From 767665bd3b4415983f9d03033184790a2ba5db50 Mon Sep 17 00:00:00 2001
From: s487174 <tomkos5@st.amu.edu.pl>
Date: Fri, 16 Jun 2023 03:08:52 +0200
Subject: [PATCH] Changes

---
 .../Wrzodak_Koszarek_Zadania-checkpoint.ipynb | 213 ++++++++++++++++++
 Wrzodak_Koszarek_Zadania.ipynb                | 115 ++++++++--
 2 files changed, 312 insertions(+), 16 deletions(-)
 create mode 100644 .ipynb_checkpoints/Wrzodak_Koszarek_Zadania-checkpoint.ipynb

diff --git a/.ipynb_checkpoints/Wrzodak_Koszarek_Zadania-checkpoint.ipynb b/.ipynb_checkpoints/Wrzodak_Koszarek_Zadania-checkpoint.ipynb
new file mode 100644
index 0000000..65c84a5
--- /dev/null
+++ b/.ipynb_checkpoints/Wrzodak_Koszarek_Zadania-checkpoint.ipynb
@@ -0,0 +1,213 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Zadanie 4.6"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'matrix' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[1;32mIn[1], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m A\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(QQ,\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m3\u001b[39m,[\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m4\u001b[39m, \u001b[38;5;241m6\u001b[39m, \u001b[38;5;241m8\u001b[39m, \u001b[38;5;241m10\u001b[39m, \u001b[38;5;241m12\u001b[39m, \u001b[38;5;241m14\u001b[39m, \u001b[38;5;241m16\u001b[39m, \u001b[38;5;241m18\u001b[39m, \u001b[38;5;241m20\u001b[39m, \u001b[38;5;241m22\u001b[39m, \u001b[38;5;241m24\u001b[39m, \u001b[38;5;241m26\u001b[39m, \u001b[38;5;241m28\u001b[39m, \u001b[38;5;241m31\u001b[39m])\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mA =\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(A, \u001b[38;5;124m'\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m)\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "A=matrix(QQ,5,3,[2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 31])\n",
+    "print('A =')\n",
+    "print(A, '\\n')\n",
+    "\n",
+    "print('b =')\n",
+    "b=vector(QQ,[-1,0,1,0,1])\n",
+    "print(b, '\\n')\n",
+    "\n",
+    "print('A^T * A =')\n",
+    "print(A.transpose()*A, '\\n')\n",
+    "print('Macierz A^T*A jest kwadratowa, więc rozwiązanie istnieje\\n')\n",
+    "\n",
+    "u=(A.transpose()*A)^(-1)*A.transpose()*b\n",
+    "print('u = (A^T * A)^-1 * A^T * b =')\n",
+    "print(u, '\\n')\n",
+    "\n",
+    "\n",
+    "print('b - A * u = ')\n",
+    "print(b - A * u, '\\n')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3> Zadanie 6 </h3>\n",
+    "\n",
+    "Rozwiąż układ równań $Ax=b$ metodą przybliżoną, gdzie\n",
+    "\n",
+    "$$A=\\left(\\begin{array}{rrr}\n",
+    "2 & 4 & 6 \\\\\n",
+    "8 & 10 & 12 \\\\\n",
+    "14 & 16 & 18 \\\\\n",
+    "20 & 22 & 24 \\\\\n",
+    "26 & 28 & 31\n",
+    "\\end{array}\\right)$$\n",
+    "\n",
+    "oraz $b=(-1,0,1,0,1)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Zadanie 4.7\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3> Zadanie 7</h3>\n",
+    "\n",
+    "Przybliż funkcją $f(t)=a+be^{t}$ zbiór punktów $(1,1)$, $(2,3)$, $(4,5)$ metodą z zadania 6.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "zbior punktów =  [(1, 1), (2, 3), (4, 5)]\n"
+     ]
+    },
+    {
+     "ename": "NameError",
+     "evalue": "name 'matrix' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[1;32mIn[2], line 3\u001b[0m\n\u001b[0;32m      1\u001b[0m zbior\u001b[38;5;241m=\u001b[39m[(\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m),(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m),(\u001b[38;5;241m4\u001b[39m,\u001b[38;5;241m5\u001b[39m)]\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mzbior punktów = \u001b[39m\u001b[38;5;124m'\u001b[39m, zbior)\n\u001b[1;32m----> 3\u001b[0m m\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m2\u001b[39m,[\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m1.0\u001b[39m),\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m2.0\u001b[39m),\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m4.0\u001b[39m)])\n\u001b[0;32m      5\u001b[0m a,b,t\u001b[38;5;241m=\u001b[39mvar(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124ma,b,t\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m      7\u001b[0m m\u001b[38;5;241m*\u001b[39mvector([a,b])\u001b[38;5;241m-\u001b[39mvector([\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m5\u001b[39m])\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "zbior=[(1,1),(2,3),(4,5)]\n",
