Presentacion.ipynb

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   "source": [
    "![Titulo](Imagenes/Logo.png)\n",
    "# Uso de Python, Numpy y Sympy en la Docencia del Método de los Elementos Finitos"
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   "source": [
    "## Presentación"
   ]
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    "En los últimos años he sido profesor de la materia de Elementos Finitos. \n",
    "Esta charla supone ser una recopilación de experiencias y lecciones aprendidas \n",
    "en el uso de Python y las librerías NumPy y SymPy en este curso. Consdiero que \n",
    "lo aprendido puede servir para la utilización de estas librerías en otros temas."
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   "source": [
    "Vale la pena decir que el utilizar estas liberías para enseñar el MEF es un reto\n",
    "doble, pues hay algunos estudiantes que no tienen mucha experiencia programando \n",
    "(aunque todos han tomado cursos usando Python). Sin embargo, la aplicación actual \n",
    "y eficiente del MEF implica necesariamente el uso de software."
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   "source": [
    "## Introducción al Método de los Elementos Finitos"
   ]
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   "source": [
    "El MEF es un método numérico que nos permite obtener una solución aproximada \n",
    "a una ecuación diferencial. Por ejemplo:\n",
    "\n",
    "$$-K \\frac {d^2 T} {dx^2} = Q $$\n",
    "\n",
    "Ecuación de transferencia de calor en sólidos (conducción). "
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    "Terminología y significado de las variables utilizadas:\n",
    "\n",
    "* $x$ y $y$ forman el sistema de coordenadas donde está definido el problema.\n",
    "* $L$ es la longitud de la barra (es decir, el **dominio** está definido de $x=0$ a $x=L$)\n",
    "* $T(x)$ es la **temperatura** de la barra. Su valor para cada parte del dominio es lo que queremos obtener.\n",
    "* $Q$ representa la **generación** de calor en la barra. Normalmente asociado a una unidad de volumen.\n",
    "* $K$ es la **constante de conductividad térmica**$^*$. Es una relación de cuanto se puede mover el calor (energía) dada una diferencia de temperatura. Su valor siempre es negativo, indicando que el calor siempre se mueve del punto más caliente a uno más frío.\n",
    "\n",
    "$^*$ No en todos los materiales/condiciones $K$ es constante. Se estudia este caso inicialmente para poder obtener una solución de manera sencilla."
   ]
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   "source": [
    "![Fig1](Imagenes/Fig1.png)"
   ]
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    "__Condiciones de frontera__:\n",
    "\n",
    "Para poder conocer la solución de este sistema, es necesario saber que ocurre\n",
    "en los límites del dominio (en la frontera):\n",
    "\n",
    "$$ \\frac {d} {dx} T(x)\\Big{|}_{x=0} = - \\frac {q} {K} $$\n",
    "\n",
    "$$T(x)\\Big{|}_{x=L} = T_L$$"
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    "Terminología y significado de las variables utilizadas:\n",
    "\n",
    "* $q$ representa un **flujo con valor establecido** en la **frontera** de la barra ($x=0$), dato conocido.\n",
    "* $T_L$ representa __la temperatura__ en $x=L$, dato conocido.\n",
    "\n",
    "$^*$ No en todos los materiales/condiciones $K$ es constante. Se estudia este caso inicialmente para poder obtener una solución de manera sencilla."
   ]
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    "El MEF inicia por __proponer__ una solución, del tipo:\n",
    "\n",
    "$$T(x) \\approx T_1 N_1 (x) + T_2 N_2 (x) + ... + T_{n+1} N_{n+1} (x) $$"
   ]
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   "source": [
    "$$T(x) \\approx \\sum_{i=0}^{n+1} T_i N_i (x) $$"
   ]
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   "source": [
    "Normalmente esto __no nos va permitir obtener una solución exacta__, por lo que tendremos que en nuestra ecuación diferencial original:\n",
    "\n",
    "$$-K \\frac {d^2 T} {dx^2} - Q \\neq 0$$\n",
    "\n",
    "Tendremos una diferencia o __residual__ ($R(T, x)$):\n",
    "\n",
    "$$R(T, x) = -K \\frac {d^2 T} {dx^2} - Q $$"
   ]
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    "Como T no es la solución exacta, no podemos forzar el residual a desaparecer en todo punto $x$, sin importar que tan pequeña hagamos la malla. La idea de los _residuos ponderados_ es que podemos multiplicar los residuos por una \"ponderación\" (o peso) y forzar la ecuación a volverse cero. Es decir:\n",
    "\n",
    "$$\\int_0^L W(x)R(T, x)dx=0$$\n",
    "\n",
    "Donde $W(x)$ es una función de ponderación. Seleccionando funciones para $W(x)$ reemplazando las en esta ecuación podemos generar varios sistemas de ecuaciones dependientes de los parámetros $a_i$ que van a determinar una aproximación $T$ en la forma de sumas finitas. Esta solución va a satisfacer la ecuación diferencial en \"promedio\" o como una \"integral\". "
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    "El tipo de función seleccionada para $W(x)$, depende del tipo de técnica de residuales seleccionado. En el procedimiento de Galerkin, los pesos son establecidos como la misma función de peso $N(x)$, de tal manera que:\n",
    "\n",
    "$$W_i(x)=N_i(x)$$\n",
    "\n",
    "y\n",
    "\n",
    "\n",
    "$$\\int_0^L N(x)R(T, x)dx=0$$"
   ]
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    "Substituyendo el residual:\n",
    "\n",
    "\n",
    "$$\\int_0^L N(x)\\left[ -K \\frac {d^2 T} {dx^2} - Q \\right]dx=0$$"
   ]
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   "source": [
    "![Fig2](Imagenes/Fig2.png)"
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   "source": [
    "Usar funciones lineales para $N_i(x)$ parece una buena idea.. pero las funciones lineales:\n",
    "\n",
    "$$\\frac {d^2 N_i(x)T_i} {dx^2} = 0$$"
   ]
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   "source": [
    "Para poder resolver esta dificultad utilizamos la integración por partes para el primer termino de la suma, usando:\n",
    "\n",
    "$$ \\int u \\cdot dv = u \\cdot v - \\int v \\cdot du $$\n",
    "\n",
    "$$ u = N(x) $$\n",
    "\n",
    "$$ dv = \\frac {d^2 T} {dx^2} $$\n",
    "\n",
    "$$\\int_0^L N(x)\\left[ -K \\frac {d^2 T} {dx^2}  \\right]dx= - KN \\dfrac {dT}{dx}\\Big|_0^L + \\int_0^L K \\frac {dN}{dx} \\frac{dT}{dx} dx $$"
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    "De manera que la ecuación queda:\n",
    "\n",
    "$$\\int_0^L K \\frac {dN}{dx} \\frac{dT}{dx} dx -\\int_0^L N(x)Q dx - KN\\dfrac {dT}{dx}\\Big|_0^L = 0$$\n",
    "\n",
    "Esto se conoce como la formulación _\"débil\"_ (_\"weak\"_ formulation) ya que la necesidad de la existencia de la segunda derivada se a \"relajado\": ya no es necesario que exista, ni que esté definida en todos los puntos."
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   "source": [
    "Las $N_i$, usando funciones lineales, quedaría algo así:\n",
    "\n",
    "![Fig3](Imagenes/Fig3.png)"
   ]
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   "source": [
    "El MEF aprovecha esta estructura __realizando la integración por elemento__ siendo que las funciones están definidas para cada elemento y las funciones solo interactuan dentro de los cada elemento:\n",
    "\n",
    "$$\\sum_{j=1}^{n+1}\\left[\\int_0^{h^{(e)}} K \\frac {dN_i}{dx} \\frac{dN_j}{dx}T_j dx -\\int_0^{h^{(e)}} N_i Q dx - KN_i \\dfrac {dT}{dx}\\Big|_{x_i}^{x_{i+1}} = 0\\right]$$\n",
    "\n",
    "Donde $h^{(e)}$ es el tamaño del elemento y $i = 1, 2, ..., n+1$. "
   ]
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    "Es común __modificar los límites de integración__ para no tener que definir las funciones de forma para cada elemento, siendo útiles definiciones como:\n",
    "\n",
    "$$N_1^{(e)} = 1-\\frac {x} {{h^{(e)}}}$$\n",
    "\n",
    "$$N_2^{(e)} = \\frac {x} {{h^{(e)}}}$$"
   ]
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    "Esto permite que el comportamiento de los diferentes elementos se \"sumen\" en el proceso que se conoce como __ensamble__ de la matriz del sistema."
   ]
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   "source": [
    "## Uso de SymPy"
   ]
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   "source": [
    "> SymPy es una biblioteca de Python para matemáticas simbólicas. \n",
    "> Su propósito es llegar a ser un sistema de álgebra por computadora (CAS) \n",
    "> completo manteniendo el código tan simple como sea posible para poder ser \n",
    "> legible y extensible de manera fácil. SymPy está escrito en Python enteramente. \n",
    ">\n",
    "> -- <cite>https://www.sympy.org/en/index.html</cite>"
   ]
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   "source": [
    "¿Cómo me puede ayudar para obtener esta integral?\n",
    "\n",
    "$$\\int_0^{h_e} K \\frac {dN_i}{dx} \\frac{dN_j}{dx} dx$$"
   ]
  },
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   "source": [
    "# Aquí vamos!!\n",
    "import sympy as sp"
   ]
  },
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   "source": [
    "__SymPy__ se apoya en varias librerías para dar la mejor presentación. Si __miketex__ (disponible en anaconda) está instalado permite una representación basada en __LaTeX__ (https://www.latex-project.org/). Esta representación está disponible automáticamente en Jupyter, pero para poder aprovechar esta representación en otros sitemas (por ejemplo Spyder) es necesario importar:"
   ]
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   "source": [
    "from IPython.display import display as pp # pretty print"
   ]
  },
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   "source": [
    "![Spyder](Imagenes/Spyder.png)"
   ]
  },
  {
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   "source": [
    "El primer paso es declarar los simbolos que utilizaremos. SymPy reconoce automáticamente la escritura de simbolos de LaTeX:"
   ]
  },
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle h^{(e)}$"
      ],
      "text/plain": [
       "h^{(e)}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = sp.Symbol('x')\n",
    "he = sp.Symbol('h^{(e)}')\n",
    "pp(x, he)"
   ]
  },
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   "source": [
    "__PARENTESIS__: Esto presenta lo que para mi es la __primera dificultad__ para explicar el uso de SymPy:\n",
    "* Los estudiantes deben de entender que lo que está a la __derecha__ es un símbolo algebraico, mientras que lo que está a la __izquierda__ es una variable de Python."
