNs68o8/jxLIo7c6ZuopnO9OnsIvPCC8DVq/rN+5//sLvA0qU5F8nWG09PJn65YkxjfsTNjfG+Varw3CZYjxzCJlGkCIOutSRGNGjguCzKw4cp30MP6Tvv/v38wTZtqu+8zsILLwDffw8kJTlmvVWrmLlXpoz1Y+rVAwIDHZepmBdHjrDLhrMkQ+TEzJnsAjJsGB1BWlm3jj1IZ8zQP2PcTDw9+d4SE5lhnZxs/5wzZjD78cMP+VsSBMF6RKEzEa2lSxo04P6OaDEVG/vgfom2sH8/UKcO78DyIz17AikpzOAymtOngQMHgL59tY8dNoxZpadO6S+XFubNA3x8mH3rrDzyCEstrFkDzJ2rbewffwCvvgr06EHLaH6jZk1mdsfFAb17A6mpts81Zw4toe+8Y3vfT0EoyIhCZyK1amlX6JRiORGjOXwYeOIJ/ec9cCB/ulstVK9O6+M33xi/1qpVLJXSubP2sT170qq3cKH+clnL5cvAF1+wf6qzu1Z69QJGjgRGj2YpC2u4cAEIDgZKlwYWL9a//I+z0KQJa7Vt28b3+88/2udYsAD417/Yn/M//9FfRkEoCNit0Cml8P7776NSpUooVqwYWrVqhWMPqIA7ZcoUNG3aFF5eXihfvjyef/55nDx50l5RXA6LQmetG6duXcZ5GO12jY8HLl3S30J38yZlz88KHXDH7XrjhnFrKAWsXAl06wYUL659fNGiwODBtDwZKWdefPopa4sNH27O+lqZPp2Fjzt2ZMHZvDh/HmjZktbaH3+kUpefeeYZWnyPHgWeftr6Iug3bgCvvEKLcWgoXa75VfEVBKOxW6GbPn06Zs+ejbCwMERHR8PHxwft27dHUh5BRFFRUQgJCcH+/fsRERGB9PR0BAcH46YjfIlORK1aDJS2tkBn0aLAY48Zr9BZEiL0Vuiio4HMzIKh0N2+DXz7rXFrxMayGG+/frbPMXIkL6iLFuknl7UkJdF9OWSItvg/MylShK70gAAWm5069X4Xo1K0VAUF8ViPiqJbsiAQGEgLfKFCQKNGPL7Onct537Q0YPlynmO++gpYsoQKvihzgmAH9qTIZmZmKh8fHzV16tSsbbdv31be3t5q/vz5Vs9z+fJlBUBFWVkjIz+ULVGKRYIBpSIjrR/Tu7dSLVoYJ5NSSk2bppSXl/5p/JMmsdZTQSgPEBjIentGMWIES4/Ym9Y/cCB70Dq6PMCsWSwmam0dRmciJUWpCRNYc9Dbm5/hnDlKvfuuUo8/zt90ixau+d704NYt1ngrU4bFYjt0UGr8eKUWLVLqk0+UGjCAfYcBpTp3ZgknQRDsxy4L3dmzZxEfH4/g4OCsbZ6enmjZsiX27dtn9TwJ/6sHUCaXW/WUlBQkJibe88gP1KjBO1KtcXRHjtiWbWctsbFcR+80/r17ad0oCOUBXnoJiIgALl7Uf+7kZODLL9nj0t7Ys3HjGOvlyP6uqanA7Nm0Llap4rh19aJIEbYhOnqUVqiDB4E33mCcXJUq/N4jI13zvelB0aLAu+/S7fzRRzxGV68GXnuNLbeOH2ciT2wssGkTULu22RILQv7ArktrfHw8AKBChQr3bK9QoULWaw9CKYXRo0cjKCgI9XLpgDxlyhR4e3tnParkkzOlpydQtap2he76dfY3NAojEiIyMlieIihI33mdlV69+P1++aX+c69dy2Pg1Vftn6tuXdawmz6dLkJHsHQpwwzefNMx6xmFvz97sh47RiX14kW62du1E9chwISdESP4mZw7xz7UKSlUgGfONCaLXhAKMpoUupUrV6JkyZJZj7S0NACAW7azl1Lqvm25ERoaiiNHjmB1HiaCiRMnIiEhIevxp5HajIPRWrrEchI0Ko7u1i3g11/1P9kePcp6VYGB+s7rrJQqxVIVS5fqb01dsABo316/oqvjxlEp+e47febLi