Crash course Julia .ipynb

{
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   "id": "818a15fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 + 3 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "304ecc72",
   "metadata": {},
   "source": [
    "## Operaciones matemáticas básicas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "43f080a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "7*6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "426559a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.32857142857142857"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.3/7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "62b7cef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "9+1\n",
    "1+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0bde404a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2^4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "320a7111",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.0^3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "be3a03c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.38905609893065"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a7f0aee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0986122886681098"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log(3) # esto en base natural"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cfc618de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8fc89cae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log10(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ec0ad4dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6805bdb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1809eb13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9880316240928618"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(30) # Epa que pasa? Acá lo que sucede es que lo toma en radianes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1d701aac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# para hacer en grados usamos sind\n",
    "sind(30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5b258099",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2246467991473532e-16"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "62f61593",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2246467991473532e-16"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "38a3305e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "π = 3.1415926535897..."
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "59353351",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49999999999999994"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(pi/6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "532bbd8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ℯ = 2.7182818284590..."
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MathConstants.e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a9118717",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log(MathConstants.e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5b2fdb54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "842d167a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0885a85f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α ^2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1cb8363e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5f9d6565",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ca7fc2a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bondiola = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2f682e00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "216"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bondiola ^ x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f71d8648",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"bondiola\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"bondiola\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5c13bf31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"bondiola con papitas\""
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"bondiola \"*\"con papitas\"  # junto palabras o strings, en realidad esto se llama concatenar"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16f15c8b",
   "metadata": {},
   "source": [
    "## Un poco de Álgebra Lineal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4f1936d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " v = [1;2;3] # hace un vector de 3 x 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "917ed0c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 adjoint(::Vector{Int64}) with eltype Int64:\n",
       " 1  2  3"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y si lo transpongo? \n",
    "v'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "cb871e06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 2\n",
       " 4\n",
       " 6"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v + v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "96137066",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 2\n",
       " 4\n",
       " 6"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "2756c6e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 4\n",
       " 5\n",
       " 6"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.+3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c78e7cbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 4\n",
       " 5\n",
       " 6"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v .+ 3 # el .+ hace que haga la operacion(suma en este caso) a cada elemento "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "1a45c159",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       "  3.0\n",
       " -1.0\n",
       "  3.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " w = [3.0; -1; 3.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "bf2e436b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 4.0\n",
       " 1.0\n",
       " 6.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v + w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "739fae4b",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "UndefVarError: dot not defined",
     "output_type": "error",
     "traceback": [
      "UndefVarError: dot not defined",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[38]:1",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "dot(v,w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ecb4675",
   "metadata": {},
   "source": [
    "Acá lo que paso es que no cargue la biblioteca de algebra lineal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "173f7098",