   ]
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   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{3}$"
      ],
      "text/plain": [
       "x**3"
      ]
     },
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    }
   ],
   "source": [
    "y = x ** 3 # Doble asterisco (**) es utilizado como potencia, x**3 = x³\n",
    "pp(y)"
   ]
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   "source": [
    "![Fig3](Imagenes/TutSympy.png)"
   ]
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   "source": [
    "(en realidad, las dos son __objetos__ de sympy...)"
   ]
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   "source": [
    "* Nada nos impide hacer cosas que pudieran no tener mucho sentido:"
   ]
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle b$"
      ],
      "text/plain": [
       "b"
      ]
     },
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     "data": {
      "text/latex": [
       "$\\displaystyle a$"
      ],
      "text/plain": [
       "a"
      ]
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    }
   ],
   "source": [
    "a = sp.Symbol('b')\n",
    "b = sp.Symbol('a')\n",
    "pp(a,b)"
   ]
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   "source": [
    "Por lo que esta diferenciación es básica y debe quedar clara para que la utilización de la librería sea posible. \n",
    "\n",
    "__FIN PARENTESIS__"
   ]
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   "source": [
    "Declaramos las funciones de forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b0c8474e-d9fd-410e-b39a-298de3da2729",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1 - \\frac{x}{h^{(e)}}$"
      ],
      "text/plain": [
       "1 - x/h^{(e)}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x}{h^{(e)}}$"
      ],
      "text/plain": [
       "x/h^{(e)}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N1 = 1-x/he\n",
    "\n",
    "N2 = x/he\n",
    "\n",
    "pp(N1, N2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "537dab18-9879-458b-a475-378a11e1da24",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = sp.plotting.plot(N1.subs(he,1), N2.subs(he,1), (x, 0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27fe312b-d20c-4b2c-b618-658de3661575",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Las acomodamos en un vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "356c66ed-61c8-4cb4-a0bb-13aca630fb6a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 - \\frac{x}{h^{(e)}}\\\\\\frac{x}{h^{(e)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1 - x/h^{(e)}],\n",
       "[    x/h^{(e)}]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = sp.Matrix([N1, N2])\n",
    "pp(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c09821e-957c-4ffb-8c73-ced08db176e0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Las derivamos usando:\n",
    "\n",
    "$\\frac {d} {dx} F$ -> `sp.diff(F, x)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4fb34a99-4cef-4ac9-a103-2edfd728113b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{1}{h^{(e)}}\\\\\\frac{1}{h^{(e)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-1/h^{(e)}],\n",
       "[ 1/h^{(e)}]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dN = sp.diff(N, x)\n",
    "pp(dN)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704ae3d7-a78c-4ab9-b8fb-9e9ee8595f6a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "La expresión:\n",
    "$$\\int_0^{h^{(e)}} K \\frac {dN_i}{dx} \\frac{dN_j}{dx} dx$$\n",
    "quedaría:\n",
    "$$ \\int_0^{h^{(e)}} K \\left[ \\frac {d}{dx}N \\right] ^T \\left[ \\frac {d}{dx}N \\right] dx $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d6cafe8-2bab-4e06-b1a9-fb9c5f0b7c93",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Integramos usando:\n",
    "\n",
    "$\\int_a^b F dx$ -> `sp.integrate(F, (x,a,b))`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1d2990d3-fbb1-485c-8497-d20a05bc4485",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{K}{h^{(e)}} & - \\frac{K}{h^{(e)}}\\\\- \\frac{K}{h^{(e)}} & \\frac{K}{h^{(e)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ K/h^{(e)}, -K/h^{(e)}],\n",
       "[-K/h^{(e)},  K/h^{(e)}]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = sp.Symbol('K')\n",
    "\n",
    "MatrizK = sp.integrate(K*dN*dN.T, (x,0,he))\n",
    "pp(MatrizK)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9253ef0-9029-46b9-b8d7-82fa73929e53",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Que coincide con la expresión que se encuentra en la bibliografia:\n",
    "\n",
    "\n",
    "$$ \\frac {K} {h^{(e)}} \\begin{bmatrix} 1 & -1 \\\\ -1 & 1 \\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77e6ad1e-fef2-4080-886d-209715d73133",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Esta solución puede parecer simple o poco interesante, pero la aplicación a funciones de forma cuadráticas empieza a demostrar su utilidad:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cfdadfa1-60b9-45c5-ac67-43afa79da854",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1 - \\frac{3 x}{h^{(e)}} + \\frac{2 x^{2}}{\\left(h^{(e)}\\right)^{2}}$"
      ],
      "text/plain": [
       "1 - 3*x/h^{(e)} + 2*x**2/h^{(e)}**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{4 x}{h^{(e)}} - \\frac{4 x^{2}}{\\left(h^{(e)}\\right)^{2}}$"
      ],
      "text/plain": [
       "4*x/h^{(e)} - 4*x**2/h^{(e)}**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{x}{h^{(e)}} + \\frac{2 x^{2}}{\\left(h^{(e)}\\right)^{2}}$"
      ],
      "text/plain": [
       "-x/h^{(e)} + 2*x**2/h^{(e)}**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N1 = 1 - 3*x/he + 2*x**2/he**2\n",
    "N2 = 4*x/he - 4*x**2/he**2\n",
    "N3 = -1*x/he + 2*x**2/he**2\n",
    "\n",
    "pp(N1, N2, N3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "547672f3-2c12-4898-bafd-9dcab561b3f9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = sp.plotting.plot(N1.subs(he,1), N2.subs(he,1), N3.subs(he,1), (x, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a6f68ab4-1c8e-4587-9b8b-644c348794d4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 - \\frac{3 x}{h^{(e)}} + \\frac{2 x^{2}}{\\left(h^{(e)}\\right)^{2}}\\\\\\frac{4 x}{h^{(e)}} - \\frac{4 x^{2}}{\\left(h^{(e)}\\right)^{2}}\\\\- \\frac{x}{h^{(e)}} + \\frac{2 x^{2}}{\\left(h^{(e)}\\right)^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1 - 3*x/h^{(e)} + 2*x**2/h^{(e)}**2],\n",
       "[    4*x/h^{(e)} - 4*x**2/h^{(e)}**2],\n",
       "[     -x/h^{(e)} + 2*x**2/h^{(e)}**2]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = sp.Matrix([N1, N2, N3])\n",
    "pp(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8e78c931-e857-4963-a2d7-7721622b3eb2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{3}{h^{(e)}} + \\frac{4 x}{\\left(h^{(e)}\\right)^{2}}\\\\\\frac{4}{h^{(e)}} - \\frac{8 x}{\\left(h^{(e)}\\right)^{2}}\\\\- \\frac{1}{h^{(e)}} + \\frac{4 x}{\\left(h^{(e)}\\right)^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-3/h^{(e)} + 4*x/h^{(e)}**2],\n",
       "[ 4/h^{(e)} - 8*x/h^{(e)}**2],\n",
       "[-1/h^{(e)} + 4*x/h^{(e)}**2]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dN = sp.diff(N, x)\n",
    "pp(dN)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f90293f0-9711-4d7e-9e18-37791bdd169b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Nuevamente, la expresión:\n",
    "$$ \\int_0^{h^{(e)}} K \\left[ \\frac {d}{dx}N \\right] ^T \\left[ \\frac {d}{dx}N \\right] dx $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f7064837-ac34-4f2a-af98-33fdad579e7a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{7 K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}} & \\frac{K}{3 h^{(e)}}\\\\- \\frac{8 K}{3 h^{(e)}} & \\frac{16 K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}}\\\\\\frac{K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}} & \\frac{7 K}{3 h^{(e)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 7*K/(3*h^{(e)}), -8*K/(3*h^{(e)}),    K/(3*h^{(e)})],\n",
       "[-8*K/(3*h^{(e)}), 16*K/(3*h^{(e)}), -8*K/(3*h^{(e)})],\n",
       "[   K/(3*h^{(e)}), -8*K/(3*h^{(e)}),  7*K/(3*h^{(e)})]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MatrizK = sp.integrate(K*dN*dN.T, (x,0,he))\n",
    "pp(MatrizK)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3b908ba-0319-4057-b60b-18a8a4f9927f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "La integral que contiene los términos de generación $Q$:\n",
    "\n",
    "$$\\int_0^{h^{(e)}} N_i Q dx $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9565355e-ee71-424e-aa37-4e44871023c0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{Q h^{(e)}}{6}\\\\\\frac{2 Q h^{(e)}}{3}\\\\\\frac{Q h^{(e)}}{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  Q*h^{(e)}/6],\n",
       "[2*Q*h^{(e)}/3],\n",
       "[  Q*h^{(e)}/6]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q = sp.Symbol('Q')\n",
    "\n",
    "VectorQ = sp.integrate(N*Q, (x,0,he))\n",
    "pp(VectorQ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f70f8b9-96e2-43f3-91e5-6961e56d0c03",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "La última parte representa, en realidad, el flujo en la frontera del elemento:\n",
    "\n",
    "$$KN_i \\dfrac {dT}{dx}\\Big|_{x_i}^{x_{i+1}} = \\begin{bmatrix}  K \\dfrac {dT}{dx}\\Big|_{x_i} \\\\ K \\dfrac {dT}{dx}\\Big|_{x_{i+1}}  \\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2daa252a-77d2-45ca-b37b-c3b1ce6c638a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Por lo que, para este problema, quedaría:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ed6497b1-86ab-4e3e-9942-8ea2dcec0a6a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}q_{1}\\\\0\\\\q_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[q_1],\n",
       "[  0],\n",
       "[q_3]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q1 = sp.Symbol('q_1')\n",
    "q3 = sp.Symbol('q_3')\n",
    "\n",
    "Vectorq = sp.Matrix([q1,0,q3])\n",
    "pp(Vectorq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98103211-5f2a-47f6-bb16-cfe8cfca12c3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Así, la expresión integral, usando elementos cuadráticos se convierte en:\n",
    "\n",
    "$$\\begin{bmatrix}\\frac{7 K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}} & \\frac{K}{3 h^{(e)}}\\\\- \\frac{8 K}{3 h^{(e)}} & \\frac{16 K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}}\\\\\\frac{K}{3 h^{(e)}} & - \\frac{8 K}{3 h^{(e)}} & \\frac{7 K}{3 h^{(e)}}\\end{bmatrix}\\begin{bmatrix}T_1 \\\\ T_2 \\\\ T_3\\end{bmatrix} = \\begin{bmatrix}\\frac{Q h^{(e)}}{6} \\\\ \\frac{2 Q h^{(e)}}{3}\\\\\\frac{Q h^{(e)}}{6}\\end{bmatrix} + \\begin{bmatrix}q \\\\ 0\\\\0\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cee5c8e-b3ae-4212-86ab-d2f53089224c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Declaramos las incognitas como simbolos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7efc85a6-2738-436b-80fe-f7d6964afd68",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "T1, T2, T3 = sp.symbols('T_1, T_2, T_3')\n",