+    "print('zbior punktów = ', zbior)\n",
+    "m=matrix(3,2,[1,exp(1.0),1,exp(2.0),1,exp(4.0)])\n",
+    "\n",
+    "a,b,t=var('a,b,t')\n",
+    "\n",
+    "m*vector([a,b])-vector([1,3,5])\n",
+    "\n",
+    "print('\\n (m^T * m)^-1 * m^T * vector =')\n",
+    "z = (m.transpose()*m)^(-1)*m.transpose()*vector([1,3,5])\n",
+    "print(z)\n",
+    "\n",
+    "plot(z[0] +z[1]*exp(t),(t,0,4))+sum([point(x) for x in zbior])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Zadanie 4.9"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3> Zadanie 9 </h3>\n",
+    "\n",
+    "Znajdź bazę ortonormalnych wektorów własnych dla macierzy\n",
+    "\n",
+    "$$\\left(\\begin{array}{rrr}\n",
+    "1 & 1 & 0 \\\\\n",
+    "1 & 2 & 2 \\\\\n",
+    "0 & 2 & 3\n",
+    "\\end{array}\\right)$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'matrix' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[1;32mIn[3], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m m\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m3\u001b[39m,[\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m])\n\u001b[0;32m      3\u001b[0m \u001b[38;5;66;03m#wartosci wlasne\u001b[39;00m\n\u001b[0;32m      4\u001b[0m eigenvalues \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mm\u001b[38;5;241m.\u001b[39meigvals(matrix)\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
+     ]
+    }
+   ],
+   "source": [
+    "m=matrix(3,3,[1,1,0,1,2,2,0,2,3])\n",
+    "\n",
+    "#wartosci wlasne\n",
+    "eigenvalues = np.m.eigvals(matrix)\n",
+    "\n",
+    "eigen=m.right_eigenvectors()\n",
+    "e1=eigen[0][1][0]\n",
+    "e2=eigen[1][1][0]\n",
+    "print(e1.dot_product(e2))\n",
+    "e3=eigen[2][1][0]\n",
+    "print(e3.dot_product(e1))\n",
+    "print(e2.dot_product(e3))\n",
+    "\n",
+    "#znormalizuj wektor wlasny\n",
+    "\n",
+    "#czy wektory wlasne sa ortogonalne?\n",
+    "\n",
+    "#postac ortonormalna i normalizacja"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/Wrzodak_Koszarek_Zadania.ipynb b/Wrzodak_Koszarek_Zadania.ipynb
index efb7766..65c84a5 100644
--- a/Wrzodak_Koszarek_Zadania.ipynb
+++ b/Wrzodak_Koszarek_Zadania.ipynb
@@ -7,11 +7,6 @@
     "Zadanie 4.6"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": []
-  },
   {
    "cell_type": "code",
    "execution_count": 1,
@@ -19,13 +14,13 @@
    "outputs": [
     {
      "ename": "NameError",
-     "evalue": "name 'QQ' is not defined",
+     "evalue": "name 'matrix' is not defined",
      "output_type": "error",
      "traceback": [
       "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Cell \u001b[1;32mIn[1], line 5\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39msympy\u001b[39;00m \u001b[39mimport\u001b[39;00m symbols, Matrix\n\u001b[0;32m      3\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mnumpy\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mlinalg\u001b[39;00m \u001b[39mimport\u001b[39;00m eig\n\u001b[1;32m----> 5\u001b[0m A\u001b[39m=\u001b[39mnp\u001b[39m.\u001b[39mmatrix(QQ,\u001b[39m5\u001b[39m,\u001b[39m3\u001b[39m,[\u001b[39m2\u001b[39m, \u001b[39m4\u001b[39m, \u001b[39m6\u001b[39m, \u001b[39m8\u001b[39m, \u001b[39m10\u001b[39m, \u001b[39m12\u001b[39m, \u001b[39m14\u001b[39m, \u001b[39m16\u001b[39m, \u001b[39m18\u001b[39m, \u001b[39m20\u001b[39m, \u001b[39m22\u001b[39m, \u001b[39m24\u001b[39m, \u001b[39m26\u001b[39m, \u001b[39m28\u001b[39m, \u001b[39m31\u001b[39m])\n\u001b[0;32m      6\u001b[0m \u001b[39mprint\u001b[39m(A\u001b[39m.\u001b[39mtranspose()\u001b[39m*\u001b[39mA)\n\u001b[0;32m      7\u001b[0m \u001b[39mprint\u001b[39m((A\u001b[39m.\u001b[39mtranspose()\u001b[39m*\u001b[39mA)\u001b[39m^\u001b[39m(\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m))\n",
-      "\u001b[1;31mNameError\u001b[0m: name 'QQ' is not defined"
+      "Cell \u001b[1;32mIn[1], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m A\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(QQ,\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m3\u001b[39m,[\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m4\u001b[39m, \u001b[38;5;241m6\u001b[39m, \u001b[38;5;241m8\u001b[39m, \u001b[38;5;241m10\u001b[39m, \u001b[38;5;241m12\u001b[39m, \u001b[38;5;241m14\u001b[39m, \u001b[38;5;241m16\u001b[39m, \u001b[38;5;241m18\u001b[39m, \u001b[38;5;241m20\u001b[39m, \u001b[38;5;241m22\u001b[39m, \u001b[38;5;241m24\u001b[39m, \u001b[38;5;241m26\u001b[39m, \u001b[38;5;241m28\u001b[39m, \u001b[38;5;241m31\u001b[39m])\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mA =\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(A, \u001b[38;5;124m'\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m)\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