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5226e850",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot(v,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "76e96773",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v ⋅ w # tambie funciona con el puntito :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "c80098e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Int64}:\n",
       " 1   2  2\n",
       " 3  -1  5"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Para las matrices usamos por convención mayusculas\n",
    "A = [1 2 2;3 -1 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "a2080b1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = [1 2 3\n",
    "    4 5 6\n",
    "    7 11 9] # Podemos usar espacio o el ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b50abff9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Int64}:\n",
       " 1  2\n",
       " 3  4"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = [1 2;3 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "f1479bf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Int64}:\n",
       " 11\n",
       " 16"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " A * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "3e6adde2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " -4.7287276974775186e-17\n",
       "  4.5231308410654523e-17\n",
       "  0.3333333333333333"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B\\v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "be9339ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10×10 Matrix{Float64}:\n",
       " 0.526865   0.901353   0.153408  0.0131389  …  0.749203  0.93366   0.937793\n",
       " 0.251606   0.551931   0.528301  0.767988      0.708409  0.10666   0.357036\n",
       " 0.35767    0.155683   0.671363  0.129434      0.279152  0.66759   0.950171\n",
       " 0.454111   0.932278   0.532241  0.120066      0.3554    0.895057  0.232614\n",
       " 0.435026   0.938426   0.442633  0.383158      0.547983  0.964333  0.559534\n",
       " 0.561881   0.488805   0.662175  0.175889   …  0.898405  0.682692  0.940351\n",
       " 0.43241    0.898374   0.627269  0.664736      0.893406  0.987379  0.517316\n",
       " 0.390537   0.934697   0.404927  0.892876      0.371555  0.525868  0.345406\n",
       " 0.528087   0.0577137  0.172641  0.443002      0.156063  0.302157  0.258696\n",
       " 0.0160111  0.0572849  0.044396  0.806058      0.356721  0.929439  0.78349"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = rand(10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "27599990",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       " 0.7221917008353105\n",
       " 0.9927884137696268\n",
       " 0.6660834389023814\n",
       " 0.06089349661982768\n",
       " 0.8924284553978893\n",
       " 0.7490638737025448\n",
       " 0.6441745617432127\n",
       " 0.21247540376113794\n",
       " 0.4860684097006256\n",
       " 0.39489262309564976"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "cf4914a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Float64}:\n",
       "  -13.477987487840249\n",
       "   53.69283401199929\n",
       "  -40.15437514176835\n",
       " -137.379505246409\n",
       " -218.62217500471195\n",
       "  190.48237205037884\n",
       "   50.15461094175185\n",
       "  -64.77301072702979\n",
       "  -11.788018966286042\n",
       "  141.26863386357377"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R\\b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7cc27b1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Int64}:\n",
       " 1   2  3\n",
       " 4   5  6\n",
       " 7  11  9"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "95f5b107",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 adjoint(::Matrix{Int64}) with eltype Int64:\n",
       " 1  4   7\n",
       " 2  5  11\n",
       " 3  6   9"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "5a44e236",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 transpose(::Matrix{Int64}) with eltype Int64:\n",
       " 1  4   7\n",
       " 2  5  11\n",
       " 3  6   9"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transpose(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "240ad579",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 adjoint(::Matrix{Int64}) with eltype Int64:\n",
       " 1  4   7\n",
       " 2  5  11\n",
       " 3  6   9"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adjoint(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3ec33f2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 1.0  1.0  1.0\n",
       " 1.0  1.0  1.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = ones(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a27158cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{ComplexF64}:\n",
       " 1.0+1.0im   2.0+1.0im  2.0+1.0im\n",
       " 3.0+1.0im  -1.0+1.0im  5.0+1.0im"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = A + im * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "89108152",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×2 transpose(::Matrix{ComplexF64}) with eltype ComplexF64:\n",
       " 1.0+1.0im   3.0+1.0im\n",
       " 2.0+1.0im  -1.0+1.0im\n",
       " 2.0+1.0im   5.0+1.0im"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transpose(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "47218ef4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×2 adjoint(::Matrix{ComplexF64}) with eltype ComplexF64:\n",
       " 1.0-1.0im   3.0-1.0im\n",
       " 2.0-1.0im  -1.0-1.0im\n",
       " 2.0-1.0im   5.0-1.0im"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adjoint(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "055b3411",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.7416573867739413"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "510958a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 4.0  1.0\n",
       " 2.0  3.0"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [4.0 1\n",
    "    2 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "323f1db0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Int64}:\n",
       " 6\n",
       " 8"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = [6;8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "fc105b43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 1.0\n",
       " 2.0"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = A\\b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "a03a26c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.0"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * x - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "cc840ff5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}\n",
       "values:\n",
       "2-element Vector{Float64}:\n",
       " 2.0\n",
       " 5.0\n",
       "vectors:\n",
       "2×2 Matrix{Float64}:\n",
       " -0.447214  0.707107\n",