    "T = sp.Matrix([T1, T2, T3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6a0a40f8-1901-4647-b5bf-7d7f4597bd49",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{7 K T_{1}}{3 h^{(e)}} - \\frac{8 K T_{2}}{3 h^{(e)}} + \\frac{K T_{3}}{3 h^{(e)}} - \\frac{Q h^{(e)}}{6} - q_{1}\\\\- \\frac{8 K T_{1}}{3 h^{(e)}} + \\frac{16 K T_{2}}{3 h^{(e)}} - \\frac{8 K T_{3}}{3 h^{(e)}} - \\frac{2 Q h^{(e)}}{3}\\\\\\frac{K T_{1}}{3 h^{(e)}} - \\frac{8 K T_{2}}{3 h^{(e)}} + \\frac{7 K T_{3}}{3 h^{(e)}} - \\frac{Q h^{(e)}}{6} - q_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[7*K*T_1/(3*h^{(e)}) - 8*K*T_2/(3*h^{(e)}) + K*T_3/(3*h^{(e)}) - Q*h^{(e)}/6 - q_1],\n",
       "[-8*K*T_1/(3*h^{(e)}) + 16*K*T_2/(3*h^{(e)}) - 8*K*T_3/(3*h^{(e)}) - 2*Q*h^{(e)}/3],\n",
       "[K*T_1/(3*h^{(e)}) - 8*K*T_2/(3*h^{(e)}) + 7*K*T_3/(3*h^{(e)}) - Q*h^{(e)}/6 - q_3]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sistema = MatrizK * T - VectorQ - Vectorq\n",
    "pp(sistema)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a5235e7-efed-4834-9345-30a90d0d539f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Substituimos los valores para este caso en particular:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "29c6768d-1481-4d2b-80cb-6fcb9c49c4d9",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{7 K T_{1}}{3 L} - \\frac{8 K T_{2}}{3 L} + \\frac{K T_{L}}{3 L} - \\frac{L Q}{6} - q_{1}\\\\- \\frac{8 K T_{1}}{3 L} + \\frac{16 K T_{2}}{3 L} - \\frac{8 K T_{L}}{3 L} - \\frac{2 L Q}{3}\\\\\\frac{K T_{1}}{3 L} - \\frac{8 K T_{2}}{3 L} + \\frac{7 K T_{L}}{3 L} - \\frac{L Q}{6} - q_{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[7*K*T_1/(3*L) - 8*K*T_2/(3*L) + K*T_L/(3*L) - L*Q/6 - q_1],\n",
       "[-8*K*T_1/(3*L) + 16*K*T_2/(3*L) - 8*K*T_L/(3*L) - 2*L*Q/3],\n",
       "[K*T_1/(3*L) - 8*K*T_2/(3*L) + 7*K*T_L/(3*L) - L*Q/6 - q_3]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L, TL = sp.symbols('L, T_L')\n",
    "\n",
    "sistema = sistema.subs(he, L).subs(T3,TL)\n",
    "pp(sistema)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4050e454-f6d5-47e9-8995-47fab0b57248",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Y resolvemos algebraicamente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c0c207bd-d44a-437c-b14e-c0df752fbd96",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{T_1: (2*K*T_L + L**2*Q + 2*L*q_1)/(2*K),\n",
       " T_2: (8*K*T_L + 3*L**2*Q + 4*L*q_1)/(8*K),\n",
       " q_3: -L*Q - q_1}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solucion = sp.solve(sistema, (T1,T2,q3))\n",
    "pp(solucion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "27727d11-e7fe-4c26-aaa5-8224d8f48b08",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 K T_{L} + L^{2} Q + 2 L q_{1}}{2 K}$"
      ],
      "text/plain": [
       "(2*K*T_L + L**2*Q + 2*L*q_1)/(2*K)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{8 K T_{L} + 3 L^{2} Q + 4 L q_{1}}{8 K}$"
      ],
      "text/plain": [
       "(8*K*T_L + 3*L**2*Q + 4*L*q_1)/(8*K)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - L Q - q_{1}$"
      ],
      "text/plain": [
       "-L*Q - q_1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp(solucion[T1],solucion[T2],solucion[q3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c1777a2-d4db-4374-b640-bafab206564f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "La solución analítica de este problema es:\n",
    "\n",
    "$$ T(x) = T_L + \\frac {Q}{2K} (L^2 - x^2) + \\frac {q_1}{K}(L-x) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "206d4c76-7602-46b7-b12f-3fbdc00adc73",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{L} + \\frac{Q \\left(L^{2} - x^{2}\\right)}{2 K} + \\frac{q_{1} \\left(L - x\\right)}{K}$"
      ],
      "text/plain": [
       "T_L + Q*(L**2 - x**2)/(2*K) + q_1*(L - x)/K"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solucion_analitica = TL + Q/(2*K) *(L**2 - x**2) + q1/K*(L-x)\n",
    "pp(solucion_analitica)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1e5d01-05ee-4772-8c16-4a0281570847",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Substituyendo $x=0$ y $x=L/2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8ab098e6-9762-4582-af2e-b00a0e38f2da",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{L} + \\frac{L^{2} Q}{2 K} + \\frac{L q_{1}}{K}$"
      ],
      "text/plain": [
       "T_L + L**2*Q/(2*K) + L*q_1/K"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solucion_analitica.subs(x,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1c8adf69-64ca-46ac-a885-10a720636bee",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{L} + \\frac{3 L^{2} Q}{8 K} + \\frac{L q_{1}}{2 K}$"
      ],
      "text/plain": [
       "T_L + 3*L**2*Q/(8*K) + L*q_1/(2*K)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solucion_analitica.subs(x,L/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a02b211c-d727-4ab9-8867-f00aacd94572",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 K T_{L} + L^{2} Q + 2 L q_{1}}{2 K}$"
      ],
      "text/plain": [
       "(2*K*T_L + L**2*Q + 2*L*q_1)/(2*K)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{8 K T_{L} + 3 L^{2} Q + 4 L q_{1}}{8 K}$"
      ],
      "text/plain": [
       "(8*K*T_L + 3*L**2*Q + 4*L*q_1)/(8*K)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp(solucion[T1],solucion[T2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ab25694-5568-4b66-8521-eda77430dbe8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Uso de NumPy:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7e93bf6-2cfb-4ff3-adbc-9ab07fb28122",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "> NumPy is the fundamental package for scientific computing in Python. \n",
    "> It is a Python library that provides a multidimensional array object, \n",
    "> various derived objects (such as masked arrays and matrices), and an \n",
    "> assortment of routines for fast operations on arrays, including \n",
    "> mathematical, logical, shape manipulation, sorting, selecting, \n",
    "> I/O, discrete Fourier transforms, basic linear algebra, basic \n",
    "> statistical operations, random simulation and much more..\n",
    ">\n",
    "> -- <cite>https://numpy.org/doc/stable/user/whatisnumpy.html</cite>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "03248cb6-842d-44ea-821e-d914ea42ac6a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44ea8f8d-9a55-428d-98ad-63d55370d39b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "__NumPy__ es la librería ideal para resolver los problemas de forma numérica, es decir, para usar el MEF con todo su potencial. Sin embargo su utilización también presenta algunos retos para los alumnos que no son expertos en programación. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "334086a9-da73-40d1-a49b-b23c793f9519",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Resolveremos, a manera de ejmplo, el ejercicio anterior, pero ahora utilizando elementos triangulares (dominio 2D, plano) con los siguientes datos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "52882b9f-d3d0-4ac7-9199-78a6b039cf53",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "L = 3 # m\n",
    "k = 50 # W/m°C\n",
    "q = 25 # W/m²\n",
    "Q = 40 # W/m³\n",
    "TL = 300 # °C"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2245c38e-dc1d-4dec-9a97-950e9526a872",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "source": [
    "Substituyendo estos valores en la solución anterior se obtiene:\n",
    "\n",
    "$$T_1 = 305.10 \\,^oC$$\n",
    "$$T_2 = 303.45 \\,^oC$$\n",
    "$$T_3 = T_L = 300.00 \\,^oC$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e446f8a-e0ca-41db-b4c6-33b7b7910d3d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Al no exigirles el uso de una herramienta en específico los alumnos, usando una\n",
    "hoja de cálculo, hacen esto:\n",
    "![hoja](Imagenes/HojaCalculo.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03fa872b-bf93-4782-a8f7-59916a5069fc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "__Eureka__: tenemos un diccionario. \n",
    "\n",
    "La propuesta es, entonces, trabajar con una\n",
    "__lista de diccionarios__, donde cada diccionario es un elemento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "341cb474-16f1-46fb-9698-964b1534f4e1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "elementos = []\n",
    "elementos.append({'x': np.array([0. , 0. , L/2]),\n",
    "                  'y': np.array([0. , L/2, 0. ]),\n",
    "                  'n': [0, 3, 1]})\n",
    "elementos.append({'x': np.array([0. , L/2, L/2]),\n",
    "                  'y': np.array([L/2, L/2, 0. ]),\n",
    "                  'n': [3, 4, 1]})\n",
    "elementos.append({'x': np.array([L/2, L/2, L  ]),\n",
    "                  'y': np.array([0. , L/2, 0. ]),\n",
    "                  'n': [1, 4, 2]})\n",
    "elementos.append({'x': np.array([L/2, L  , L  ]),\n",
    "                  'y': np.array([L/2, L/2, 0. ]),\n",
    "                  'n': [4, 5, 2]})\n",
    "elementos.append({'x': np.array([0. , 0. , L/2]),\n",
    "                  'y': np.array([L/2, L  , L  ]),\n",
    "                  'n': [3, 6, 7]})\n",
    "elementos.append({'x': np.array([0. , L/2, L/2]),\n",
    "                  'y': np.array([L/2, L  , L/2]),\n",
    "                  'n': [3, 7, 4]})\n",
    "elementos.append({'x': np.array([L/2, L/2, L  ]),\n",
    "                  'y': np.array([L/2, L  , L  ]),\n",
    "                  'n': [4, 7, 8]})\n",
    "elementos.append({'x': np.array([L/2, L  , L  ]),\n",
    "                  'y': np.array([L/2, L  , L/2]),\n",
    "                  'n': [4, 8, 5]})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39f607fd-9830-41f2-b8f9-298a54a672a9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Una representación gráfica ayuda para entender mejor lo anterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b5dcc34a-66ec-4c5b-92cd-e405bae21b1a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "for i, e in enumerate(elementos):\n",
    "    plt.fill(e['x'],e['y'], alpha=0.6)\n",
    "    x = np.array(e['x']).mean()\n",
    "    y = np.array(e['y']).mean()\n",
    "    plt.text(x,y,i, ha='center', va='center')\n",
    "    for x, y, n in zip(e['x'],e['y'],e['n']):\n",