+RkKkF9+1KZzC+IAvdgPDzMlkAQ8jeaFLouXbogNjY261G2bFkAuM8ad/ny5fusdjkxYsQIbNq0CTt37kTlypVz3c/T0xOlSpW655FfqFVLW3HhypWZMWeUQnfsGC01eit0e/fS9ZJfCwrnxGuvsc7bjz/qN2dsLC2dQ4boN2dQEBXt994z3ko3Zw67CkhpCkEQBH3RpNB5eXmhVq1aWQ9/f3/4+PggIiIia5/U1FRERUUhICAg13mUUggNDcX69euxY8cO1KhRw/Z34OLUrs2LvrUXUjc3ul1jY42R5/Bhxrjl4v22mT17gMaNbSux4ao0b07F+JNP9JtzxgzWunv+ef3mdHNjxmZMDDMOjeLaNa4zdGjByfwUBEFwFHbF0Lm5uWHUqFGYPHkywsPDcfToUbz00ksoXrw4+t5Vvr5t27YICwvL+j8kJAQrVqzAqlWr4OXlhfj4eMTHx+PWrVv2iOOS+PnRzXn+vPVjGjUCDh0yRp7YWCqZeitee/cWHHerBTc3FkvdskWbWz03zp2jwvXGGywNoSdBQezW8PbbjHMygvffZ7mKd94xZn5BEISCjN35huPGjcOoUaMwfPhwNGnSBBcvXsS2bdvg5eWVtc/p06dx9a7uzfPmzUNCQgJatWqFihUrZj2+MtI84KTUqcPnX3+1fkyjRlQQ7GkWnhuHD+vvbj1/no+CkhBxN336sM7axx/bP9fHHzM27+WX7Z8rJ6ZModI4Z47+cx88CISFMX7OimgMQRAEQSNuShlZAMMYEhMT4e3tjYSEBJePp8vMBEqWZDPqN96wbsyxY3SJRkayGr1eKMX4vIkTgQkT9Jt39WoGwV++DJQrp9+8rsKHHzJm7MwZ9gW1hYsXmUDz5ptUioxixAgWeT12jK5dPUhPB5o147EeHa2/dVEQBEGQXq6m4+7O7g8nTlg/5rHHgGLFGPOkJ3/8wUxUIxIiatcumMocQCWpRAlawGzlgw/oBh8zRj+5cmLyZFoUhw3TLzv3k08YIrBwoShzgiAIRiEKnRNQp442ha5QISpdeit0lkQLvWvQ7dlTMN2tFkqVomVtwQKWb9HKiRPsufrOO5zLSLy8gHnzgK1bWXLFXn76iRbfN94oWBnOgiAIjkYUOidAq0IHMI7ul1/0lePwYVrRfHz0mzMhAYiLK9gKHQCMHs0SNUOGaCsNkpnJMTVqAK+/bpx8d/Pcc8DgwUBIyJ2+vrZw6RLQsyfw5JP2WScFQRCEByMKnRNQpw7w99+sz2UtjRszkeLmTf3kiI2l5U/PIqn79lEpKegKnacnXY4//URLnbV89hktnJ9/zjkcxdy5dO336MFjUyvp6UDv3vzuv/6a7bIEQRAE4xCFzgnw8+OzFitdo0aMcbLHgpIdI1p+RUYClSrROlXQad6cxYYnTGDtwQfx00/s4jBsmL7JL9ZQrBiwbh1jKtu0Aa5csX5sWhqTYPbupTJXqZJxcgqCIAhEFDonwNeXyRFaFDp/f1o99Iqju36dSRF6J0RERgKtWklrJAvTpzPTtW1b4OzZ3Pc7cYKuzyZN2ODcDB59lN/fpUtU6qxpz5yURKvehg3AN99QiRUEQRCMRxQ6J8DTkxdPLQpdkSJA/fqs76UHlni8Jk30mQ+gdeeXX6jQCaR0aWD7dn7nbdvmXHD4yBGgQwdatjZuBIoWdbycFvz9qdT9/Tf/XrAg9xjAXbto4d25k3Lr2c1CEARByBspIuAk+PlpKy4MMNg8MlKf9Q8eZD282rX1mQ+gyy0jQxS67FSqxP6urVtTSRo2jF00ihRhJ4j16xlXuWUL8NBDZkvLY/PwYWD8eMo6fz6VtaefBm7fpmV3zRq6iAMCgIgIae0lCILgaMRC5yTYkunarBmVQD06Rhw8yEQLdx2PCImfy51q1Zj9+957wPLlwIsvAt27U3GaNg3Yvx+oXNlsKe9QrhwLDu/ZA1SpwtpyHToAXbuyNl7RokB4OK10oswJgiA4Hpey0M2dOxdz585FRkaG2aLoTp06bLt08yaL0FpDs2ZMjIiOBtq1s2/9gwcZ+6QnEj+XNyVKsHfqW2/RPZ2QQGXJmT+vwEBg0ya6XU+fplW3QgV9bwQEQRAE7bjUaTgkJATHjx9HdHS02aLojqWnqxYrXe3agLc3cOCAfWtfvUq3mcTPmYObG7/HqlWdW5m7G3d3JvNUrCjKnCAIgjMgp2InoW5dXszj4qwf4+7O6vv2KnRGJERI/JwgCIIgOA5R6JyEkiWZ6aq1rlyzZlTo7Om7efAgLUSPPmr7HNmR+DlBEARBcByi0DkRjz9um0J3+TJw/rzt6x48SOucnu4+iZ8TBEEQBMchCp0T8fjjrEGmxdrWrBmf7XG7WhQ6vbh+XeLnBEEQBMGRiELnRDz+OPDPP8DFi9aPKV8eqF6dNcBs4dIl4MIFfRW6HTsYP9e+vX5zCoIgCIKQO6LQORENGvBZq9s1MJBJCLZgseyiJiGIAAAKkElEQVQ1bWrb+JzYto0ZuNWr6zenIAiCIAi5IwqdE1GtGpMTjhzRNq55c/Z0vXFD+5o//cTSE1Wrah+bE0oBW7cCwcH6zCcIgiAIwoMRhc6JcHOjlU6rha55c7o49+/Xvub+/WzhpFfywunTrGnXoYM+8wmCIAiC8GBEoXMybMl09fMDypRhWyYtpKezy8RTT2kblxfbtgGFC0tChCAIgiA4ElHonIwGDYBTp4Bbt6wf4+4OBAUBu3drW+voUbYae/ppbePyYts2NmgvWVK/OQVBEARByBtR6JyMxx9nn8xjx7SNa96c7tO0NOvH7N8PFCoENGqkba3cSEtjhqvEzwmCIAiCYxGFzsmoV48Wt0OHtI0LCgKSk7WN27+fCmTx4trWymu+pCRR6ARBEATB0YhC52QUL86+rgcPahvXqBFQrBgQFWX9mH379HW3bt0KPPywfhY/QRAEQRCsw6UUurlz58Lf3x9N9Sya5oQ0aaJdoStShG7XHTus2/+vv4DffuMYvdi8GXj2WVoYBUEQBEFwHC516Q0JCcHx48cRHR1ttiiG0qQJa9Hdvq1tXNu2wK5dQGrqg/e1JFDopdCdO8fs3C5d9JlPEARBEATrcSmFrqDQtClLimgtMNy2LePorKlHt3s34OvLosJ68O23LFci9ecEQRAEwfGIQueENGhAF6qlLZe1PPEE8NBDwI8/PnjfXbuAFi1sky8nNm0CWrcGSpXSb05BEARBEKxDFDonxNMTaNyYbbm04OFBpepBCt0//wBxcfq5WxMTgchIoHNnfeYTBEEQBEEbotA5KQEBzELVSvv2dLlev577Pnv3sueqXha6rVtZg04UOkEQBEEwB1HonJSAACYaXLyobdyzz7Kva0RE7vtERgKVKwPVq9sj4R02bWI9u2rV9JlPEARBEARtiELnpFjqw2l1u1arxjp2332X+z4REbTkubnZLp+F27ep0D3/vP1zCYIgCIJgG6LQOSkVKwI1atjmdu3UCfj+e7YQy058POPn2re3X0aA7tbERKB3b33mEwRBEARBO6LQOTEBAcCePdrHdewIXLoExMTc/9r27Xxu29Y+2SysWcOs3Dp19JlPEARBEATtiELnxLRsCfzyC5CQoG1cQABQujRdodmJiGC8W/ny9st38ybXePFF++cSBEEQBMF2RKFzYtq0odvU0tXBWgoXBrp2BdauvXe7Unfi5/Rg82YWMhZ3qyAIgiCYiyh0TkzNmkDVqtb3Z72bnj2BEyeAY8fubIuLYw9XvRS6NWuAJ5+knIIgCIIgmIcodE6MmxutdLYodO3bs2vDN9/c2RYezm2tWtkv299/M/FCrHOCIAiCYD6i0Dk5bdqw6f3ly9rGeXrS7ZpdoevUiW3F7OWLL+