       "  0.894427  0.707107"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ, V  = eigen(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "30c5af7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 2.0\n",
       " 5.0"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "λ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6317030f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " -0.447214  0.707107\n",
       "  0.894427  0.707107"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "f21b76df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LU{Float64, Matrix{Float64}}\n",
       "L factor:\n",
       "2×2 Matrix{Float64}:\n",
       " 1.0  0.0\n",
       " 0.5  1.0\n",
       "U factor:\n",
       "2×2 Matrix{Float64}:\n",
       " 4.0  1.0\n",
       " 0.0  2.5"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lu(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "29825001",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVD{Float64, Float64, Matrix{Float64}}\n",
       "U factor:\n",
       "2×2 Matrix{Float64}:\n",
       " -0.767752  -0.640747\n",
       " -0.640747   0.767752\n",
       "singular values:\n",
       "2-element Vector{Float64}:\n",
       " 5.116672736016927\n",
       " 1.9543950758485482\n",
       "Vt factor:\n",
       "2×2 Matrix{Float64}:\n",
       " -0.850651  -0.525731\n",
       " -0.525731   0.850651"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "6833f18f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}}\n",
       "Q factor:\n",
       "2×2 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}}:\n",
       " -0.894427  -0.447214\n",
       " -0.447214   0.894427\n",
       "R factor:\n",
       "2×2 Matrix{Float64}:\n",
       " -4.47214  -2.23607\n",
       "  0.0       2.23607"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "eec243f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Vector{Float64}:\n",
       " 1.0"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "427d28c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Matrix{Float64}:\n",
       " 1.0  1.0  1.0"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones(1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "e410f922",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Matrix{Float64}:\n",
       " 1.0  1.0  1.0\n",
       " 1.0  1.0  1.0\n",
       " 1.0  1.0  1.0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "bc3f28e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Matrix{Float64}:\n",
       " 0.0  0.0  0.0\n",
       " 0.0  0.0  0.0"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "42b72cd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 0.6499305412912476\n",
       " 0.9108276649767569\n",
       " 0.7273844289296367"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "10885678",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100-element Vector{Float64}:\n",
       " 0.31359179875879006\n",
       " 0.2157109734388739\n",
       " 0.8373504926303326\n",
       " 0.701764900379686\n",
       " 0.3777481066387818\n",
       " 0.32656759588707374\n",
       " 0.16698373957657042\n",
       " 0.9477831180266652\n",
       " 0.42718350277240347\n",
       " 0.13559074146731698\n",
       " 0.6256199414355037\n",
       " 0.946561745145686\n",
       " 0.5870739192587793\n",
       " ⋮\n",
       " 0.16135886873714578\n",
       " 0.1641901358505793\n",
       " 0.9893496997232516\n",
       " 0.2850282351640111\n",
       " 0.07648416901960453\n",
       " 0.21704992178528826\n",
       " 0.49471083416531403\n",
       " 0.2685382764929515\n",
       " 0.7998789208629697\n",
       " 0.09252394250296692\n",
       " 0.6188842447173084\n",
       " 0.2557356327487508"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "8403690c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Int64}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "37bad238",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[1] # vemos el primer elemento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "bba5e43a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "11895f40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "eb7ee8b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Matrix{Float64}:\n",
       " 4.0  1.0\n",
       " 2.0  3.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d6f8c035",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "0a269fcc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 1.0\n",
       " 3.0"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "ac7cd76c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 4.0\n",
       " 2.0"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "a67a8d73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       " 4.0\n",
       " 1.0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "db20e7c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       " 0.403479  0.605646   0.685335  0.0823729  0.614565\n",
       " 0.746297  0.619729   0.550817  0.901454   0.487228\n",
       " 0.556383  0.37363    0.376544  0.733754   0.518286\n",
       " 0.580477  0.0256462  0.707944  0.80491    0.220469\n",
       " 0.635881  0.409318   0.619708  0.346141   0.892902"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = rand(5,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "f4e92980",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 0.619728799622239\n",
       " 0.5508165346919494\n",
       " 0.9014544442601317"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2,2:4] # de la fila 2 quiero columnas 2,3,4"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4c91e34",
   "metadata": {},
   "source": [
    "## Funciones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "1ef0df6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = x^2 - 3x + 4 # Esto es de R1 a R1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "debddcfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "a345401f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "g (generic function with 1 method)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(x) = sqrt(x^2 + 1),2x+1 # Esta es de R1 a R2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "56dc55dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.23606797749979, 5)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "a78966da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.23606797749979, 5)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valor = g(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "e8cac457",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.23606797749979"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valor[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "0736f9f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valor[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "1c9394c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.23606797749979, 