    "         plt.text(x,y,\"{}\".format(n), va='center', ha='center', bbox= dict(boxstyle='round', facecolor='yellow'))\n",
    "plt.axis('equal')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b00174a-a90f-4ca8-ad3a-9441baf5e507",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Con un ciclo for, podemos ir actualizando y los diccionarios. Por ejemplo, para \n",
    "la matriz $\\mathbf{K}$ , hacemos:\n",
    "\n",
    "$$\\mathbf{K} = \\left[ k_{ij} \\right] = \\left[ \\int\\limits_{\\Omega} K \\left( \\dfrac {\\partial N_i} {\\partial x} \\dfrac {\\partial N_j} {\\partial x} + \\dfrac {\\partial N_i} {\\partial y} \\dfrac {\\partial N_j} {\\partial y}\\right) d\\Omega \\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68e10bf3-afad-4cce-a748-e451e10f4fe3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "No entraré en detalle, pero de esta integración se obtiene:\n",
    "\n",
    "$$\\mathbf{K}^{(e)}= \\dfrac {K} {4 A^{(e)}} \\begin{bmatrix} b_1b_1+c_1c_1 & b_1b_2+c_1c_2 & b_1b_3+c_1c_3 \\\\ b_2b_1+c_2c_1 & b_2b_2+c_2c_2 & b_2b_3+c_2c_3 \\\\ b_3b_1+c_3c_1 & b_3b_2+c_3c_2 & b_3b_3+c_3c_3 \\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "607bb5fe-ffba-481a-a332-b5721736560f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Donde:\n",
    "\n",
    "|$i$|$b_i$|$c_i$|\n",
    "|:---:|:-----:|:-----:|\n",
    "|$1$|$y_2-y_3$|$x_3-x_2$|\n",
    "|$2$|$y_3-y_1$|$x_1-x_3$|\n",
    "|$3$|$y_1-y_2$|$x_2-x_1$|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "24154720-ed88-44a3-9910-09a4455b8b0c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x': array([0. , 0. , 1.5]),\n",
       " 'y': array([0. , 1.5, 0. ]),\n",
       " 'n': [0, 3, 1],\n",
       " 'A': 1.125,\n",
       " 'b1': 1.5,\n",
       " 'c1': 1.5,\n",
       " 'b2': 0.0,\n",
       " 'c2': -1.5,\n",
       " 'b3': -1.5,\n",
       " 'c3': 0.0}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = (L/2)**2/2 # m^2 , todos los elementos son iguales \n",
    "\n",
    "for e in elementos:\n",
    "    e.update(A=A)\n",
    "    e.update(b1=e['y'][1]-e['y'][2])\n",
    "    e.update(c1=e['x'][2]-e['x'][1])\n",
    "    e.update(b2=e['y'][2]-e['y'][0])\n",
    "    e.update(c2=e['x'][0]-e['x'][2])\n",
    "    e.update(b3=e['y'][0]-e['y'][1])\n",
    "    e.update(c3=e['x'][1]-e['x'][0])\n",
    "    \n",
    "elementos[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1ac8b7fa-fa3a-41a1-9cb1-dcf3f34b2500",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}25.0 & 0.0 & -25.0\\\\0.0 & 25.0 & -25.0\\\\-25.0 & -25.0 & 50.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 25.0,   0.0, -25.0],\n",
       "[  0.0,  25.0, -25.0],\n",
       "[-25.0, -25.0,  50.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for e in elementos:\n",
    "    K_e = np.zeros((3,3))\n",
    "    for i in range(0,3):\n",
    "        for j in range(0,3):\n",
    "            K_e[i,j] = e['b{}'.format(i+1)]*e['b{}'.format(j+1)]+e['c{}'.format(i+1)]*e['c{}'.format(j+1)]\n",
    "    K_e = k / 4 / e['A'] * K_e\n",
    "    e.update({'K':K_e})\n",
    "\n",
    "pp(sp.Matrix(K_e)) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0502677f-8f41-4995-a832-12a39cde8411",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "El término de generación $\\mathbf{Q}$ se integra al diccionario usando:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "07fc605a-9285-4b1d-ad0e-744616ee10e5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}15.0\\\\15.0\\\\15.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[15.0],\n",
       "[15.0],\n",
       "[15.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for e in elementos:\n",
    "    F_e = Q*e['A']/3 * np.array([1,1,1])\n",
    "    e.update({'F':F_e})\n",
    "\n",
    "pp(sp.Matrix(F_e))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88d43571-111f-4385-8797-33e2d4c9f017",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Y, el flujo conocido se integra con el siguiente vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b0794fa3-8d74-4950-97ca-814b612177dc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}18.75\\\\18.75\\\\0.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[18.75],\n",
       "[18.75],\n",
       "[  0.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F1 = q * (L / 2) / 2 * np.array([1,1,0])\n",
    "\n",
    "for i, e in enumerate(elementos):\n",
    "    if i in (0,4):\n",
    "        e['F'] = e['F'] + F1\n",
    "\n",
    "pp(sp.Matrix(F1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6741f4da-3f58-46e0-99a0-23c89b492c41",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "El ensambe de matrices se puede hacer con un doble ciclo for (columnas y renglones de la matriz de cada elemento):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c8b29c68-f578-44b4-8ed0-ec50510a0ff8",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}50.0 & -25.0 & 0.0 & -25.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-25.0 & 100.0 & -25.0 & 0.0 & -50.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -25.0 & 50.0 & 0.0 & 0.0 & -25.0 & 0.0 & 0.0 & 0.0\\\\-25.0 & 0.0 & 0.0 & 100.0 & -50.0 & 0.0 & -25.0 & 0.0 & 0.0\\\\0.0 & -50.0 & 0.0 & -50.0 & 200.0 & -50.0 & 0.0 & -50.0 & 0.0\\\\0.0 & 0.0 & -25.0 & 0.0 & -50.0 & 100.0 & 0.0 & 0.0 & -25.0\\\\0.0 & 0.0 & 0.0 & -25.0 & 0.0 & 0.0 & 50.0 & -25.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -50.0 & 0.0 & -25.0 & 100.0 & -25.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -25.0 & 0.0 & -25.0 & 50.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 50.0, -25.0,   0.0, -25.0,   0.0,   0.0,   0.0,   0.0,   0.0],\n",
       "[-25.0, 100.0, -25.0,   0.0, -50.0,   0.0,   0.0,   0.0,   0.0],\n",
       "[  0.0, -25.0,  50.0,   0.0,   0.0, -25.0,   0.0,   0.0,   0.0],\n",
       "[-25.0,   0.0,   0.0, 100.0, -50.0,   0.0, -25.0,   0.0,   0.0],\n",
       "[  0.0, -50.0,   0.0, -50.0, 200.0, -50.0,   0.0, -50.0,   0.0],\n",
       "[  0.0,   0.0, -25.0,   0.0, -50.0, 100.0,   0.0,   0.0, -25.0],\n",
       "[  0.0,   0.0,   0.0, -25.0,   0.0,   0.0,  50.0, -25.0,   0.0],\n",
       "[  0.0,   0.0,   0.0,   0.0, -50.0,   0.0, -25.0, 100.0, -25.0],\n",
       "[  0.0,   0.0,   0.0,   0.0,   0.0, -25.0,   0.0, -25.0,  50.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 8 # Número de nodos\n",
    "K = np.zeros((n+1,n+1))\n",
    "F = np.zeros((n+1))\n",
    "\n",
    "for e in elementos:\n",
    "    for i, j in enumerate(e['n']):\n",
    "        for k, m in enumerate(e['n']):\n",
    "            K[j,m] = K[j,m] + e['K'][i,k]\n",
    "        F[j] = F[j] + e['F'][i]\n",
    "\n",
    "pp(sp.Matrix(K))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "686ae017-3055-40f2-8d1b-0a90cde22848",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "El vector fuerza, ensamblado en la misma operación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "29319cc1-c548-48d0-ab19-2c7a761bb37f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}33.75\\\\45.0\\\\30.0\\\\97.5\\\\90.0\\\\30.0\\\\33.75\\\\45.0\\\\30.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[33.75],\n",
       "[ 45.0],\n",
       "[ 30.0],\n",
       "[ 97.5],\n",
       "[ 90.0],\n",
       "[ 30.0],\n",
       "[33.75],\n",
       "[ 45.0],\n",
       "[ 30.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp(sp.Matrix(F))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "845cfcb6-f22b-40ab-9dc7-50b874df556b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Para implementar algo equivalente al $T_3 = T_L$ del desarrollo anterior\n",
    "se puede substituir toda una linea por $0$, dejando solamente un $1$ en\n",
    "la diagonal principal. Para automatizar esto generamos el vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9b4fb57c-44c4-4055-a816-d91237746f81",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\text{NaN}\\\\\\text{NaN}\\\\300.0\\\\\\text{NaN}\\\\\\text{NaN}\\\\300.0\\\\\\text{NaN}\\\\\\text{NaN}\\\\300.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  nan],\n",
       "[  nan],\n",
       "[300.0],\n",
       "[  nan],\n",
       "[  nan],\n",
       "[300.0],\n",
       "[  nan],\n",
       "[  nan],\n",
       "[300.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Tf = np.array([np.nan,np.nan,TL,np.nan,np.nan,TL,np.nan,np.nan,TL])\n",
    "\n",
    "pp(sp.Matrix(Tf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c6e8c122-9731-4a98-b59d-788a0b57f145",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}50.0 & -25.0 & 0.0 & -25.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-25.0 & 100.0 & -25.0 & 0.0 & -50.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\-25.0 & 0.0 & 0.0 & 100.0 & -50.0 & 0.0 & -25.0 & 0.0 & 0.0\\\\0.0 & -50.0 & 0.0 & -50.0 & 200.0 & -50.0 & 0.0 & -50.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -25.0 & 0.0 & 0.0 & 50.0 & -25.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -50.0 & 0.0 & -25.0 & 100.0 & -25.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 50.0, -25.0,   0.0, -25.0,   0.0,   0.0,   0.0,   0.0,   0.0],\n",
       "[-25.0, 100.0, -25.0,   0.0, -50.0,   0.0,   0.0,   0.0,   0.0],\n",
       "[  0.0,   0.0,   1.0,   0.0,   0.0,   0.0,   0.0,   0.0,   0.0],\n",
       "[-25.0,   0.0,   0.0, 100.0, -50.0,   0.0, -25.0,   0.0,   0.0],\n",
       "[  0.0, -50.0,   0.0, -50.0, 200.0, -50.0,   0.0, -50.0,   0.0],\n",
       "[  0.0,   0.0,   0.0,   0.0,   0.0,   1.0,   0.0,   0.0,   0.0],\n",
       "[  0.0,   0.0,   0.0, -25.0,   0.0,   0.0,  50.0, -25.0,   0.0],\n",
       "[  0.0,   0.0,   0.0,   0.0, -50.0,   0.0, -25.0, 100.0, -25.0],\n",
       "[  0.0,   0.0,   0.0,   0.0,   0.0,   0.0,   0.0,   0.0,   1.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, t in enumerate(Tf):\n",
    "    if not np.isnan(t):\n",
    "        for j in range(n+1):\n",
    "            K[i,j] = 0\n",
    "            if i == j:\n",
    "                K[i,j] = 1\n",
    "            F[i] = t\n",
    "            \n",
    "pp(sp.Matrix(K))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "748b4e84-694a-4683-8d68-2c6d3105de87",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "El vector fuerza modificado:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "887fddb3-873f-44b3-addc-5541befc1f63",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}33.75\\\\45.0\\\\300.0\\\\97.5\\\\90.0\\\\300.0\\\\33.75\\\\45.0\\\\300.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[33.75],\n",
       "[ 45.0],\n",
       "[300.0],\n",
       "[ 97.5],\n",
       "[ 90.0],\n",
       "[300.0],\n",
       "[33.75],\n",
       "[ 45.0],\n",