jCHTDA/rkEQRAEQbAPl1Lo5s6dC39/fzRt2tRsURxGcDCfv/9e+9iePYHjx+l2PXuWimG3bvbLlJkJzJ/P+cuVs38+QRAEQRDsw00ppcwWQiuJiYnw9vZGQkICShWAbvDNmjGW7m5rmzWkpACVKgEvv8zniROBK1cALy/75ImIoKK5ezcQFGTfXIIgCIIg2I9LWegKKs89xwK+qanaxnl6AgMHAsuWAevXA+3a2a/MAcC8eUC9ekBgoP1zCYIgCIJgP6LQuQDPPQckJQG7dmkf++qrtMrt3auPu/XiRdaeGzZMn9ZhgiAIgiDYjyh0LsATT7BHq1aXK8C+rtWr8+8uXeyXZfFioGhRSYYQBEEQBGdCFDoXwM0N6NuXCp1Wt6tSQEYGn7V2nMhOcjLdrf37s/yJIAiCIAjOgSh0LkLfvsC1a8C2bdrGxcQAf/4JeHsDM2bYJ8O8eaw/N26cffMIgiAIgqAvotC5CPXqAfXrA8uXaxu3eDHwyCPA2LGsHffXX7atf/MmMG0aMHiwdIYQBEEQBGdDFDoX4rXXmK164YJ1+1+7BqxcCbz0EjBiBGPfpk2zbe2wMOD6deDtt20bLwiCIAiCcYhC50IMGgQUL86ivtbwySdAWhqVOW9vYPx44LPPgN9+07bu+fPApEnMbK1WTbvcgiAIgiAYixQWdjFGjqTV7ezZvGvKJSRQ+Ro8GPjoI267dQvw82PW7IYN1pUdUQro3BmIjWXXiQL2cQuCIAiCS2C3hU4phffffx+VKlVCsWLF0KpVKxw7dszq8VOmTIGbmxtGjRplrygFgrFjgRs3gFmz8t5v1izg9u17ExiKFQNmz2YduRUrrFtv5Upgyxa6XEWZEwRBEATnxG6Fbvr06Zg9ezbCwsIQHR0NHx8ftG/fHklJSQ8cGx0djYULF6JBgwb2ilFgqFKFLtQZM4DTp3Pe58gRYOpUKn8VK977Wo8erCE3fDhw8mTea+3dy8LEAwYAzz+vj/yCIAiCIOiPXQqdUgoff/wx3n77bXTv3h316tXDsmXLkJycjFWrVuU59saNG+jXrx8WLVqEhx56yB4xChzvvgtUqEBFKzn53teuX2eduNq1gX//O+fxYWFUDNu1o+s2J44eBbp2ZR/ZRYv0lV8QBEEQBH2xS6E7e/Ys4uPjERwcnLXN09MTLVu2xL59+/IcGxISgk6dOqFdu3YPXCclJQWJiYn3PAoyXl50hR45ArRvz9ZeAPDrr8CzzzILdvVq9nLNiVKlgO3bmfXarBnw9ddAejpfS01lMkWTJkClSkB4eO7zCIIgCILgHNil0MXHxwMAKlSocM/2ChUqZL2WE2vWrEFMTAymTJli1TpTpkyBt7d31qNKlSq2C51PePppYMcOKnE+PsBjjwF16jAjdetW1qzLi0qVgD17gMBAoHdv4KGHqMR5ewOjRjGj9cABoEwZx7wfQRAEQRBsR5NCt3LlSpQsWTLrkZaWBgBwy5YuqZS6b5uFP//8EyNHjsSKFStQtGhRq9adOHEiEhISsh5//vmnFrHzLU8+SdfowoVA69bA0qXAmTNA06bWja9QgXXt9u8H3nqLfV8nTwYOHwY+/phJFIIgCIIgOD+aypYkJSXh0qVLWf+npKSgXr16iImJQcOGDbO2d+3aFaVLl8ayZcvum2PDhg3o1q0bPDw8srZlZGTAzc0N7u7uSElJuee1nCjIZUsEQRAEQRCyU0jLzl5eXvC6q/iZUgo+Pj6IiIjIUuhSU1MRFRWFabm0JGjbti3i4uLu2TZ48GD4+flh/PjxD1TmBEEQBEEQhHvRpNBlx1I/bvLkyfD19YWvry8mT56M4sWLo2/fvln7tW3bFt26dUNoaCi8vLxQr169e+YpUaIEHn744fu2C4IgCIIgCA/GLoUOAMaNG4dbt25h+PDhuHbtGpo1a4Zt27bdY