5)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a , b = valor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "5c65c2e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.23606797749979"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "c8528f1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "374cd6ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "h (generic function with 1 method)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h(x,y,z) = x* y * z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "010c4c3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h(2,3,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "01303d3b",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching +(::Matrix{Float64}, ::Int64)\nFor element-wise addition, use broadcasting with dot syntax: array .+ scalar\n\u001b[0mClosest candidates are:\n\u001b[0m  +(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\operators.jl:655\n\u001b[0m  +(\u001b[91m::T\u001b[39m, ::T) where T<:Union{Int128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8} at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\int.jl:87\n\u001b[0m  +(\u001b[91m::T\u001b[39m, ::Integer) where T<:AbstractChar at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\char.jl:237\n\u001b[0m  ...",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching +(::Matrix{Float64}, ::Int64)\nFor element-wise addition, use broadcasting with dot syntax: array .+ scalar\n\u001b[0mClosest candidates are:\n\u001b[0m  +(::Any, ::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any...\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\operators.jl:655\n\u001b[0m  +(\u001b[91m::T\u001b[39m, ::T) where T<:Union{Int128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8} at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\int.jl:87\n\u001b[0m  +(\u001b[91m::T\u001b[39m, ::Integer) where T<:AbstractChar at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\char.jl:237\n\u001b[0m  ...",
      "",
      "Stacktrace:",
      " [1] f(x::Matrix{Float64})",
      "   @ Main .\\In[86]:1",
      " [2] top-level scope",
      "   @ In[98]:1",
      " [3] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [4] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "f(A) #No puedo hacer esta operacion con una matriz asi porque tiene un valor sumando"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "87741d0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Vamos a redefinir f(x) de manera que podamos hacer el calculo\n",
    "f(x) = x^2 - 3x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "d38f059d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×5 Matrix{Float64}:\n",
       "  0.224265  -0.68751   -0.748661   1.11398   -0.378536\n",
       " -0.335717  -0.594778   0.347896  -0.785828   0.218183\n",
       " -0.200823  -0.180719   0.439906  -0.772323  -0.211176\n",
       " -0.486768   0.665913  -0.738855  -1.10015    0.449062\n",
       " -0.232104   0.01673   -0.166138   0.425333  -0.89371"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(A) #estamos haciendo A^2 - 3A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a556b21",
   "metadata": {},
   "source": [
    "#### Otras maneras de definir funciones\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "65a6b422",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cuadratica (generic function with 1 method)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function cuadratica(a,b,c)\n",
    "    Δ = b^2 -4 * a * c\n",
    "    x1 = (-b+√(Δ)) / 2a\n",
    "    x2 = (-b-√(Δ)) / 2a\n",
    "    return x1,x2\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "97b06113",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0, 1.0)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cuadratica(1,-4,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "e5e498fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#1 (generic function with 1 method)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "funcion =  x -> log(x^2+1) # Esta se llama funcion anonima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "d8e2d833",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.302585092994046"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "funcion(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "ab1496f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "funcion(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84843b5f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ff6f1c0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a31a5dd6",
   "metadata": {},
   "source": [
    "$$ f'(x) = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "cb968086",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "derivada (generic function with 1 method)"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function derivada(f,x,h) #aproximacion de diferencias finitas f es la funcion, x el punto y h que tanto me alejo\n",
    "    (f(x + h) - f(x)) / h\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "7f7ebf11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = x^2 - 3x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "1c20d5db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0099999999999554"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivada(f,2.0,0.01) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "fb9a7367",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0099999999999554"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivada(x-> x^2 - 3x,2,0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "88c7de66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "derivada2 (generic function with 2 methods)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function derivada2(f,x,h=1e-8) # Aca ya estoy especificando el h pero si quiero puedo modificarlo\n",
    "    (f(x + h) - f(x)) / h\n",
    "end\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "d96d616a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.999999993922529"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivada2(x-> x^2 - 3x,2) # La diferencia existe por el valor de h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "425522b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0099999999999554"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "derivada2(x-> x^2 - 3x,2,0.01) # Ahora como lo especifique me da lo mismo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "2f6f1762",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       "  3.0\n",
       " -1.0\n",