       "[300.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp(sp.Matrix(F))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "934368b2-a605-45b2-b212-83a320ccfd71",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Finalmente utilizamos `np.linalg.solve()` para obtener el vector T:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "17adc60d-047c-4573-b798-fbe25f07aa61",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}304.994117647059\\\\303.432352941177\\\\300.000000000001\\\\305.205882352942\\\\303.467647058824\\\\300.0\\\\304.994117647059\\\\303.432352941177\\\\300.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[304.994117647059],\n",
       "[303.432352941177],\n",
       "[300.000000000001],\n",
       "[305.205882352942],\n",
       "[303.467647058824],\n",
       "[           300.0],\n",
       "[304.994117647059],\n",
       "[303.432352941177],\n",
       "[           300.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = np.linalg.solve(K,F)\n",
    "\n",
    "pp(sp.Matrix(T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f178a4df-63c2-4438-b34f-5494ec10de79",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PtWZ7ZGsG/dkX05EDGDu3YOzagrFpLfy4xLH2W0DT30bektpCWGS9Kd6EEEKIy51bRtbqSm2NrP2es99g9h05ybJ1m0lJiKVzYgxrd2azdGUGsfEtGdgxmUA/13+TMQyDgnw7Bfl2mrdwtLrKWl2Kb4BGVHMLHqdyMXZshl1bMHZuhlMnHTs2aeoo2pLaopLaooKauTy2c5Fv2K4nOXUtyafrSU5dS0bWXO+yHFm7HMWFNSVuaJ/qn/MLS6C8mNyNGXy08Sf0gHBaJSaQ3ikZD4trfluUUjRpaqZJU8fx7DaDkhI7Ofsr2b6xnNCIpsQkptOszxWO7gnHD2Ns3wTbN2Js2QA/LXWMvIWEOYq31u1QrVJR/k1cEp8QQgghLkyKNTcZ1Kk1Azu0InNnDms3baX86AF2rD1Kv7QkPCyw93Ae0SGBWMyum5VjMit6DvCjqNBOzt5KcvZXcuRQFW07eTlG3n5d963PEMeab7nZGNt+xti+0dH3dMUCR/EW2RzVuj0qpT0ktEF5eFzgzEIIIYS4WFKsuZGmaXRNak7XpOZU2ezsOHQcH08ruq4zfcYsNHslnqHN6ZSaTOfEaJfNKPXzN5Hc3oukVE+O5FYRHOq4DLL3VnAou4rm8VZCIy2YIpujIptD+rUYdjtk73EUbtt+xlg6F2PRTDBbICEZldIBlZLmKOTkeTchhBDCZaRYqycsZhNtmocBYADJaZ3ZsWMnVYf3sPrwLlYs8aZFakenOyQ4QzMpIqJ/a1+lFJQU2Vn3YykWqyI61kpMvBW/ABPKZIK4RFRcIlw5AqOiwvGs29YNGFs2YHz9AcbXHzgmKyS3h5Q0VHJ7lF+Ay+IVQgghLkdSrNVDJk1jaLdUhnZLJb+olMXrtrJ/727MJsfI2v6j+Sxdu4m+HdsQF9bUZeeNjvMgqrmV48dsZO+tZN/uCk7m2eg9yA8AXTfQNMeomfLwgDYdUG06AGCczMPYlgVbNjh6nP4607R5S1RqR1RqJ4hNcLTZEkIIIc4hMjKS66+/njfffBNwLFiblpZGWloaU6dOZdq0aTz//POEhYVV7zNlyhS8vLzo168f8fHx1a9/9913WK2u6an9ww8/8PTTT6PrOqNHj+aee+45YxvDMHj66adZsmQJXl5eTJ48mdTU1Es+txRr9Vygnzcj+nWCfp2qX1u3fS+Fe7KYvSeLSq+mRMa1ZEDHFEID/S75fEpTNAuz0CzMQkW5TkW5Y7JwZaXOD3OLCIu0EBNvpUlT02m3O1XTYFTPdOiZjqHbIXuvY8Rt8zqM777CmDMN/AIcxV1qZ1RKe5S3+5ZfEUIIcemW7Svg46zj5JXaCPY2c0v7EPrGXdodFW9vb3bs2EFZWRleXl4sX778tMIM4Nprr+WFF1447bWcnByaN29+1ibtl8put/PEE0/w+eefEx4ezlVXXcXgwYNJTEw8bbslS5awb98+Vq5cyfr163nssceYM2fOJZ9fhjkaoBv6duSqEWPwi2+HYavi+NY1fP7xR5wqcbTB0nX9Akdwjoenhn8TxwQHuw1CIywcOlDJykXFLJtfxN6dFVRVnnkupZlQsQloQ0dienQC2mtTUXc9hGrdHmPjWoz/TkR/4Gbskx5D/346xqFsGvEKMkII0Sgt21fAlNVHOF5qwwCOl9qYsvoIy/YVXPKx+/fvz+LFiwFHY/fhw4df8jEBrrvuOjZv3lz9868L8l/I+vXriY2NpXnz5litVoYNG8b8+fPP2G7+/PmMGDECpRQdO3akoKCAo0ePXnLcMrLWQLWMCKZlRF+gLxv35rLjwCGa+HgBMPmjr9DMFpISE+mf1gpPq+X8B3OCl7dG+y7epKR5kZtdSfbeSrZsKKNZmBmL1THyZrGos04uUL7+qK59oWtfx6jb3p0Ym9Y6CrfpH2FM/8jRVaFdFyr6DsZoFtWgm9ELIURj8cTCA2e81rO5P1clBjI16zgV9tO/aFfYDd5de5S+cQEUltuYsOLQae+/MOjMllFnM2zYMCZPnkx6ejrbtm3jpptuYvXq1dXvz5o1izVr1pz2M8CBAwcYNGgQAJ07d+bFF1887bijR4/myy+/pE2bNuzZs4fKykqSk5NZtWoVzzzzzBlxeHl5MWvWLI4cOXLaOmjh4eFs2LDhjO3Ptt2RI0cIDQ116nOfi/yL2Ai0jY+gbbzj4rDrOp4+fpQfO8Cu1QfZtmY55uBoundsR+fEmEs+l8WiaN7Cg+YtPCgpsuPj5xh525hZRkG+neh4K9GxVry8zz5oqzQTtGyNatkarrvF8azb5l8KtxULOLVkDnj7oNp0gvZdUW06oLxkgUYhhKhvTpSefZHYorPccamp5ORkDh48yMyZMxkwYMAZ75/tNihwwdug11xzDa+//jpPPfUU06ZNY+TIkQD07NnzvPud7e7P2QYnnN2upqRYa2RMmsa4kVdRUWVjxcZdbN6+A3teNtv3NqVzYgynSsrYfeg4HVpGXfJSIL8WagARMRaqKg12bCpnx+ZymoWZiUv0oFnY+Uf1VNNgVJ8roM8VGBXl+B3cQ+HyRY5JCmuWYZjMkJSKat8V1a4rKjDokmIWQgjhvPONhAV7mzl+loItxNtRWvh7mp0eSTubwYMH8+yzz/L111+Tn59/0cf5PS8vL3r37s38+fOZPXs2c+fOBbjgyFp4ePhpXZEOHz581tEyZ7erKSnWGikPi5n0jq1J79ia4rIK9F+q/cXrtnEoayU/mH1oEhlHrw4ptI6+9AspItpKRLSVkmI72XsrydlXycnjNpqFWdB1g7IS/bTi7myUhyeeXftS3CLFcbt0zw6MrJ8wslZjfPpvjE//7ZhdmtYN1bEHKizqkuMWQghxcW5pH8KU1UdOuxXqYVLc0j7EJccfNWoUfn5+tG7dmoyMDJccE2DMmDGMHTuWLl26EBgYCFx4ZC0tLY19+/aRnZ1NWFgYM2fOZMqUKWdsN3jwYD788EOGDRvG+vXr8ff3l2JNOMfX67cOA/3at2KJ3c6BPbsoPbCZhQc2M8cjgLvG3OiS/qQ+viZat/WiVRtPdLvjtWOHbWSuLCEoxERMvAfhURZM5vMPCyvN5FhsNyEZY8TtcDjHUbRlrcaY8QnGjE8gIsZRtHXoIYvxCiFEHft11qerZ4P+KiIigrvuuuus7/3vM2svvvjiGTNGz6Vt27b4+voyatQop2Mxm808//zzjBkzBl3XGTVqFK1atQJg6tSpANx6660MHDiQJUuW0LNnT7y8vHjttdecPsf5SCP3S9SQGxDnHD/F0nVbOJF3nPtvHg7AB3OW4e3lxcBOKQQH+LjkPBXlOtn7HJMSSot1zBaIam6ldVsvzJbTCyxn8mmczMPY8BPG+lWwaysYhqNVVsfuqI49IaaFFG6/05Cv0fpI8ul6klPXkkbu53fkyBFGjBjB8uXLnX4cSBq5C7eJDmnCLVf0rP5Z13XyDu3Ho6KAT7asxu4XSsvERAZ0aI2f18X3//Tw1Eho7UnLJA9OHHcsuJt3zIbpl6vvZJ4NP38TFqtzBZZqGowaeDUMvBqjMB9jw2qM9RkY87/FmDfdMbO0wy+FW3wrKdyEEEIA8NVXXzFhwgTGjx/vshaOdUFG1i5RY/tGqOs6WXtyWb1xKyVH9mO1l+MR1Zo/Xz+IKpsd3TDwsFx6jf9rNwTdbrBwdiE2m0FEtIW2ac3QLMUXVWAZxYUYP6/BWJcB27LAZoOmIajOvVCde1+2I26N7Rp1N8mn60lOXUtG1lxPRtZEvaJpGh0SouiQEIVd18nYso+IYMfzBys372HDisVYQqJJS2lN95Q4TBf5zaS6bZUGXfv4kL23kkMHKjm4/xA+fhopaV6EhtdsfTjl6/9bF4XSEkfhlrkCY9FsjPnfQrNwVKfeqC69HQ3qhRBCiAZAijVxTiZNo3dqi+qfm/h6owWGYTt2gPXH9vLTck98wmIZfUXv6gV5a0opRZOmZpo0NZPc3ouifA+2bjyB+ZcJCMVFdkqKdZqFmlGa86NiytsH1b0/dO+PUVKEsf5HjLUrMeZ9jTH3SwiPRnXu7Rh1k1mlQggh6jEp1oTT0lpGkdYyiqKyCpas28buXTspObIfH4+BAPyQtZOokEASIi9u2rbZrEho7U9gSGX1awf2VLJ3RwWeXoqYeCvRcVa8fc6/BMj/Uj5+qN6DofdgjMJTjufbMldgzP4cY9ZnEB2H6toP1aWPrOMmhBCi3pFn1i7R5f6sRXmlDU+rGV3Xee2d97Day6nwbEJ485b065RCVFDNpnD/bz51u8GR3Cqy91Zy/IjjeYHwKAudel76TFUj/wTGulUYa5bDvp2gFLRKRXXrh0rrjvJ2zWxYd7vcr1FXk3y6nuTUteSZNddz9zNrUqxdIvlL5jf7j+azbP1mjmXvwaOiEAPwb9Ge24f2cfoY58tnaYlOzr5KwKBVGy8Mw2D39grCIiz4BdRstO1/GcdyMX5ahrF6KRw7DGYLql0XVLd+0KYDynzp/VXdRa5R15J8up7k1LUaerEWGRnJ9ddfz5tvvgmAzWYjLS2NtLQ0pk6dyrRp03j++edPW1dtypQpeHl50a9fP+Lj46tf/+6777BarZcck9ls5r777mPRokUEBwezZMmSs26XkZHBHXfcQXR0NABXXXUVDzzwwBnbyQQD4TaxoYHEXtkb6M227COs3LCVhOaO58E27TvMwmUrSUxsRf8OSfh41vwPj7ePRqs2ntU/lxbr7NhczvaN5QQGmYiJd3RR+N+125yhmkWgrh2Ncc1NsH8Xxk9LHbdK160CHz9Up56Owq1F68tyRqkQQpzNwQMVbN9YTlmpgZe3IqmtJ1HNL36pJwBvb2927NhBWVkZXl5eLF++/IwFb8/WGzQnJ+eCvUEvxciRI7n99tv529/+dt7tunTpUr1Qrqs0nEVGRIPSOiaMPw4bQK82jm84h0+cQi8+yd61S/nvu+/yr09nsHj9dqps9os+h4+fiUHX+JPc3pOqSoOfM8tYMKuA/BMXP1StlELFJaKN/hPaxA/Q7nsalZKG8eMS9An/QH/iz+izv8DIO3rR5xBCiMbg4IEKNmaWUVbquEFXVmqwMbOMgwcqLvnY/fv3Z/HixQDMmDGD4cOHX/IxAa677jo2b95c/fOwYcPYunWrU/t269aNJk2auCSOmpKRNVEnBndqTf/2iWRs2cvPW7djy8th48qDdE6KxWI2cfhEIaGBvjU+roenRotWnsQnepB/ws7B/ZX4/3JLNGd/JVWVBlHNLVg9av69RJnNkNoJldoJo7wUY/1PGD/98NvEhFapqB4DUB16oDwvbjasEELUZxlLis54LSLaSmyCB9t+Lsf+P9+37XbYvL6cqOYeVFTorFtVctr7PQb4OXXeYcOGMXnyZNLT09m2bRs33XQTq1evrn7/f9tNzZo1C4ADBw4waNAgADp37syLL7542nFHjx7Nl19+SZs2bdizZw+VlZUkJydfsJF7Taxbt4709HTCwsJ46qmnqttSXQop1kSdsZhN9G2XQN92CZRXVrFxby7+3o7bmp98/Q3KVkXTmAQ6t2lFalx4jY6tlKJpsJmmwb9d0sdyq8jNqWLbz2WER1mIibcS1Mx8Ubcxlac3qscA6DEA48QxjB9/wMhYjPHB6xif/QfVsSeqx0BHP9MGtCq2EEJcrPKysz/yXlV56Y/CJycnc/DgQWbOnMmAAQPOeP9st0GBC94Gveaaa3j99dd56qmnmDZtGiNHjgQu3MjdWampqaxZswYfHx8WL17MHXfcwapVqy75uFKsCbfwtFrokuRYmFbXdVq0bsu+3bso2reJH/Zt5HuLH63aduDanu0u+hwde/jQMt/2y4K7VRzKriI61kr7rpf28KwKaoa6ehTG0JGwe5ujaFu7EiNjMQSHoroPQHXvjwpxrqmwEELUV+cbCfPyVtW3QP/3dQAPD83pkbSzGTx4MM8++yxff/01+fn5F32c02Lz8qJ3797Mnz+f2bNnM3fuXACXjaz5+f32eQcOHMjjjz/OyZMnadq06SXFLcWacDtN07i+Twfo04EKzHyzaCUH9+2msqoKgMMnCvlh3Rb6d0whPMi/RscOCDST2tFMcjuDw4eq8PJyjHqVlepsWldKTLwHzcLN1R0VakIp5RhJS0jGuOmPGBt+xMhYgjHnC4zZn0Prdqjeg1Htu6EsDXc2qRBCnE1SW082ZpaddivUZHK87gqjRo3Cz8+P1q1bk5GR4ZJjAowZM4axY8fSpUsXAgMDAdeNrB07doyQkBCUUmzYsAFd16vPcSmkWBP1SmRwE0andwO6oes6ABmbd5G3PZNp29di8w0hrkUCAzsl16hrgsmsiGr+2wzUkiI7p07aOZpbgoenIjrOseCur9/FLQGiPDxR3fpDt/4YJ447RttWLcL47yQMXz9Ut/6oXoNRkTEXdXwhhKhvfp316erZoL+KiIjgrrvuOut7//vM2osvvnjGjNFzadu2Lb6+vowaNapG8dx99938+OOPnDx5ko4dO/Lwww8zevTo6pmft956K9999x1Tp07FZDLh6enJ22+/7ZIVBGSdtUsk6wO51rnyuWnfYX7M2kJh7j6s9jLsaNw69naC/C9+4VpdNzh22Eb23gqOHrahgMHD/C9qMsLZGLoO23/GWL4AI2s12G3QIgnVaxCqU686m5Qg16hrST5dT3LqWg19nbXaduTIEUaMGMHy5cvRnHzG2N2L4srImmgQUuPCSY0LR9d11uzIZlf2oepC7V+ffIummUhNTqJXmxZYzM6NjmmaIizSQlikhbJSnfw8W3WhtnaVY8QtJt6DgMCLHG3TNEhOQyWnYRQVOCYlrFyI8dGbGF+852go33swxCbI2m1CCFEHvvrqKyZMmMD48eOdLtTqAxlZu0TyjdC1appPXdd5a9p32PKyMRt2qjQPvEJj6NGhLe1bRF5UDLpukLWmlMM5Veg6BAQ6FtyNbG7FchEL7v6eYRiwZzvGygUYmSuhssLRm7TvlaiufVCerv9GK9eoa0k+XU9y6loysuZ6MrImxCXQNI37Rl9DSXklSzdsZ8fOnVQe3sOGbd60bxFJSXkl+4+eJKW58zMzNU3RoZsPlWk6hw5UcWBvBZvWlWG3G7Ro5YmhG6C4uCVAlIKWrVEtW2OM+iPG6mUYy77H+ORtjK8/cPQl7XsFKiquxscWQgjROEmxJhoFH08rQ7u3ZWj3tuQXlaL/8vqS9dvYt3YZc63+NItpQd+ObYgNdW5mjtVDIy7Rg9gEKwUn7Xj7OobMDx6oYve2cmLirUTFWvHwvLihdOXljep3JUbfK2DvDkfRtmoxxtJ5jmfb+l7paHNlufS+dkIIIRouKdZEoxPo99vQcqfWcRQUlXD4wB4Kdm9g1u4NVHgFcceo4U5PTlBK0STotz8qVk+FxarY+nM52zaVExbhWHA3JOwiF9xVylGctUjCGHWnY/mPZd9j/N9kjGnvObok9LkCFXZxt3WFEEI0bFKsiUYtPNCfm4f0AHqw69BxVmzYQtXxYwT6OmZifrbgR7y8PBnYsXV1N4ULCQ23EBpuoajATvbeSg4eqKSkWKdZuGMxxKpKA4v14p5tUz5+qEHDMNKvhe0bHUXbkjkYC2dC63ZoA4ZC284o7eImPQghhGh4pFgTl42EyBASIvtV/6zrOof27sCjspD3N6yCwAiSk1rRt10rPK0X/qPhF2AiJc2L1m09KStz3HitqjJYOLuApsFmYuKthEVY0EwXOdrWuh2qdTuMUycds0iXz0ef8iIENUP1vwrVMx3lW7NFgoUQor6LjIzk+uuv58033wTAZrORlpZGWloaU6dOZdq0aTz//POnras2ZcoUvLy86NevH/Hx8dWvf/fdd1itl/4oSXl5OcOGDaOiogK73c7QoUN5+OGHz9jOMAyefvpplixZgpeXF5MnTyY1NfWSzy/FmrhsaZrGg3+6ldXb9rN+8zYqjmez48eD7M0+yF9vGIKu69h144JLgWgmhY+vYxvDMGjRyoPsfZWsyyjF6qGIirUSn+iBl/dFPtvWpKmjvdWVIyDrJ/Ql32F8/SHGzM9QXfui+g9FxcRf+EBCCOFiO3bsICMjg6KiIvz8/OjRo8clNy739vZmx44dlJWV4eXlxfLly89Y8PZsvUFzcnIu2Bv0Ynl4ePDll1/i4+NDVVUV1113Hf3796djx46nbbdkyRL27dvHypUrWb9+PY899hhz5sy55PNLsSYuayZNo0dKPD1S4qmosrFi4y4iQxwTEDK27uenpQvxCWtOl7YppLWMvOC6PFarRqs2XiQme3L8qKMv6b6dFUTHWvHyhvIyHbNFYTZfxGibyQQde2Lq2BPj4D6MJd9hrF6KsXIhtExGDbgaldYNZZY/1kKI2rdjxw4WL15cvaRFUVERixcvBrjkgq1///4sXryYq6++mhkzZjB8+HBWr159yTFfd911PPfcc7Rp0waAYcOG8dJLL5GcnHze/ZRS+Pg4nnO22WxUVVWd9Rnl+fPnM2LECJRSdOzYkYKCAo4ePUpoaOglxS1/qwvxCw+LmfSOrX/72WpG+TalIncXq3J3ssTsQ9OoeG4Y2O2Cra6UpmgWbqFZuIXKCr16sd2tWWUcza0iIsZK83grAU1NFzcpISoOdes9GDeMxVi1EOOHuRj/nYjRpKlj6Y++V6L8Amp8XCGE+L3p06ef8VpCQgJt27Zl1apVZ6w9ZrPZWLZsGa1ataKsrKy6UfqvbrjhBqfOO2zYMCZPnkx6ejrbtm3jpptuOq1Y+992U782Wz9w4ACDBg0CoHPnzrz44ounHXf06NF8+eWXtGnThj179lBZWUlycrJTjdztdjtXXHEF+/fvZ+zYsXTo0OGM7Y8cOXLaemnh4eEcOXJEijUhakvnxBg6J8aQV1DCknVbyN67m1PZO/C09Abgxy17iWoWSHTI+ZcC+X37qtgED5QGBw9Ukr23Ev8mGvGJnkTHXdwzFcrHFzX4OseEhE3r0X+YgzHzM4zvvnKs2ZZ+LQQHX9SxhRDifIqLi8/6enl5+SUfOzk5mYMHDzJz5kwGDBhwxvtnuw0KXPA26DXXXMPrr7/OU089xbRp0xg5ciTgXCN3k8nEwoULKSgo4M4772T79u0kJSWdts3Z+gy4okONFGtCXEBwgA8jB3SBAV0oLC3H02pG13VWLVuCxVZKlXcwMfEtGdAxheCA8y8H0jTYTNNgM23SDA5lOwq24kI7AIZucCLPTlBIzUfblGaCdp0xteuMcTgHY9FsjJ+WYKxcSH67zhh9r4SUDo4WWEII4aTzjYT5+flRVFR01tfBMSrl7Eja2QwePJhnn32Wr7/+mvz8/Is+zu95eXnRu3dv5s+fz+zZs6tH/pwZWftVQEAAPXr0YOnSpWcUa+Hh4ad1Tzp8+PAlj6qBFGtC1Mivy3tomsbV11zLqg1bOHlwL0c2/8Qnm1cT2LIdt13V54LHsVgVsS09iG3pga47vokdP2pj9fISvH01YuKsRMdZ8fSqeXGlwqNRt9yNcd3NGMvnY1s2D/2NZyEsCjXwGlT3ASgPjxofVwghfq9Hjx6nPbMGjrZMPXr0cMnxR40ahZ+fH61btyYjI8MlxwQYM2YMY8eOpUuXLgQGOu6MXGhkLS8vD6UUAQEBlJWVsWLFCu6+