      ]
     }
    ],
@@ -51,6 +46,25 @@
     "print(b - A * u, '\\n')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<h3> Zadanie 6 </h3>\n",
+    "\n",
+    "Rozwiąż układ równań $Ax=b$ metodą przybliżoną, gdzie\n",
+    "\n",
+    "$$A=\\left(\\begin{array}{rrr}\n",
+    "2 & 4 & 6 \\\\\n",
+    "8 & 10 & 12 \\\\\n",
+    "14 & 16 & 18 \\\\\n",
+    "20 & 22 & 24 \\\\\n",
+    "26 & 28 & 31\n",
+    "\\end{array}\\right)$$\n",
+    "\n",
+    "oraz $b=(-1,0,1,0,1)$."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -59,10 +73,38 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
+   "source": [
+    "<h3> Zadanie 7</h3>\n",
+    "\n",
+    "Przybliż funkcją $f(t)=a+be^{t}$ zbiór punktów $(1,1)$, $(2,3)$, $(4,5)$ metodą z zadania 6.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "zbior punktów =  [(1, 1), (2, 3), (4, 5)]\n"
+     ]
+    },
+    {
+     "ename": "NameError",
+     "evalue": "name 'matrix' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[1;32mIn[2], line 3\u001b[0m\n\u001b[0;32m      1\u001b[0m zbior\u001b[38;5;241m=\u001b[39m[(\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m),(\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m),(\u001b[38;5;241m4\u001b[39m,\u001b[38;5;241m5\u001b[39m)]\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mzbior punktów = \u001b[39m\u001b[38;5;124m'\u001b[39m, zbior)\n\u001b[1;32m----> 3\u001b[0m m\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m2\u001b[39m,[\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m1.0\u001b[39m),\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m2.0\u001b[39m),\u001b[38;5;241m1\u001b[39m,exp(\u001b[38;5;241m4.0\u001b[39m)])\n\u001b[0;32m      5\u001b[0m a,b,t\u001b[38;5;241m=\u001b[39mvar(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124ma,b,t\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m      7\u001b[0m m\u001b[38;5;241m*\u001b[39mvector([a,b])\u001b[38;5;241m-\u001b[39mvector([\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m5\u001b[39m])\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
+     ]
+    }
+   ],
    "source": [
     "zbior=[(1,1),(2,3),(4,5)]\n",
     "print('zbior punktów = ', zbior)\n",
@@ -87,13 +129,41 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
+   "source": [
+    "<h3> Zadanie 9 </h3>\n",
+    "\n",
+    "Znajdź bazę ortonormalnych wektorów własnych dla macierzy\n",
+    "\n",
+    "$$\\left(\\begin{array}{rrr}\n",
+    "1 & 1 & 0 \\\\\n",
+    "1 & 2 & 2 \\\\\n",
+    "0 & 2 & 3\n",
+    "\\end{array}\\right)$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'matrix' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[1;32mIn[3], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m m\u001b[38;5;241m=\u001b[39m\u001b[43mmatrix\u001b[49m(\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m3\u001b[39m,[\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m0\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m])\n\u001b[0;32m      3\u001b[0m \u001b[38;5;66;03m#wartosci wlasne\u001b[39;00m\n\u001b[0;32m      4\u001b[0m eigenvalues \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mm\u001b[38;5;241m.\u001b[39meigvals(matrix)\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'matrix' is not defined"
+     ]
+    }
+   ],
    "source": [
     "m=matrix(3,3,[1,1,0,1,2,2,0,2,3])\n",
     "\n",
+    "#wartosci wlasne\n",
     "eigenvalues = np.m.eigvals(matrix)\n",
     "\n",
     "eigen=m.right_eigenvectors()\n",
@@ -102,8 +172,21 @@
     "print(e1.dot_product(e2))\n",
     "e3=eigen[2][1][0]\n",
     "print(e3.dot_product(e1))\n",
-    "print(e2.dot_product(e3))"
+    "print(e2.dot_product(e3))\n",
+    "\n",
+    "#znormalizuj wektor wlasny\n",
+    "\n",
+    "#czy wektory wlasne sa ortogonalne?\n",
+    "\n",
+    "#postac ortonormalna i normalizacja"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -122,7 +205,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.11"
+   "version": "3.10.9"
   }
  },
  "nbformat": 4,