       "  3.0"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "bab0cdc0",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "MethodError: no method matching exp(::Vector{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  exp(\u001b[91m::Union{Float16, Float32, Float64}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\special\\exp.jl:296\n\u001b[0m  exp(\u001b[91m::StridedMatrix{var\"#s859\"} where var\"#s859\"<:Union{Float32, Float64, ComplexF32, ComplexF64}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\dense.jl:560\n\u001b[0m  exp(\u001b[91m::StridedMatrix{var\"#s859\"} where var\"#s859\"<:Union{Integer, Complex{<:Integer}}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\dense.jl:561\n\u001b[0m  ...",
     "output_type": "error",
     "traceback": [
      "MethodError: no method matching exp(::Vector{Float64})\n\u001b[0mClosest candidates are:\n\u001b[0m  exp(\u001b[91m::Union{Float16, Float32, Float64}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\base\\special\\exp.jl:296\n\u001b[0m  exp(\u001b[91m::StridedMatrix{var\"#s859\"} where var\"#s859\"<:Union{Float32, Float64, ComplexF32, ComplexF64}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\dense.jl:560\n\u001b[0m  exp(\u001b[91m::StridedMatrix{var\"#s859\"} where var\"#s859\"<:Union{Integer, Complex{<:Integer}}\u001b[39m) at C:\\Users\\Juan\\AppData\\Local\\Programs\\Julia-1.7.0\\share\\julia\\stdlib\\v1.7\\LinearAlgebra\\src\\dense.jl:561\n\u001b[0m  ...",
      "",
      "Stacktrace:",
      " [1] top-level scope",
      "   @ In[114]:1",
      " [2] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [3] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "exp(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "be1974ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       " 20.085536923187668\n",
       "  0.36787944117144233\n",
       " 20.085536923187668"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp.(w) #hago a cada elemento"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d580d121",
   "metadata": {},
   "source": [
    "### Rangos y listas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "c1a8f949",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Int64}:\n",
       " 1\n",
       " 2"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v[1:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "1431e6c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1:2"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1:2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13f7742d",
   "metadata": {},
   "source": [
    "dd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "dffe12c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3:100"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3:100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "01ab81d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Vector{Int64}:\n",
       "  1\n",
       "  2\n",
       "  3\n",
       "  4\n",
       "  5\n",
       "  6\n",
       "  7\n",
       "  8\n",
       "  9\n",
       " 10"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(1:10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "c0a9d374",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0:0.1:3.0"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2:0.1:3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "f4cdd2f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       " 2.0\n",
       " 2.1\n",
       " 2.2\n",
       " 2.3\n",
       " 2.4\n",
       " 2.5\n",
       " 2.6\n",
       " 2.7\n",
       " 2.8\n",
       " 2.9\n",
       " 3.0"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(2:0.1:3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "18dfabd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.7853981633974483\n",
       " 1.5707963267948966\n",
       " 2.356194490192345\n",
       " 3.141592653589793\n",
       " 3.9269908169872414\n",
       " 4.71238898038469\n",
       " 5.497787143782138\n",
       " 6.283185307179586"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(0:π/4:2π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "667a6fb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0:0.7853981633974483:6.283185307179586"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(0,2π,length=9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "2f21cece",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.7853981633974483\n",
       " 1.5707963267948966\n",
       " 2.356194490192345\n",
       " 3.141592653589793\n",
       " 3.9269908169872414\n",
       " 4.71238898038469\n",
       " 5.497787143782138\n",
       " 6.283185307179586"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(range(0,2π,length=9))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad886a53",
   "metadata": {},
   "source": [
    "## For "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "fa168ddf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "# para cade elemento de un conjunto pasa una cosa\n",
    "for x in 1:5\n",
    "    println(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "4549ae6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "for x = 1:5\n",
    "    println(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "5b149a6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12345"
     ]
    }
   ],
   "source": [
    "for x in 1:5\n",
    "    print(x)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "deb0213c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.010000000000000002\n",
      "0.04000000000000001\n",
      "0.09\n",
      "0.16000000000000003\n",
      "0.25\n",
      "0.36\n",
      "0.48999999999999994\n",
      "0.6400000000000001\n",
      "0.81\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "for x in 0:0.1:1\n",
    "    println(x^2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "ed99613e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = length(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "12dacc3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "producto_interno (generic function with 1 method)"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function producto_interno(v,w) # Es lo mismo que hacer v ⋅ w\n",
    "    n = length(v)\n",
    "    S = 0.0\n",
    "    for i = 1:n\n",
    "        S = S + v[i] * w[i]\n",
    "    end\n",
    "    return S\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "b3715987",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "producto_interno(v,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "21e2c64e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vi= 1,wi = 3.0\n",
      "vi= 1,wi = -1.0\n",
      "vi= 1,wi = 3.0\n",
      "vi= 2,wi = 3.0\n",
      "vi= 2,wi = -1.0\n",