++4zths8eDAffvghw4YNY/369fj7+0uxJoQ7JUU3Iym6Gbrel6w9uazeuIXocMcfyh0HjzFvaQYpSa3o0y4BD8u5/6hpmmMULSjETFpXb7L3VbJ9Uzk7NpfTLNxMu87eF9UlQfn6o666kaDRd3F8/kyMRbMwPn0HY8YnqD5DHLNIA4Mu7sMLIS57v04icPVs0F9FRERw1113nfW9/31m7cUXXzxjxui5tG3bFl9fX0aNGuV0LEePHuXee+9F13V0Xeeaa66pfjZu6tSpANx6660MHDiQJUuW0LNnT7y8vHjttdecPsf5SCP3SyQNiF2rseRzfuYWtvy0HLNRRZVmwSMkhg5tWtO1dSwmJ25FFhfZydlXSd5RG70G+qI0xbHDVfj4adXLhDjr15wahgG7t6EvmgkbVoOmUJ17o4ZcJ71Ia6CxXKP1ieTUtaSR+/kdOXKEESNGsHz58gvO8P+VNHIXohEa0jmFvu1aseznHWzdvoOqo/tYc3QvraLvIMjfhxNFpQT6eJ7zLwpfPxOt2/4249QwDH7OLKW8zCComWPB3fAoC6YaLLirlIKEZEwJyRjHjzg6I6xYgPHTUkhOQxtynWMhXhc8DCuEEPXRV199xYQJExg/frzThVp9ICNrl0i+EbpWY81nYWk5WXsO0ie1JQCT/vsJ2CsJioqnd4cUEiJDLniMslKdnP2V5OytpLREx2JVpLT3uuBM0vPl1Cgpxlg2D2PJHCjIh5h41ODrUJ16OdZ1E2dorNeoO0lOXUtG1lzP3SNrUqxdIvlLxrUuh3zqus5XP6wlZ98urKUnAKjwDCS5bXuGdrtwWxLDMDhxzLHgbkwLK8HNLBQX2ck7aiOyuRWL5fSRMWdyalRVYfz0A8aCGXDkIDQNQQ26FtVrMMrz/GvKXW4uh2u0rklOXetS8llSUlK9+Kv4jauLtbPlWW6DClGPaJrGqIFdgC7sP3qSZeu2cCx7D4XFJQDkFZSwdMM2BnZMJtDvzG+4SimCQy0Eh1qqXzucU8X2TeVszSojIsZKTLyVwCDnlwBRFguq92CMnumwaS36/G8wpr2PMfsLxwK7A69BBZx/PTkhRMOnaRo2mw2zdEKpNTabrca3YGVk7RLJN0LXupzzadd1TJrGN8vXczBrJToaekAYrRIT6ZeWhI/nuW93GobBqZN2svdWcii7ErsNAgJN9B7kS0hIyEXl1NizHX3Bt7DhJzCZUb3SHbdIQ5ybcdVYXc7XaG2RnLrWpeTTMAzKy8vRdV2eX/0dDw8PKioqLvk4hmGgaRqenp5n5Lfe3QatrKxk/Pjx2Gw27HY73bp1Y+TIkRQXFzN58mSOHz9OSEgIDzzwAL6+vtX75eXl8cADD3DjjTdy7bXXXvA8Uqw1PJJPx23StTtzWLtpK2VHD2DRK7EpMzffehvNLrDoLoCtyiA3p5KKCoOE1p4EBwezfFEOwaFmQkLNKK1mfwEbR3Mx5n+D8eMS0HXHDNIrR6Aim1/sR2zQ5Bp1Pcmpa0k+Xa8uclrvboNaLBbGjx+Pp6cnNpuNp59+mvbt27NmzRpSU1MZPnw4M2bMYMaMGdx8883V+3344YekpaW5I2Qh6oymaXRJak6XpOZU2eys3LyHvdmHqgu1t774DqUpOqYm06VVzBnD6WaLIib+t0VvS0tsZO+rZM+OCry8FdFxHkTHWfH2cW4YXoVGOPqQXjMaY9FMjGXfY6xeBu26oF05AtUi6cIHEUIIcdHcMm9VKYWnp2MleLvdjt1uRylFZmYmffv2BaBv375kZmZW77NmzRpCQ0OJiopyR8hCuIXFbKJ/+0TuvLY/4Bh1s9mrqDyylzULZ/HaO+/z328XsS37yDmP4e1jZtC1/nTs4Y2vv4mdW8pZPKeQY4erahSLCgxCu/EOtJffQ10z2rFm28t/x/7KExhbNpy1J54QQohL57YnCHVd59FHH+XIkSMMGTKEhIQECgoKqls/BAYGUlhYCDiaws6cOZOnnnrqjB5dv7do0SIWLVoEwMsvv0xwHTSwNpvNdXKey4Xk88Ke/9tdnCwsYc7KtWzfuoWynK2stlrp3aEN5ZWV5BzNJyH6t/YmZrOZ0NAQQkOhbRoUFVaxe3sRCUlNsFg0dm4tpCC/koRkf5oEOtFQPjgY7rgXffSdlC2cRemsz9H/NR5ziyR8brgFj659G3UPUrlGXU9y6lqST9dzd07dVqxpmsakSZMoKSnhlVdeITs7+5zbfvnllwwdOrR6NO5c0tPTSU9Pr/65Lu7Zy7MBriX5dN5VXVK4qksKh08UommKvLw85mduYcePi6nwakpUnKO5fEpC3Bk5jY6HgoKTABzJLWPvzgo2Z52iabCJmHgPwqMtmM1OPNvWIx0690X99AO276dTMPEJCI9GDR2J6tzL0WC+kZFr1PUkp64l+XS9y/KZtd/z8fEhOTmZrKwsAgICyM/PJzAwkPz8fPz9/QHYvXs3q1ev5tNPP6WkpASlFFarlSuuuMLN0QvhfuFB/tW/To6NIPdoOypy9nJ86xo+35qJ7h/KzdcNPefkhOT2XrRI8iBnfyXZeyvJWlNKbo6Zrn18z7r9//pt2Y+BGGtXYXz3JcZ7rzqW/bjqRlTXvrLArhBCXAK3FGuFhYWYTCZ8fHyorKxk06ZNDBs2jE6dOrFs2TKGDx/OsmXL6Ny5MwDPPvts9b5ffvklnp6eUqgJcRbRIYHcfnVfoC8b9+by089bKTp5jCA/x8K2Xy9di4+XJ/3TWuFp/W2dNg9PjZZJnrRo5cHJPDu/zigvL9NZs6KE6Dgrkc0tWK3nvr2pNBOqSx+MTr1gw0/oc6ZhfPAvjDlfOGaPdu+PMlvOub8QQoizc0uxlp+fz5QpU9B1HcMw6N69Ox07diQxMZHJkyezZMkSgoODefDBB90RnhCNQtv4CNrGR1QP3+u6zr5tm/CoKmLbmuWYg6Jom9KaninxWMyOkS+lFEEhv/21UFGuA7B5fRlbs8oIj7YQE28lKMR8zjWYlKZBxx5oHbrDz2scRdvUtzDmTENdeQOq5yCURYo2IYRwliyKe4nk2QDXkny63u9zWlFlY+Wm3WzetgP95EFMhh1zeCJ333gFuu4ozM62snZBvqO91cEDldiqIP0af7y8NQzduOC6bYZhwOb16HO+gL07oEkQ6orrUb0Ho6we5923PpJr1PUkp64l+XS9y/6ZNSFE3fGwmBnYIYmBHZIoKa/kh/XbiQoNAmDd7oMsXbSAJhFx9OqQQuuY3zoVBASaSe1opnU7L/LzbHh5Owq6zFWOFlkx8R40CzejnaVwU0pBake0Nh1g28/oc77A+OJdjHnTHbdH+wxGWZyYhSqEEJcpKdaEuEz5eFq5ukfb6p913UB5+FCavYWF2VuY4+FPs5gWXNe3M/7ejpnYZrMiJMxxC9MwDPwCTOTsq+RobgkenoroOCvN4614+545oUApBcntMSW3x9ixCX3mpxhf/Bfj++mooTfK7VEhhDgHKdaEEAB0TWpO16TmHDxRwNK1Wzh8YDcndm/C1L8rABt2HyQyJLB6VqlSitZtvWjVxpOjuVVk761k9/YKLBZFy9YmdLuBAZhMZxlta5WK9shLsH2jo2j79N+OkbahI1E9BqKkibQQQlSTvxGFEKeJCgrg5iE9gB4cKyjBx9OKrussWrgAS1UJdr9mtGiZyICOrfH39kTTFOFRVsKjrJSV6ph++Vsl92AVm9eXEdXcQky8B/5NTh9tU0pB63ZoSW1ha5ajaPt4Csbcr1BXj0J16y9FmxBCIMWaEOI8fr82W/qgwaz+eSvFR/aTvWEF72/IICihHbde2at6m1+fZQPw9dMICTVzYE8l+3ZV0qSpiZh4KzFx1tMmJSilICUNLbk9bF6HPvMzjI/e/KVou0nWaRNCXPakWBNCXJCmaaS1jCKtZRR2XefHLfvI2rKdkKZNANh/9CSzf8igfUpreqTEYdI0mjQ107GHmYoKnUO/LLi7b2cFMfGOyQSlxXa8fLTqJUAcExE6obXpCBsz0Wd95linbe5XqGFjUB17Nuo2VkIIcS5SrAkhasSkafRKbUGv1BbVr+3IPozt+AE2/LCX1cs98QmLpWvbZNq3iMDDQyO+lSdxiR5UVhgopbBVGSydX4SXt0ZMvJWo5lY8PB2FmFIK2nVBa9vZsbjurM8w/jsJI+prtOtuhtRO51zjTQghGiP5miqEuGRDOqdw11130bxjH5R3EyoO7WD5vG85XuBY2qOkvBKl1G8FmQZt0rywWBRbs8pZOLuQtRklFBXYq4+plEJ16I729L9Qdz4IFWXobz6HPuFRjB2b3fI5hRDCHWRkTQjhEn5eHgzr2R56tievoIT1Ow8QGugHwDufTsewVRHWvAX9OqYQHdKEmHgPYuI9KDxlJ3tfJQf3V5LQ2rFGd2mxHaUpvLw1Rxurbv0wOvXCWLUIY84X6K88DslpaNfdjIpNcOOnFkKI2ifFmhDC5YIDfBjcORkAXdcJjYrhyP7d5O9cxzc711HlHUxqu3YM6ZyCfxMTbdK8SG7rifbLMh87tpRzcH8VzcLNxMRbCQ23oJnNqL5XYHTvj7F0Lsa8r9FfeAg6dEcb9gdURIw7P7IQQtQaKdaEELVK0zRuGdIT6Mm2nKOsWr+F/EP7OHbiFACnSspY8fNO+qcl4evlaD/VKsUTL2+NnH2VrF1VitVDEZ/oQUKyJ8rqgRp8HUbvIRiLZmEs+BZ9w2pUt76oa8eggkPd92GFEKIWSLEmhKgzraNDaR0diq7rVNkdvUiXbdjBgfXL2b1uJappJG2SWtG7bQJJqV60SvHk2BFHX9KqKsctUsMwyM2pIjTCC/M1N2H0vwrj++kYS77DyFyB6jcUddWNKD9/N35SIYRwHSnWhBB1TtM0PH5ZhuOqbqlk+Pvw85bt2PJy2Loqm59/XMqYP/yB8EB/QiMshEZYHA3hgZPH7az/sRSzBSJjrMTEexNww1jUgGswZn+OsXg2xqqFqCHXo9KvRXl4uvOjCiHEJZNiTQjhVhazib5tE+jbNoHyyiqWZu1kX84hwgMdI2P/nr4ApRTd2ieTGhtO0xATPfr7kr23gpz9lRzYU4l/ExOdewXifdu9GIOGoX/7McaMTzB+mIu69iZH31FZWFcI0UBJsSaEqDc8rRau6JICXVKqXysrKUadOsSyg9tYYPEjODqePh1TSOsWTJtKnUMHqjiSW4Wnl2Ok7ogehuXGv9N00C6Mbz7E+PhtjIUz0a67FdK6yRptQogGR4o1IUS99sCt13M0v4gl67ZwaN9uivb+zIKKCv56w2DQDDyaVtAtwTEKZxgGOzaXU1Sg4+MbRfS1zxJVugnrzA/Q33kJ4luh3TAWlZhygbMKIUT9IcWaEKLeCw30Y3R6N6Ab+46cxGxyjKKt3LyHjcu/p8onhNgWCQzsmEyvdD8OH6wie28F2zeVs0MlkDT6VeJPrMCY9Rn6pMccHRJuGIsKj3LvBxNCCCdIsSaEaFDiwppW/zo2LJjdMSkU5O4jd2MGH238CT0gjJuHDaHnAD+KCx0L7jYJNqMlD6YouTcHl28jatX7eD9zD6rPFahrR6P8Atz4iYQQ4vykWBNCNFhxYU354/CB6LpO5s4c1m7aSumJowT6egPww+bN+Hp7kdDU0cc0v0Bjd1U8uzu/QJBxhOgt3xK6+m7MV16HGngNyurhzo8jhBBnJcWaEKLB0zSNrknN6ZrUHF3X0X5ZFmT7z+vxqCpi/UornqHN6ZTamgFXRXHogI3sveFktfkrnvZi+n17L9rSeajrbkF16YPSpG2yEKL+kGJNCNGoaL8rtMbd8Qd+2LCDHTt2UnV4D6sP72JdeAJ333glCcke5B21UVzkhbnjs+hf/h8bV+UTsOZTotI7YEmWSQhCiPpBijUhRKPl7WFlaLdUhnZLJb+olCXrtxEVGgzA5v1H+H7+fEKi46FjGyL//gr53x0jp8qLbRvKCc/MoHm3WAITw1FKcfBABds3llNWegovb0VSW0+imsttUyFE7ZNiTQhxWQj08+aGvh2rfy4prwDNROGeLGbvyaLSqykRsS3pk5hE3roT5JbHczDLk/ZZC6B9NzZtMrDbHfuWlRpszCwDkIJNCFHrnC7WTp06xcaNG9m/fz+lpaV4e3sTGxtL27ZtadKkSS2GKIQQrtetdSzdWseyOzePFeu3kJezh6Pb1uLbox1R16dg2rwHc9YGQlZ9xIqKlpzSC8gv3oBdL8Gk+RDom8b2jS2kWBNC1LoLFmsHDx5k2rRpbNmyhfj4eCIjI2nSpAllZWUsX76cDz/8kJSUFEaNGkVUlKxZJIRoWFpGBNMyoi+63pvs4wU08fEC4PtVKzFXFEGX62lSsZfisp0YOIbW7HoJJwp//OUIHdwUuRDicnHBYu3tt9+mQ4cO3HfffVgsljPet9lsZGZm8s477/DCCy/USpBCCFHbNE0jNjSw+udevXqzbvM2Ko5nU6QfOWN7Azsni9cjxZoQorZdcH76iy++yNKlSykvLz/r+2azmY4dO0qhJoRoVLqnxHPPqKHc8+c/YpxjG7teilFaXKdxCSEuP04tJtS7d29eeeUV7L8+Xfs7x44d48knn3R5YEIIUR94WMxUmTzP+l6VsqA/8RdOLlyObrfVcWRCiMuFU8XaqFGj8PPz49133z3t9S1btvDYY4+RnJxcK8EJIUR90KJtZ+z/89elAWiGncUt+rPqRBvW/d9qqrZtdU+AQohGzelluu+55x727dvH3LlzAZg7dy4TJ07ktttuY+zYsbUVnxBCuN11vdOITetJpckTA6g0eRLQoj12izfb9BJOVK7hiG8rVvwIBe+/h5F/wt0hCyEaEWUYxrkex6iWl5dHcHAweXl5PPHEE8TGxnLw4EEefvhh4uLi6iLOi5Kbm1vr5/g1L8I1JJ+uJzl1rd/ns7C0nP/7Zh7GyUP06TOcvB0W7HaDtjs/IqJrC1T6MNRZJmaJ08k16lqST9eri5xGRESc8z2n1lkbN24cvr6+xMbGEhYWxu7du3nooYdo3ry5y4IUQoiGxt/bk/vGDGPHwWO0jgmjvJXOsgUHKYtJxfjm3xgrF6HddBcqtZO7QxVCNGBOFWv/93//x/79+9m/fz/79u2jtLSU5557DpPJRHR0NLGxsfz5z3+u7ViFEKLe0TSN1jFhAMxfv5F9B1aSn9KF+E7jOTlnId7/fh3PVgmOoq3Zub85CyHEuThVrPn4+JCSkkJKym+NjW02G9nZ2dVFnBBCXO66p7Rg147tHNvyE28FNadV6z+itbSRlvUmTcffgxo0HHXVjShPL3eHKoRoQC66N6jZbCY+Pp74+HhXxiOEEA1WsyZ+/O3WG5k6dznF+zexpTCfVmEDWd3+IZLKM4md9xbqp6Voo+6CDt1RSrk7ZCFEA3DB2aBz586lqqrqvNtUVVVVzxIVQojLmcVs4s5r+9Om12Cwl2GEnCQ0wso2jy5k3fgfdJ8A9H+/jP76MxhHa38SlBCi4bvgyNqpU6e499576dChA8nJyURERODp6Ul5eTm5ubls3bqVDRs20Ldv37qIVwghGoSBHZJonxBDkJ83hmGw8Ic9KK9QTE9MgqVzMWZ+iv7MPagrbkBdOQJllYbwQoizu2CxNmbMGIYOHcqyZctYsmQJ2dnZlJSU4OvrS0xMDGlpaYwePRo/P7+6iFcIIRqMID9vAA4cy2fr5nnYvJoSmng1AV2GUhjVi/AVH2DMmYbx01K0m/6EatfZzRELIeojp55Zu//++/nggw+49tprazseIYRodGJDmxKb1ot9GzKY9vnnJMYNgOJmxHe6m6Reg+Dz/6C/9Ry064J20x9RwaHuDlkIUY841cHgbD1BhRBCOG947zQGXXs9usnC3j3zyTc2s3dnBT8djqPykddQ198G235GHz8O/bsvMS7wrLAQ4vLhVLEmM5aEEOLStYkN54+3jkFvEkG5RwVp3bwpOGlnxZJySnoOR3v2bWjTEWPGJ+j/vA9j+0Z3hyyEqAecug1aUVHBpEmTaN68ObGxscTGxtKsWbPajk0IIRqdJj5e/O3m6zAAk6axJy+HsmMa3j7+KFMIpr8+hrF5Hfpn/0F/9UlU9/6oG+9A+QW4O3QhhJs4VayZTCbi4uLYv38/K1as4NixY3h7exMTE1NdvPXv37+2YxVCiEZB0xw3NXRdZ83aVZgrCin26sawHh3ZuaWcVm06YHrmTYzvvsSY/y3GxrWoG25D9UxHaU7dEBFCNCJOFWtms5kRI0ZU/1xWVsaBAwequxcsWLBAijUhhKghTdO4eeRwPp0+h9yNGbybc4RIS3eOHamiU08f/K67BaNrX/RP3saY+hZGxhK0W+5GRcS4O3QhRB1yqlgzDOO0n728vEhKSiIpKalWghJCiMtFeKA/fxs7ig9mL6U8Zwt7rCdoZb6CFQt12nfxJiI6Bu3hFzEyFmN8/SH6s/ejhlyHGjpS1mYT4jLh1Hj6nXfeWdtxCCHEZctiNvGn6waS1D0dzS+AvlcE4edvYl1GKft3V6A0Da3XILTn3kZ16Y0x9yv0Z+7F2Lze3aELIeqAU8WadCcQQojaN7hzMvf/YTi+vmYikivJ07MICv3tr2nlF4B2xwNoDz0Pmgn99WfQ/zsJoyDfjVELIWqbPKkqhBD10Mqft1B0fCP/mfYVuXkFbFhdwsnjNgBUUlu08W+grh2DseFH9KfvRl+58IxHVoQQjYNTz6y5WmVlJePHj8dms2G32+nWrRsjR46kuLiYyZMnc/z4cUJCQnjggQfw9fVl9+7d/Oc//6ne/8Ybb6RLly7uCF0IIerEbVf14eul3uRs/InPv/iC+Gb9OXSgGcntvYhLsKIsFtQ1N2F07oX+8RSMj950tK26ZRwqNMLd4QshXEgZbvgqZhgGFRUVeHp6YrPZePrppxk7dixr1qzB19eX4cOHM2PGDIqLi7n55pupqKjAbDZjMpnIz8/nkUce4T//+Q8mk+m858nNza31zxIcHExeXl6tn+dyIfl0Pcmpa9V1PrP2HGLh/HlYbGXERA/AUhlJZIyFtp29MZsdC5Ybuo6xcgHG1x+BrQp1zU2oQcNRZrd8H68xuUZdS/LpenWR04iIc3/JcsttUKUUnp6egKOVld1uRylFZmZm9fNxffv2JTMzEwAPD4/qwqyqqko6KgghLhvtW0Ry1y1jsIYnMHBwPEmpnhzKqWJdRkn1NkrT0PpcgfbsW5DaEeObqegvPISxf5cbIxdCuEqNv3adOnWK3bt3U1RUdNrzEQMGDKjRcXRd59FHH+XIkSMMGTKEhIQECgoKCAwMBCAwMJDCwsLq7Xft2sU777zD8ePHuffee886qrZo0SIWLVoEwMsvv0xwcHBNP16Nmc3mOjnP5ULy6XqSU9dyRz6Dg+Hpv978y6/L+H7NJ8RH9iM4OBjDMH77AhscDE+9SvlPyyj676voLz2C99Uj8R39R5SnV53GXBNyjbqW5NP13J3TGhVra9as4c033yQ8PJycnByio6PJyckhKSmpxsWapmlMmjSJkpISXnnlFbKzs8+7fUJCAq+99hoHDx5kypQptG/fHqvVeto26enppKenV/9cF8PAMtzsWpJP15Ocupa787lp32Eqi4+x4LvP2JnbnUS/1mgKWqV6omm/FG0tU+CZN1DTp1I66wtKVy1Bu/luVJsObov7fNyd08ZG8ul6Deo26LRp07j77ruZOHEinp6eTJw4kT/96U/ExcVddHA+Pj4kJyeTlZVFQEAA+fmOKej5+fn4+/ufsX1UVBSenp7k5ORc9DmFEKKhSo0LZ9Tom7B5NSFnw0pWZS1l17ZSflpWQkW5Xr2d8vZFu+VutEdeAovFsczH+5MxSorcGL0Q4mLUqFjLy8uje/fup73Wt29fli9fXqOTFhYWUlLieN6isrKSTZs2ERkZSadOnVi2bBkAy5Yto3PnzgAcO3YMu90OwPHjx8nNzSUkJKRG5xRCiMYiKiiA+2+/CWtkEuWFuzhYmUH+CRvLFxRxMs922rYqMQXt6ddRQ0diZC5Hf3ocxroMN0UuhLgYNboN6u/vz6lTp2jSpAkhISHs3LkTPz8/dF2/8M6/k5+fz5QpU9B1HcMw6N69Ox07diQxMZHJkyezZMkSgoODefDBBwHYvn07M2bMwGQyoWkad95551lH3YQQ4nJhMZv4yw2Dmbc6goToMEK8fFmzspjVy4tJv9ofi/V3i+larKjhN2N06IH+0Rvo/34ZOvZAG/NnlH+gGz+FEMIZNVq645tvviEiIoJu3bqxbNky/vvf/6KU4uqrr+amm26qzTgviizd0fBIPl1Pcupa9TWfuq7z+sff4u8TyK3D+2Ixm9DtBprp9Nnzhs2GseBbjNmfg4cX6qY/orr2dess+/qa04ZK8ul67n5mzemRNV3XmT59Oh9++CHguP2ZkpJCeXk5UVFRlxykEEKIi1dp09HMZkpyN/P61GNc0WUIeQdNdOrpg6/fb7PnldmMuupGjLRu6B++gfH+axiZKxwTEAKD3PgJhBDn4vQza5qmERERQVHRbw+nBgcHS6EmhBD1gKfVzL2jryGsTTfMxXksWPY1J/KPsmJhEUcOVZ2xvQqPRnv0ZdTIO2H7z+jjx6GvWCAtq4Soh2o0waBXr15MmDCBpUuXsmnTJjZv3lz9nxBCCPfSNI2RA7rQ+4ph6MD+Ez/g6W2QubKEbRvL0PXTCzGlmdAGDUMb/wbEtMCY+hb65Kcxjh9xzwcQQpxVjSYYLFiwAICvvvrqtNeVUrz11luui0oIIcRF65gYTWzYGPYdOUFaiyZsWlfKzq3FBIeaCQm1nLG9ahaB9uBzGMvnY0z/EP2f96FGjEX1uQKluaXRjRDid2pUrE2ZMqW24hBCCOFCQf4+BPn7ALDuyBoKTu6jZflVhBBGZYWO1eP0IkxpGqrflRipndCnvonx6b8x1v+Idtu9qKBmbvgEQohfyVcmIYRo5Fo0j8LQK1kwazrfLs5i0ZxC9u+qOOvzaSooBO3+f6JuuRv27kQffy/68vnyLJsQblSjkbVp06ad871Ro0ZdcjBCCCFcr1+7BFpEBPPFt9+Rs2U53v5Hsa3rxMkTnrTt5I3ZfPqyHUopVJ8rMJLT0D96E+PjKRjrMtBuuwfVVBYkF6Ku1Whk7cSJE6f9t2fPHmbPns3Ro0drKz4hhBAuEB0SyH2334Q5IpHiwp34hBVx6EAVKxcVUVJkP+s+KjgU7YFnUWP+Anu2oT9zL/rKhTLKJkQdq9HI2t13333Ga1lZWaxcudJlAQkhhKgdHhYzd4+4gl2HOpIQGcKxw1X8uOIIh7KtJKaYzrqP0jRU/6sw2nRwrMv20ZuOUbZb75F12YSoI5f8zFrbtm3JzMx0RSxCCCHqQEKk41bmpsN72H/kW1bu+Qm7rlNSbMfQzz5qpkLC0B56HnXTn2DnJvTx96BnLJFRNiHqQI1G1v73dmdFRQUrV64kODjYpUEJIYSofZ2TYtm0NZri/Rt5/cOjtAroT9Mgbzp098bD48zv8krTUAOvxkjtgP7BGxgf/Atjw49ot4xD+Tep+w8gxGWiRsXafffdd9rPVquVuLg4xo0b59KghBBC1D5/b0/uGzOMaUvWcHRrJrvKZhFd0Z+SBcF06uFDk6Cz/xOhmkWgPfICxqLZGN9+jP7MvY6CLa1bHX8CIS4PLpsNKoQQouHRNI3R6d1YExXO8sXzsTU9CbYQVi0pJiXNi+YtrGdt8q40E2rwcIyUDuj/9xr62y+iug9wNIb39nHDJxGi8arRM2uzZs066+tz5sxxSTBCCCHco0tSc+4aews3Du5In0G+6NbjHDpYdsH9VGQM2mOTUFePwli9FP2f92Fs31gHEQtx+ahRsTZ9+vQavS6EEKLhaOLjhaZpnCovY3f2AjK2f8vOQ8cpLXFMPjgXZbagDfsD2qMTwGxBf/VJ9GnvYVRW1GH0QjReTt0G/bVRu67rZzRtP3r0KF5eXq6PTAghhFs0C/Chbc+B/LzqB7779iuiw3rhZ4olrZs3oRFn9hb9lYpvhfb06xjTP8RYNAtj83q0Ox9AxSbUYfRCND5OFWvvvPMOAJWVldW/Bscq1wEBAdxxxx21E50QQgi3GNghiRaRzfhq5hwOH15Gkd8xKpd3IjHFk1YpnijtzOfYAJSHB2rMnzHad0H/4A30lx5BDR2FuupGlLlGj0kLIX7h1J+cXxu4v/XWW9xzzz21GpAQQoj6ITa0KfeOHc173y6kjCpi4jzYtbWCUyftdOjmfUYz+N9TyWloz7yJ8fl/MGZ/jrFpLdqdD6LCIuvuAwjRSNToa84999zDqVOn2L17N0VFRacthjhgwACXByeEEMK9PK0W7hl1FXZdR1OK/KpjHD5cjqa1uuC+yscXdddDGO27on/8Nvpz96NG3YnqPeSsM0yFEGdXo2JtzZo1vPnmm4SHh5OTk0N0dDQ5OTkkJSVJsSaEEI2YSXOMoq3fsRpz8VE+WXCMPwzqybEjdiKiLectvlSnXmgtWqN/8C+Mj9/G2LgW7bZ7UX4BdRW+EA1ajWaDTps2jbvvvpuJEyfi6enJxIkT+dOf/kRcXFxtxSeEEKIeuXPUtehNoijck8V/Pp5B5qpT/JxZht12/rZTKjAI7f5/okbeCVvWoz9zL8amdXUUtRANW42Ktby8PLp3737aa3379mX58uUuDUoIIUT91MTHi7/dPJymrTphK8nlwMnZ7Nudz8rFxZSeZ3kPcLSr0gYNQ3viNfALQH/jn+if/RujoryOoheiYapRsebv78+pU6cACAkJYefOnRw9ehRd12sjNiGEEPWQpmncPKQHXdOvxggIonOvIMpKdJYvLCbvWNUF91dRsWhPvIpKH4bxw1xOPHwHxoE9dRC5EA1TjZ5ZGzhwINu3b6dbt24MHTqUf/7znyiluPrqq2srPiGEEPVU9+Q4uic7HoOpUuX8sDgTQ+sNnHsttl8pixU16k6M1I4YH/2yxMewP6CGDEdpplqOXIiGRRm/n9J5Abquo2m/Dcbl5eVRXl5OVFRUrQR3qXJzc2v9HMHBweTl5dX6eS4Xkk/Xk5y6luTz7L5eupbcjRlUWP0Zfs1QKPSjebz1vMt7/Kqp1cLx15+D9RmQmIJ2x4OooJA6iLpxkmvU9eoipxEREed8z+nboLquc8stt1BV9dsQd3BwcL0t1IQQQtSdEf06kdQ9HVNVKXO++Yp1mbtYvqCIUydtF9xX8w9A+8ujqLF/gwN70Z+9D2NdRh1ELUTD4HSxpmkaERERFBUV1WY8QgghGqjBnZMZNmIkNqsPx079wPGC3axaXMyBPRfuEaqUQus5EO3pydAsAv3fL6NPfUsmHwhBDZ9Z69WrFxMmTODKK68kKCjotHV12rRp4/LghBBCNCwtwoMZN3Y0n8xdTt9eiRzYoti4toySYp3kdhfuI62aRaA9+jLGzM8w5n+DsWsr2h8fRsXE10H0QtRPNSrWFixYAMBXX3112utKKd566y3XRSWEEKLB8vaw8qfr0gEI7F7F/32yAJ+ytiTT0qn9ldmCuuE2jOT26O9PRn/pYdQNt6EGXiudD8RlqUbF2q89QoUQQghnHMkvorTiJBvXzOPQqQ50a94B/yZmQsOdmDHauh3a+DfQP3oDY9r7GFuy0G6/D+UfWAeRC1F/1GidNYCNGzfyzjvv8PLLLwOwd+9eNm/e7PLAhBBCNHxxYU2565Yx6P5h5O9cx5KV8/lpaT47NpfjzGIEys8fbdwTqDF/hu0b0f/5N4zN6+sgciHqjxoVa/PmzePdd98lPDycbdu2AWCxWPjiiy9qJTghhBANX6CfN/ffegMBCWmUl+VwqHgFO7eUs2ZFCZUVF15UXSmF1n8o2pOvga8/+uvPoH/5PkbVhRfgFaIxqFGxNnfuXJ566imGDx9evd5aZGRknaxnJoQQouHSNI3bruxNx/5X0Tu9O6kdvTh2uJKVi4ux251b7lNFNnd0Puh/FcbCmegv/x3jmPz7Ixq/GhVrZWVlBAcHn/aazWbDbK7Ro29CCCEuU71SW5AaF0FMvIUDlSvZeWIlFTUYIVNWD7Qxf0Eb9zjkHUV/7gH01ctqMWIh3K9GxVrr1q2ZMWPGaa/NmzePlJQUV8YkhBCikTMAs48nlfm7efa1KWzYdIyfM0udH2Vr3w3t6dchKhbjvVfRP3xD1mQTjVaN2k3l5+czYcIEioqKOHnyJM2aNcPb25tHH32UJk2a1GKYF0faTTU8kk/Xk5y6luTTteat3sy2NcsxoREW0JvwsBg69fTB28e5sQTDbseY9TnGvK8gLArtz39HRTav5ajrN7lGXc/d7aZqVKwBGIbB7t27ycvLIygoiJYtW57WL7Q+kWKt4ZF8up7k1LUkn653tKiCqZ9+jqWqjBZhN2Axe9ChuzfNwi68vMevjK1Z6O+/BmWlqJvuQvUectmuySbXqOu5u1ircZWllCIhIYHu3buTmJhYbws1IYQQDUNKXCR3jx1DryFD6X9FEB6ekPFDPgX5dqePoZLbo41/HRJSMD5+G+M/EzFKS2oxaiHqTo1mBthsNqZPn86qVavIz88nMDCQHj16cP3112O1WmsrRiGEEI2cj6eVTokxABxiC3kntrD96CC6BsZiGIZTo2TKPxDtb+Mx5n+LMeNjjAO70f70CCousbbDF6JW1WhY7N1332Xz5s3cfvvtvPTSS9x+++1s27aN9957r7biE0IIcZlJbhmDTYMfF8zmk+8yWPp9IQX5Nqf2VZqGduUNaH9/GQwDfcKj6Au+dWoBXiHqqxqNrGVmZvLmm2/i4+MDQFRUFAkJCdx77721EpwQQojLT4eEKJqHjuHD6d9xcs9ayjyPU1zYg/ZdAoiOc+4ujmqRhPbUv9Cnvonx1QcYO7eg3X4/yse3lqMXwvVqNLLWpEkTKioqTnutsrKSwEDp0yaEEMJ1gvx9uP+2EfjFt6OkPBu79SRZa0rZuLYGy3v4+KL95R+om/4Im9ejP3c/xr6dtRy5EK5Xo5G1Pn368OKLL3LFFVcQFBTEiRMnmD9/Pn369DmtP2ibNm1cHqgQQojLi0nTuP3qvuw/mkpMSCA7NpWzdfNRfHzDaJHk6dQxlFKogddgxLdC/89E9An/QI0Yixp4zWU7W1Q0PDUq1hYuXAjAt99+e8brv76nlOKtt95yUXhCCCEud7GhTQEosB7l4IlZHNmYwJ3xg7BoJkxm5wouFZeI9tRk9A9ex5j2HsauLWi33Yvyltuiov6rUbE2ZcqU2opDCCGEOK+0llGs35KILXcnb32YR+uQgSS2akrL1h7OzRb18UMb9wTGwhkY30xFf/5BxyK6zVvWQfRCXDxZJE0IIUSD4GExc/eIK4jv1A9TRSF7Ds5mw9q9ZK4soapSd+oYSim0wdehPfIS2G3oL/8d/YfvZLaoqNdqNLJWWlrK3Llz2b9/P+Xlp/dge/LJJ10amBBCCHE2V/doy7boUObMmUuFz0mOHY5g+cJiOvf0wb+JyaljVM8W/b9/YXz2H9i5BW69B+XlXcvRC1FzNSrWXnvtNXRdp0uXLrIIrhBCCLdpHR1KzO1/wMtq5tQJnR8W72XD2qb0TQ92+hjK1x/tnid/W0Q3ew/aX/+BioqrxciFqLkaFWu7du3i/fffx2yu0W5nqKysZPz48dhsNux2O926dWPkyJEUFxczefJkjh8/TkhICA888AC+vr5s3LiRTz/9FJvNhtls5pZbbpEZp0IIcZnz8XQMGnj42dift4T9J0z4xAyhbfMoTGaFyeTEc2yahrryBowWSejvTkJ/6RHUH/6K1mNgbYcvhNNq9MxaUlIShw4duuSTWiwWxo8fz6RJk5g4cSJZWVns3LmTGTNmkJqayhtvvEFqaiozZswAwM/Pj0cffZRXX32VcePG8eabb15yDEIIIRoHH08rfQZfhYHByu9n8vX0TFYtLqKs1Lnn2ABUYgraU5MhrhXGB6+jT30Lo6qyFqMWwnk1GiK7++67eemll2jZsiVNmjQ57b0RI0Y4fRylFJ6ejjVy7HY7drsdpRSZmZk888wzAPTt25dnnnmGm2++mbi434ako6OjqaqqoqqqCovFUpPwhRBCNFKdE2NoHvoHPp4+h7y81ZQVH6ekuCedevoSEurcvxXKPxDtgWcxZn6KMe9rjAN70P7yKCokrJajF+L8alSsff7555w4cYKQkBDKysqqX7+YhQV1XefRRx/lyJEjDBkyhISEBAoKCqq7IQQGBlJYWHjGfqtXryYuLu6shdqiRYtYtGgRAC+//DLBwc4/u3CxzGZznZznciH5dD3JqWtJPl3PVTkNDg7muYf+whufz6Y4vwAfHwurl5XQoWtTUjsEOv9v1Z8epCKtCwX/ehbjhYfwv/9pPDr1vOT46opco67n7pzWqFjLyMjg9ddfd0l7KU3TmDRpEiUlJbzyyitkZ2dfcJ+cnBw+/fRTnnjiibO+n56eTnp6evXPeXl5lxznhQQHB9fJeS4Xkk/Xk5y6luTT9Vyd01uv6IWu6+h2xZIlB1mx6gAh4W2xWGswsBCXhHryNfR/v8ypFx5BXXUjatgYlObcbFN3kmvU9eoipxEREed8r0bPrIWGhmIyufZC9fHxITk5maysLAICAsjPzwcgPz8ff3//6u1OnDjBK6+8wrhx4wgLkyFpIYQQ56ZpGmaLYuvxdRzNW8Z7s+ZTWl5FUaHd6WOokDC0Ryegeg3CmPsV+r+ewSg8VXtBC3EONSrWevfuzcSJE1m5ciWbN28+7b+aKCwspKSkBHDMDN20aRORkZF06tSJZcuWAbBs2TI6d+4MQElJCS+//DKjR48mKSmpRucSQghx+frLyKsxhbWkKncn73/0FUvmHeXgfucnDiirh6Mt1dj7YPc29OcewNi9rRYjFuJMyqjBss3jxo07+0Fq2A/0wIEDTJkyBV3XMQyD7t27M2LECIqKipg8eTJ5eXkEBwfz4IMP4uvry/Tp05kxY8ZpI2pPPvkkAQEB5z1Pbm6u0zFdLBludi3Jp+tJTl1L8ul6dZHTmSuz2Lt+FWbNTETgEBKTmpHS3gvNieU9fmVk70X/98tw8jjqxjtQA66ul83g5Rp1PXffBq1RsdbQSLHW8Eg+XU9y6lqST9erq5xuPnCERSt+on/SQLL32AkMMtGxhw9e3s7fZDJKi9H/71/w8xpUl76oW+9BeXjUXtAXQa5R13N3sVbj1W03btzIqlWrKCgo4B//+Ad79+6ltLRUFqkVQghRr7VpHkab5sMB8PAtIGPlKpon9yTa28/pYyhvX7S7H3cs7THzU4zcA2h/fQzVLLyWohaihs+szZs3j3fffZfw8HC2bXPcs7dYLHzxxRe1EpwQQghRG7KLDlFYuotpM6axftdBjuZWOd3MXWka2tCRaPeNh5N56C88iLFpbS1HLC5nNSrW5s6dy1NPPcXw4cPRNMeukZGRdXK7UQghhHCVwZ2T6Zp+NRg6y+fNYPGCLNZmlFJV5fyTQapNB7QnX4OgZuhvPoc+63MM3fmuCUI4q0bFWllZ2RmLwv3ar1MIIYRoSLonx/GHMTdh8wkir/BHtu/IYsXCIooKarq8x0RU134Ysz9Hf+t5jJLiWoxaXI5qVKy1bt26ul/nr+bNm0dKSoorYxJCCCHqRHigP3+7bSR+8e3o3CcZW5XBioVF5ObUYHkPDw/UHfejxvwZtm5w3BY9uK8WoxaXmxoVa3fccQdr1qxh3LhxlJeX87e//Y2ffvqJ2267rbbiE0IIIWqVxWzi9qv7ktQykO4DvMnJ/4F1O3fW6BhKKbT+Q9EefhEqK9FfegR99bJailhcbpy6f7ly5Up69epFYGAgL730Env27OH48eMEBQXRsmXL6ufXhBBCiIaszF5OoV5IxZYl/KfgMFem9SIk1MPp5T1Uy9ZoT01G//cEjPdeRd+/C3XDWJQ8LiQugVNX37vvvlv9a6UULVu2pHv37iQmJkqhJoQQotFo1sSPcWNHo5rFU3FwG/Pmz2Lx3GPkHaty+hgqIBDtoedRA6/BWDQL/V/jMYoKajFq0dg5VWk14nVzhRBCiNN4e1i596ariWzfi7LK4+QcX8KPPxSzZ3u588t7mM1oN/0Rdfv9sGc7+gsPYWTvqd3ARaPl1LisrusX7P8pi+IKIYRoTG7o04Gfo0KpqLCjnbSyJauUkydsdOrh43SbKa3HAIyIaPS3X0Kf8Cjq1nvRuvat5chFY+NUsVZVVcW///3vc36jqGlvUCGEEKIhaBcfCTjuMK3/dCU520tIaH8lTXy8nD6Gik1Ae/LV355jy96Luv5WlMlUW2GLRsapYs3T01OKMSGEEJctpRSeQT6U7trJux99Ru9ug4kODiUyxurc/v6BaA8+h/Hl+xgLvsU4uA/tT4+gfJxvdSUuXzI7QAghhHDCrVf2otOAoSjdxpqVs1i2ZBObN5Sh684+x2ZBG/MX1K33wM7N6M/LemzCOTLBQAghhHBSrzbxjBk9mkqvJhwv/Ild2/L58YdiysucbzOl9R7sWI/NVoX+0t8x1q6sxYhFY+BUsTZ16tTajkMIIYRoECKC/Pnb7TfR64pr6dIzmIJ8O4vnHqes1PmCTbVIQnviNYiOQ//PRPRvPsLQnW9zJS4vchtUCCGEqCGL2UTHxGgim1spCdjN7txvWLF1e42OoZo0RXv4BVSfIRjzpqO/9QJGWWktRSwaMinWhBBCiEvQPrk5lRYvtmcs4t3pi1n/UxG2qho8x3bLONQf/uLoK/rSIxjHcms5YtHQSLEmhBBCXIKEyBDuHjsGgmMpO7SFtVnfs2jeMYoKnb+tqfW7Cu3+f0LRKfQXHsbYmlV7AYsGR4o1IYQQ4hL5eFq5b8y1hKd2p7TyKAVFx1ixsIjcnEqnj6GS2qI9/ioEBqG//gz64tkywU8AUqwJIYQQLnNj/87cMPpmrr0uBf8AEz8uO0TO/nKn91chYWj/mABtO2N88S7G1LcwqpzvSyoaJynWhBBCCBeKDmmCl7dGQItiDp6cw/TlcyksrUHB5umN9tfHUENHYqxciP7akxiF+bUYsajvpFgTQgghakFy81D8W7RDnTrIfz/6jHlzsjlx3ObUvkrT0IbfjPrTI5C9RxrBX+akWBNCCCFqgUnTuH1oH9r3uxLNXsmufXNYMHcTe3dWOP0smta5N9rfJ4AB+oRHZQHdy5QUa0IIIUQt6ts2gRtHjaLS058K7RRbNpSx/qdS55f3aN4C7clXITresYDuzM8wdOcX4BUNn1ON3IUQQghx8aJDArl37E0o4MBuG1lrcygq86PfgDCn9lf+gWgPvYDxydsYc76Awzlw+/0oD4/aDVzUCzKyJoQQQtQBD4sZq8VMbIKFnKLlrN86gx+ydjrfCN5iQY29DzXidoz1GeiTHsPIP1HLUYv6QIo1IYQQog5ZzCauuuYa7CYPNi7/nqmfLmPzhhKnijalFNqQ69DGPQFHDqG/+BDGgd11ELVwJynWhBBCiDqWFN2Mv4wdg9E0hsL8jfy4eh4rluRTUe7cs2iqXRe0f7wMmgl94j8w1q2q5YiFO0mxJoQQQriBn5cH9425lpDkrlR4mCnKVyxfUMTJPCeX94iKQ3viFcfEg39PQJ8zTToeNFJSrAkhhBBuomkao9O7cvdt19JnkD8VtiLmzVuPrcq5vqKOiQfPo7r1w5j5KcZ7r2JUVNRy1KKuSbEmhBBCuJmmafg3MZFj38yJ/J94a9psCkrKsdmceI7NYkXd8QDqulsw1iwn/+l7MAqk40FjIsWaEEIIUU/86YbB+MSmok5m89FHX/D97ByKiy48yqaUQrvqRrS//oOqA3scEw+y99ZBxKIuSLEmhBBC1BMmTePOa/uT2nsIdns5+w5+x/zZezl8sNKp/VWHHjR98R1Hx4OJ/8D4eU0tRyzqghRrQgghRD0zIK0V140chREYQWDTpqxdVcrWn8ucWt7DEt8K7fFXICwKfcoL6ItmysSDBk6KNSGEEKIeig0N5L6bh9F3UFPCYuCn1UvYtd+5Z9FUk6Zoj7wI7btiTHsf47P/YNidm7Qg6h8p1oQQQoh6zGRSVPmfpKBiP3PmfsmyjbsoLbnwemzKwxPtL/9ADbkOY+lc9LeewygrrYOIhatJsSaEEELUcz1S4hl07Q3oJitZS+fx9bRV7NlRdsHbm0rT0EbcjrplHGzNQp/wKMaJY3UUtXAVKdaEEEKIBqBN8zD+eOtojCZRnCrewMoVGWxYXerU8h5anyFof3sGTuahv/gwxr6dtR+wcBkp1oQQQogGoomPF/fdPJyQ1l1ISEnh0IEqViwsdG55j+T2aP+YAFYP9EmPS4uqBkSKNSGEEKIB0TSN0YO60aN7GJ17e7EnZynfLV3v1L4qIgbtsUkQ80uLqnnTZaZoAyDFmhBCCNFAeTcxKDCVcnTfj7zx2Sxycy+8vIfyb+JoUdW5N8Y3H2F89CaGraqOIhYXQ4o1IYQQooHy9/bkvttG4hWTAnn7mTnja77+YisV5eefLaosVtRdD6GuHoWxahH6G89ilJbUUdSipqRYE0IIIRowi9nEH4cPpHWPQVTYi9m+ax7L5heQf8J23v2UpqEN+wNq7N9g52ZHx4MTx+soalETUqwJIYQQjcCgTq25dsSNdOl/BZrJxMpFhezeceF11bSeA3+ZKXoc/aVHMLL31H6wokakWBNCCCEaifjwYK7o04Y+g3zJq/iZeUtnkXui8IL7qdbt0B6dACYNfeJjGJvW1kG0wllSrAkhhBCNjNVDw7+5P7aKPD77/HN+WLObkuLzL++hIps7ZoqGRqC/9Tz6su/rKFpxIVKsCSGEEI3QDX07MvDq6zE0M5t+msc3X/3E4YMV591HNQlCe+QlSOmA8cnb6F9/iKFfuLWVqF1SrAkhhBCNVNv4CO66ZTS6fzj5RRvIWHaE7ZvKMM6zvIfy9EIb9wSq7xUY87/BeO9VjKrKOoxa/C+zO05aWVnJ+PHjsdls2O12unXrxsiRIykuLmby5MkcP36ckJAQHnjgAXx9fSkqKuK1115j9+7d9OvXjzvvvNMdYQshhBANTqCfN/fdej1Zu3MxnWrKrq0V5OYW0mdAM8wWddZ9lMkEf/grBIdiTP8IIz/PUcD5+tdx9ALcVKxZLBbGjx+Pp6cnNpuNp59+mvbt27NmzRpSU1MZPnw4M2bMYMaMGdx8881YLBZGjRpFdnY2OTk57ghZCCGEaLA0TaNDYhQA+/J3s3nHCvI9u3FD347n3EcphbriBvSgUIz/m4z+0t/R/jYe1Sy8rsIWv3DLbVClFJ6engDY7XbsdjtKKTIzM+nbty8Affv2JTMzEwBPT0+SkpKwWq3uCFcIIYRoNLp0iqXSO5BDP6/irc/msGtH8XlbTmmde6E99ByUFqG//HdpAu8GbhlZA9B1nUcffZQjR44wZMgQEhISKCgoIDAwEIDAwEAKCy883fj3Fi1axKJFiwB4+eWXCQ4Odnnc/8tsNtfJeS4Xkk/Xk5y6luTT9SSnrnWhfAYHB5P00N1M/vhbSvZvYvHiAo4dG8LQaxIxm88xhhPcB1t0LKeeexD7q0/S5KHn8Ojcs5Y+Qf3j7mvUbcWapmlMmjSJkpISXnnlFbKzsy/5mOnp6aSnp1f/nJeXd8nHvJDg4OA6Oc/lQvLpepJT15J8up7k1LWczeed1/Zn3poQdq5ewYE9B5g5zYNOPb3x8TWdfQcPb4xHXoI3n+PUS4+ibv4rWp8hLo6+fqqLazQiIuKc77l9NqiPjw/JyclkZWUREBBAfn4+APn5+fj7y4OMQgghRG25sksbbrr5ZgYObktZqc782fs5fvTcy3uogEC0h1+AlPYYH09Bn/nZeW+hCtdwS7FWWFhISYmjYWxlZSWbNm0iMjKSTp06sWzZMgCWLVtG586d3RGeEEIIcdkIDfQjNMJCXJqNg8e/Z+qcbziaX3TO7R1LezyJ6jkQY84XGB+9gWE7fx9ScWncchs0Pz+fKVOmoOs6hmHQvXt3OnbsSGJiIpMnT2bJkiUEBwfz4IMPVu8zbtw4SktLsdlsZGZm8uSTTxIVFeWO8IUQQohGp1VsEBtTu3Bo02o+/uxz2rQcSP9+cXh4nDmuo8xmuO0+aBqCMfsLjIJ8tD8/ivL0ckPkjZ8yGvH4ZW5ubq2fQ561cC3Jp+tJTl1L8ul6klPXutR8bth9kB/mf4/ZXkbTJp24emhnmgSde2xHX7EA45O3ISoO7b6nUQGBF33u+uqyf2ZNCCGEEPVHWssobrt1DLpvGFVVRaxaUsyBPRXnfDZN6z0Y7Z4n4chB9JcewThysI4jbvykWBNCCCHEaYL8vLl37A2MvKk/Qc3MZP54kOUrz12EqdROaA+/CJUV6C8/irF7Wx1G2/hJsSaEEEKIM5g0DR8fC517epFbnMH6rFnMXJl1zu1VXALaPyaCjx/6a09hZK2uu2AbOSnWhBBCCHFOJrOJ6264BptnAAfWL+fdj+aRc6D0rNuqZuFo/5gAUbHob7+EvmJBHUfbOEmxJoQQQojzig5pwn1jb8ISnkhZwS6+++5b1mWexNDPfI5N+QWgPficYy22qW+hz5kma7FdIinWhBBCCHFBHhYzf73xCuI79sOwenFoD6xeUUJlhX7GttVrsXXrjzHzU4zP/oOh290QdePgtnZTQgghhGh4ru7ZFqNHKgf2VJK19gTTpmUx+g/dMZtOb1OlzGa4/W8Q0ARj/rcYRafQ7nwQZbG6KfKGS0bWhBBCCFEjSiliW3pwynM3+afW8/pHX3P0VPGZ22ka2ojbUSPvhHUZ6P96BqO0xA0RN2xSrAkhhBDiotx6bS9CkrtiKj7G559+wfff78VuP/P5NG3QMNRdD8Ge7eiTHsM4dcIN0TZcUqwJIYQQ4qJomsbo9K70vGIYCti5cy4zpm+ltOTM59O0rn3R7nsKjh91rMUmi+c6TYo1IYQQQlySzokxjL55NOamcXhoISxfUMyxw1VnbKeS09AeecGxeO6ERzH27XRDtA2PFGtCCCGEuGTNAny4++ah9B8ShNVDZ/bs+WzcdfiM7VTzlo612Lx80F95AmPzejdE27BIsSaEEEIIl/HxMxHUqozCyoMs/v4b5vy4Ef1/nmNTzSLQHp0AoRHobz2Pvma5m6JtGKRYE0IIIYRLtWsRwXU3jsLm4c/ezKV8+NFCjh+vOG0bFRDo6CfaIgnjvVfRf/jOTdHWf1KsCSGEEMLlYkMDuXfsaCwhCRQXb2fWjEVk7/2fgs3bB+3+Z6BdF4zP/oM+6zPpdnAWUqwJIYQQolZ4Ws38dfSVxLTvQ0R4Kj9nlpG1puS05T2UxYr2l3+geg7EmP0Fxuf/wdDP7IpwOZMOBkIIIYSoVcP7tEfXDbZtLGP1mh/Iyvbjlut7YdIcY0bKZILb7gNff4z530JxEdxxP8pscXPk9YOMrAkhhBCi1mmaokWylWKPSgpzs/jXR19zJO+3rgdKKUe3gxFjMTJXoL/1PEZFuRsjrj+kWBNCCCFEnfC0mrnnlmEEJXXCVHSU6dO+ZPHSA6c9p6YNuR419j7Y+jP6q09iFBe6MeL6QYo1IYQQQtQZTdP4w+AedB14DXbDzvbNC/hxaQGVlb89p6b1TEf76z8gZx/6xMcwTua5MWL3k2JNCCGEEHWue0osI8eMIqFNf07mwfL5RRw9Vlb9vkrr5pgpmp/n6HZwGbenkmJNCCGEEG4R1tSfwf1a0qO/L4dPbGLa9K/Ydeh49fuqVSraIy9CVaVjhC17jxujdR8p1oQQQgjhVk2DzTRLCsJmK2H2N1/x3cpN1ct7qJgWaH9/GSxWR3uqXVvdHG3dk2JNCCGEEG43pFtrho+4EbvVlz3rf2Dq1MUUFjqawauwSLRHX4aAQPR/PY2xeZ2bo61bUqwJIYQQol6IDw/m3ttHY2nakqKibSyae4DjR34p2JqGoD3yEoRFob/1AsbalW6Otu5IsSaEEEKIesPTauGvN19Fr0HX0zSgGT8tK2H16mMYhoHyb4L20AsQl4j+31fQVyxwd7h1Qoo1IYQQQtQ7HVpH0muQH7r3EVav/pKp81ai6/ov/UT/CSlpGFPfQl/wrbtDrXVSrAkhhBCiXjKbFX36x2APCKdg9wZen/oNOYeKUB4eaOMeR3XqhfHVB+jfftKoG8BLsSaEEEKIeivQ15u/3XIdgYkd0QoPM3vG16z8KQdltqD++BCq92CMuV826gbwUqwJIYQQol7TNI1bruhJ+95XYTds7N92kE3rSjEMDXXLONSQ6zB+mIvxwb8wbDZ3h+tyZncHIIQQQgjhjL5pLUiOC+XoPsW+nZXsyz5Mr/6RBN4wFrx9Mb79GKOsFO3Pf0dZrO4O12VkZE0IIYQQDUZIE1/apPmQ0E5x4OAC/m/aNPYeOYF21Y2oMX+Bn9egv/kcRkW5u0N1GSnWhBBCCNHgJCUF0LJrb7TKEmZ+/RWzF21B9bsSdfvfYPsm9H+NxygtcXeYLiHFmhBCCCEapCu7tOGa629EM3uzb+tiPvz4B6o69EP78yOwbxf6a09hFBW6O8xLJsWaEEIIIRqshMgQ7hp7E5aAeIzyclYtLqGoRTe0cY9Dbjb6K49jnDrp7jAviRRrQgghhGjQfL08+OttVzP02oHYbAaL5mbzQ1Eg2n1Pw4lj6JMewzhxzN1hXjQp1oQQQgjRKISGedBnsB9Hi9eyae1cPj1QDH/7JxQXok/8B8bRXHeHeFGkWBNCCCFEo+HppTFy9FBs/mGc3LGWf6/YTt4fn4WqKkfBduiAu0OsMSnWhBBCCNGoBPl5c/+tN+Af2x578UGmL1vFllFPgaahT3ocY/8ud4dYI1KsCSGEEKLRMWkaY6/tQ5tuV2CyBLB/XxB7R03C8PRCf/VJjF1b3R2i06RYE0IIIUSjNaBLAnfePpyIaE+27LLzcfJoygObof/raYytWe4OzylSrAkhhBCiUTNbFB17eFPufZCiU1t4O7Iz+yOTHJ0ONma6O7wLkmJNCCGEEI2eUoqbhnWiRed+mCqLmO0XxfcpI9Dffglj/Y/uDu+8pFgTQgghxGVjaPe2XDlsBGaTF3v043yddie2/76CnrnC3aGdkxRrQgghhListI4J5bbbRuHVpBUe/h1Y3f2flH30PnrGYneHdlZSrAkhhBDisuPn48kfbx1C555BFHhH8Hnqdfz03UL05d+7O7QzSLEmhBBCiMtWZIyVuDSdYttx1oRG8vnKTdgWznZ3WKeRYk0IIYQQl7XklsHcfPNo7L7NOOHrwXu7yjjx3Qx3h1XN7I6TVlZWMn78eGw2G3a7nW7dujFy5EiKi4uZPHkyx48fJyQkhAceeABfX18Avv32W5YsWYKmadx+++20b9/eHaELIYQQohEKDvDh/rE3MvWr5RQd3cjX2WEEfjifY8U56HopmuZNWHwHRlzVoc5jc8vImsViYfz48UyaNImJEyeSlZXFzp07mTFjBqmpqbzxxhukpqYyY8YMAA4ePEhGRgavvfYaTzzxBO+//z66rrsjdCGEEEI0UiZN4/ZR/WiVNghPSzOOFu5G10sB0PVSDu/+ka/nrq/zuNxSrCml8PT0BMBut2O321FKkZmZSd++fQHo27cvmZmOheoyMzPp0aMHFouFZs2aERYWxu7du90RuhBCCCEauSG9W1NUvhsD+2mvG9g5srfuizW33AYF0HWdRx99lCNHjjBkyBASEhIoKCggMDAQgMDAQAoLCwE4efIkCQkJ1fs2bdqUkydPnnHMRYsWsWjRIgBefvllgoODa/1zmM3mOjnP5ULy6XqSU9eSfLqe5NS1JJ+u8euI2tler+v8uq1Y0zSNSZMmUVJSwiuvvEJ2dvY5tzUMw6ljpqenk56eXv1zXl7eJcd5IcHBwXVynsuF5NP1JKeuJfl0Pcmpa0k+XUPTvM9asGmad63kNyIi4tyxuPxsNeTj40NycjJZWVkEBASQn58PQH5+Pv7+/gAEBQVx4sSJ6n1OnjxJ06ZN3RKvEEIIIRq/sPgOKEynvaYwERZ/mUwwKCwspKSkBHDMDN20aRORkZF06tSJZcuWAbBs2TI6d+4MQKdOncjIyKCqqopjx45x+PBhWrZs6Y7QhRBCCHEZGHFVB8JbdkfTvAHHiFp4y+5umQ3qltug+fn5TJkyBV3XMQyD7t2707FjRxITE5k8eTJLliwhODiYBx98EIDo6Gi6d+/Ogw8+iKZp3HnnnWia2wcFhRBCCNGIOQqzDm6/tawMZx8Ia4Byc3Nr/Rzu/g1sbCSfric5dS3Jp+tJTl1L8ul6dZHTev3MmhBCCCGEODcp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6jEp1oQQQggh6rFG3cFACCGEEKKhk5G1S/SPf/zD3SE0KpJP15Ocupbk0/Ukp64l+XQ9d+dUijUhhBBCiHpMijUhhBBCiHpMirVLlJ6e7u4QGhXJp+tJTl1L8ul6klPXkny6nrtzKhMMhBBCCCHqMRlZE0IIIYSox8zuDqAhyMrK4oMPPkDXdQYOHMjw4cNPe98wDD744AM2bNiAh4cHd999N/Hx8e4JtoG4UE63bNnCxIkTadasGQBdu3ZlxIgRboi0YXj77bdZv349AQEBvPrqq2e8L9dozVwon3J91lxeXh5Tpkzh1KlTKKVIT0/nqquuOm0buU6d50w+5TqtmcrKSsaPH4/NZsNut9OtWzdGjhx52jZuu0YNcV52u9245557jCNHjhhVVVXGww8/bOTk5Jy2zbp164wXXnjB0HXd2LFjh/HYY4+5KdqGwZmcbt682XjppZfcFGHDs2XLFmPPnj3Ggw8+eNb35RqtmQvlU67Pmjt58qSxZ88ewzAMo7S01Ljvvvvk79JL4Ew+5TqtGV3XjbKyMsMwDKOqqsp47LHHjB07dpy2jbuuUbkNegG7d+8mLCyM0NBQzGYzPXr0IDMz87Rt1q5dS58+fVBKkZiYSElJCfn5+W6KuP5zJqeiZpKTk/H19T3n+3KN1syF8ilqLjAwsHoEwsvLi8jISE6ePHnaNnKdOs+ZfIqaUUrh6ekJgN1ux263o5Q6bRt3XaNSrF3AyZMnCQoKqv45KCjojD8QJ0+eJDg4+LzbiN84k1OAnTt38sgjj/Diiy+Sk5NTlyE2OnKNup5cnxfv2LFj7Nu3j5YtW572ulynF+dc+QS5TmtK13UeeeQR7rrrLlJTU0lISDjtfXddo/LM2gUYZ5ks+7+VtjPbiN84k6+4uDjefvttPD09Wb9+PZMmTeKNN96oqxAbHblGXUuuz4tXXl7Oq6++ytixY/H29j7tPblOa+58+ZTrtOY0TWPSpEmUlJTwyiuvkJ2dTUxMTPX77rpGZWTtAoKCgjhx4kT1zydOnCAwMPCMbfLy8s67jfiNMzn19vauHo7u0KEDdrudwsLCOo2zMZFr1LXk+rw4NpuNV199ld69e9O1a9cz3pfrtGYulE+5Ti+ej48PycnJZGVlnfa6u65RKdYuoEWLFhw+fJhjx45hs9nIyMigU6dOp23TqVMnli9fjmEY7Ny5E29vb/kL5jycyempU6eqv8Hs3r0bXdfx8/NzR7iNglyjriXXZ80ZhsG///1vIiMjufrqq8+6jVynznMmn3Kd1kxhYSElJSWAY2bopk2biIyMPG0bd12jsiiuE9avX89HH32Eruv079+f66+/ngULFgAwePBgDMPg/fff5+eff8ZqtXL33XfTokULN0ddv10op99//z0LFizAZDJhtVq59dZbadWqlZujrr/+9a9/sXXrVoqKiggICGDkyJHYbDZArtGLcaF8yvVZc9u3b+fpp58mJiam+rbR6NGjq0cp5DqtGWfyKddpzRw4cIApU6ag6zqGYdC9e3dGjBhRL/69l2JNCCGEEKIek9ugQgghhBD1mBRrQgghhBD1mBRrQgghhBD1mBRrQgghhBD1mBRrQgghhBD1mBRrQgghhBD1mBRrQgghhBD1mBRrQohG78EHH2TLli0XvV1hYSGPPPII+/btq43w+Oyzz/juu+8uev/HHntMmnQL0YjJorhCiHpn3LhxnDp1Ck3T8PT0JC0tjTvuuKO6z2FdstlsTJo0iRtuuIHExESXH//XQvDNN9/EarVe1DEyMjLIyMjg4YcfdnF0Qoj6QEbWhBD10qOPPsrHH3/MhAkT2LNnD9OnT3dLHGazmccee6xWCjWApUuXkpaWdtGFGjj6FW7ZsoX8/HwXRiaEqC/M7g5ACCHOp2nTprRv3776Nt/Bgwd577332L9/P02bNmXMmDF06tQJgBkzZjBv3jzKysoIDAzkrrvuIjU1lXHjxvHnP/+Ztm3bApCXl8eHH37Itm3bMAyDnj17cuedd56x3fnONW7cOIYMGcLy5cs5fvw47du3Z9y4cWctuj755BMOHz7MI488AsDHH3/Mvn37ePzxx9mwYQP9+/c/bfvFixfz008/0axZMzIyMvD39+eRRx5h48aNzJ49m8rKSv70pz/RtWtXAKxWK/Hx8fz888/069fP9b8JQgi3kpE1IUS9lpeXx4YNG4iNjcVmszFhwgTatm3Le++9xx133MEbb7xBbm4uubm5zJ8/n5deeon/b+deQtrY4jiOf4kSX9hWScRHfRQUBBVpdCEoulYpioLQRaXgAxVx1VqwOwVFXGrAhW6EiKB00aUbuyjtRtFFFUFbMtP0AYYUuohiotzFxblM08pNuXDH8vuscs6cOf8zWf04h5mVlRWeP3+O1+tNmO/y8pLZ2Vk8Hg9+v5/FxUUaGxsTxl1X68rbt2+ZmJjA7/djmiavXr366TN0dHSwv79PMBhkc3OTvb09njx5QmpqKqZpUlhYaBtvGAbv37+noaGB5eVliouLmZ6eBmB+fp7u7m5evHhhu6eoqAjDMJL9e0XkBtDOmog40tzcHCkpKWRmZuLz+ejq6uLo6IizszM6OztxuVxUV1fj8/l4/fo1zc3NxGIxQqEQt27dIi8v76fzHh8fE4lEePToESkpKQBUVlYmjLuuVk9PDwCtra3k5uYCUFdXRzAY/GnN7Oxs2traWFhYIBqNMjk5SWZmJgDRaJSMjAzbeMMw6OzspKamBoC7d+8Sj8dpa2sDoLi4mIuLC9s9GRkZOgYV+UMprImIIz19+tQ6jrzy7ds3PB4PLtc/hwJer5dIJEJ+fj6PHz9mfX2dUChEbW0tvb29Vpi6Eg6H8Xq9VlD7letqXblz54712+1226796N69e2xsbDA2NobH47H6s7KyOD09tY01TZPBwUGrHQqF8Pl8tvaPu3Gnp6dkZWVd+0wicjPpGFREboycnBzC4TCXl5dWXzgctgJZU1MTU1NT+P1+AAKBQMIcHo+HcDicsDOVbK1kmKbJ0tISLS0tbG1t2a6Vlpby5csXq31yckI8HqegoMDqMwyDsrKyX7YBPn36RGlpadJrExHnU1gTkRujoqKC9PR0Xr58STweZ39/n52dHRobG/n8+TPv3r0jFovhdrtxu922XbEr5eXl5OTkEAgEODs74/z8nMPDw6RqJSMSiTA7O8vAwAD9/f2Ypmn7ltv9+/c5ODiw2oZhUFJSYq09Go1ycnJiC2I/hrVYLMaHDx8SdiJF5M+gsCYiN0Zqairj4+Ps7u7S19fH0tISo6OjFBUVEYvFCAQC9PX1MTAwwPfv33n48GHCHC6Xi2fPnvH161dGRkYYHh7mzZs3SdX6t6LRKDMzM7S3t1NfX09aWhoPHjxgbW3NGtPc3Mzu7i7n5+cABINBWzAzTZP8/HzS0tKAv1+Q+Pjxoy2sbW9vU1VV9Vu7fiLifPoorojI/2x1dZXbt2/T3t7+W/dPTEwwNDRESUnJf7wyEXEChTURERERB9MxqIiIiIiDKayJiIiIOJjCmoiIiIiDKayJiIiIOJjCmoiIiIiDKayJiIiIOJjCmoiIiIiDKayJiIiIONhfBXqcSV6BL9MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solución analítica\n",
    "x = np.linspace(0,3,50)\n",
    "T_analitica = 300 + 4*(3**2 - x**2)/(2*5) + (3 - x)/2\n",
    "\n",
    "xx = np.array([0.0,L/2,L])\n",
    "\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.plot(x,T_analitica,label='Solución\\nAnalítica')\n",
    "plt.plot(xx,T[0:3],'--o', label='MEF y=0.0')\n",
    "plt.plot(xx,T[3:6],'--o', label='MEF y=1.5')\n",
    "plt.plot(xx,T[6:],'--o', label='MEF y=3.0')\n",
    "plt.xlabel('Posición $x (m)$')\n",
    "plt.ylabel('Temperatura $T (K)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8af16d4-1c2b-4d4f-8510-99e8e2364fe5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Conclusiones:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97b60da5-ba7c-4a07-9f11-265e4e9c7616",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Sobre __SymPy__:\n",
    "\n",
    "* Todos los símbolos deben ser declarados, habiendo una diferencia entre los símbolos y las variables que los contienen.\n",
    "* Las operaciones matriciales, derivadas e integrales definidas se pueden hacer de forma fácil.\n",
    "* Las funciones se pueden graficar de una manera sencilla.\n",
    "* Es posible resolver sistemas de ecuaciones con relativa facilidad hasta cierto número de variables.\n",
    "* Al substituir valores numéricos estas se pueden convertir automáticamente a __arrays__ de NumPy."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6297ca2-5653-41e2-b79d-07991ca17277",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "Sobre __NumPy__:\n",
    "\n",
    "* Cuando no hay experiencia con el uso de __objetos__ los diccionarios pueden ser utilizados para organizar los elementos y trabajar con ellos de una manera automatizada.\n",
    "* La función `sp.Matrix()` puede ser utilizada para una representación más amable de los NumPy array.\n",
    "* Una vez implementado fácilmente se puede automatizar y escalar (a un gran número de elementos)."
   ]
  },
  {
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