8k7ffo0rl69au9SgiAIgiAIQg5I6y9BEARBEAQXx+5OEYIgCIIgCIK5iEInCIIgCILg4ohCJwiCIAiC4OKIQicIgiAIguDiuGRShFIKSUlJ8PLyyrUjhSAIgiAIQkHBJRU6QRAEQRAE4Q7ichUEQRAEQXBxRKETBEEQBEFwcUShEwRBEARBcHFEoRMEQRAEQXBxRKETBEEQBEFwcUShEwRBEARBcHFEoRMEQRAEQXBxRKETBEEQBEFwcUShEwRBEARBcHFEoRMEQRAEQXBx/h+varo/6lpGngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 2 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = sage.plot.graphics.Graphics()\n",
    "for i in range(2 ):\n",
    "    p += plot(bessel_J(0, (2+0.5*i)*x),(x,0,4*pi))\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\epsilon_{z_{z}} \\mu \\omega^{2} E_{z}\\left({\\rho}, {\\phi}, z\\right)}{c^{2}} + \\frac{\\frac{\\partial\\,E_{z}}{\\partial {\\rho}}}{{\\rho}} + \\frac{\\frac{\\partial^2\\,E_{z}}{\\partial {\\phi} ^ 2}}{{\\rho}^{2}} + \\frac{\\partial^2\\,E_{z}}{\\partial {\\rho} ^ 2} + \\frac{\\partial^2\\,E_{z}}{\\partial z ^ 2}</script></html>"
      ],
      "text/plain": [
       "epsilon_z_z*mu*omega^2*E_z(rh, ph, z)/c^2 + d(E_z)/drh/rh + d^2(E_z)/dph^2/rh^2 + d^2(E_z)/drh^2 + d^2(E_z)/dz^2"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_z = eq_z.subs()\n",
    "\n",
    "eq_z.subs(epsilon_z_z * mu * omega^2 / c^2 == kappa_z^2 + k^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 4 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = sage.plot.graphics.Graphics()\n",
    "for i in range(4):\n",
    "    p += plot(bessel_J(i, x).diff(x),(x,0,4*pi))\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$-\\frac{1}{2} \\, J_{2}(x) + \\frac{1}{2} \\, J_{0}(x)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Math(latex(bessel_J(1, x).diff(x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$-\\frac{1}{2} \\, J_{1}(x) + \\frac{1}{2} \\, J_{-1}(x)$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Math(latex(bessel_J(0, x).diff(x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 9.0",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}