      "vi= 2,wi = 3.0\n",
      "vi= 3,wi = 3.0\n",
      "vi= 3,wi = -1.0\n",
      "vi= 3,wi = 3.0\n"
     ]
    }
   ],
   "source": [
    "for vi in v, wi in w\n",
    "    println(\"vi= $vi,wi = $wi\")\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "03936555",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vi= 1,wi = 3.0\n",
      "vi= 2,wi = -1.0\n",
      "vi= 3,wi = 3.0\n"
     ]
    }
   ],
   "source": [
    "for (vi,wi) in zip(v,w)\n",
    "    println(\"vi= $vi,wi = $wi\")\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "ad0fc910",
   "metadata": {},
   "outputs": [],
   "source": [
    "z = zeros(3)\n",
    "for i = 1:3\n",
    "    z[i] = v[i]^2 * w[i] + 1\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f187d75e",
   "metadata": {},
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "f0200c8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Vector{Float64}:\n",
       "  4.0\n",
       " -3.0\n",
       " 28.0"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.^2 .*w .+1 #Recordemos que podiamos usar el .(operacion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "03ea55b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "factorial (generic function with 1 method)"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function factorial(n :: Int)\n",
    "    resultado = 1\n",
    "    for i in 1:n\n",
    "        resultado = resultado * i\n",
    "    end\n",
    "    return resultado\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "a5de677e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorial(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "4a05b315",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "120"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factorial(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03095940",
   "metadata": {},
   "source": [
    "### Condicional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "a5657073",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Si pasa alguna cosa entonces pasa algo.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "5ce4db75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "señal (generic function with 1 method)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function señal(x)\n",
    "    if x > 0 \n",
    "        return 1\n",
    "    elseif x < 0 \n",
    "        return -1\n",
    "    else\n",
    "        return 0\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "31e37665",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, -1, 0)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "señal(2.3),señal(-1.0),señal(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "2ac59885",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Vector{Int64}:\n",
       " -1\n",
       " -1\n",
       " -1\n",
       " -1\n",
       "  0\n",
       "  1\n",
       "  1\n",
       "  1\n",
       "  1"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "señal.(-1:0.25:1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "24f2023d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "factorial (generic function with 1 method)"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function factorial(n :: Int)\n",
    "    if n < 0\n",
    "        error(\"No existe el factorial de un numero negativo\")\n",
    "    end\n",
    "    resultado = 1\n",
    "    for i in 1:n\n",
    "        resultado = resultado * i\n",
    "    end\n",
    "    return resultado\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "d0a44614",
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "No existe el factorial de un numero negativo",
     "output_type": "error",
     "traceback": [
      "No existe el factorial de un numero negativo",
      "",
      "Stacktrace:",
      " [1] error(s::String)",
      "   @ Base .\\error.jl:33",
      " [2] factorial(n::Int64)",
      "   @ Main .\\In[147]:3",
      " [3] top-level scope",
      "   @ In[148]:1",
      " [4] eval",
      "   @ .\\boot.jl:373 [inlined]",
      " [5] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)",
      "   @ Base .\\loading.jl:1196"
     ]
    }
   ],
   "source": [
    "factorial(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52fb70a9",
   "metadata": {},
   "source": [
    "Modificar el ejercicio de la cuadratica para los casos donde $\\Delta=0$ y $\\Delta <0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7312b9d",
   "metadata": {},
   "source": [
    "## While"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "f94dce5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mientras se cumpla una condicion \n",
    "# Repetir ciertos pasos\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f46417dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7be437ac",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df25319e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01d63438",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d54788a3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "4919072c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100-element Vector{Float64}:\n",
       " 0.06438199976031378\n",
       " 0.12318112906465628\n",
       " 0.43761406460089836\n",
       " 0.3968213335426436\n",
       " 0.8166443439981055\n",
       " 0.4468183726442545\n",
       " 0.5471774855035877\n",
       " 0.49974693460472286\n",
       " 0.6609717550147004\n",
       " 0.18042032557971865\n",
       " 0.5719330498933525\n",
       " 0.20115908177729014\n",
       " 0.6867366755126253\n",
       " ⋮\n",
       " 0.4389770324580642\n",
       " 0.3705362765105433\n",
       " 0.9670530943220123\n",
       " 0.16441126896578195\n",
       " 0.788612192928478\n",
       " 0.10564527320960593\n",
       " 0.1250073033502601\n",
       " 0.4038539915077436\n",
       " 0.17810075129130287\n",
       " 0.23097445201899924\n",
       " 0.8037641200261652\n",
       " 0.21261958864469366"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = collect(1:1:100)\n",
    "y = rand(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "5f427ee0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "  <clipPath id=\"clip720\">\n",
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       "  </clipPath>\n",
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       "<path clip-path=\"url(#clip720)\" d=\"\n",
       "M0 1600 L2400 1600 L2400 0 L0 0  Z\n",
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     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a230a9b6",
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
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   "metadata": {},
   "outputs": [],
   "source": []
  }
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