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‎book/_toc.yml‎

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- file: sympy/introduction.ipynb
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title: "Introduction"
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- file: sympy/variables.ipynb
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title: "Variables, Expressions and Functions"
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title: "Variables"
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- file: sympy/functions.ipynb
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title: "Functions"
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- file: sympy/expressions.ipynb
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title: "Evaluating Expressions"
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‎book/sympy/functions.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Functions"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You will also work with undefined mathematical functions in addition to variables.\n",
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"These will play an important role in setting up differential equations, where\n",
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"you typically don't know the function, but only its derivative(s). You can\n",
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"create arbitrary functions of variables. In this case, you make a function of\n",
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"$x$. First create the function name:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"tags": [
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"disable-execution-cell"
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]
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},
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"outputs": [],
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"source": [
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"f = sym.Function('f')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now you can create functions of one or more variables like so:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {
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"tags": [
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"disable-execution-cell"
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]
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},
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"outputs": [
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{
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"data": {
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"image/png": "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",
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"text/latex": [
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"$\\displaystyle f{\\left(x \\right)}$"
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],
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"text/plain": [
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"f(x)"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f(x)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The same `UndefinedFunction` can be used to create multivariate functions:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {
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"tags": [
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"disable-execution-cell"
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]
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},
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"outputs": [
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{
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"data": {
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"image/png": "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",
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"text/latex": [
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"$\\displaystyle f{\\left(x,y \\right)}$"
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],
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"text/plain": [
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"f(x, y)"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f(x,y)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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":::{card} Test yourself!\n",
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"Create a function $H(x,y,z)$\n",
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"\n",
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"All variables have been defined with:\n",
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"\n",
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"```python\n",
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"x, y, z = sym.symbols('x, y, z')\n",
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"```\n",
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"\n",
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"Click {fa}`rocket` --> {guilabel}`Live Code` to activate live coding!\n",
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":::"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {
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"tags": [
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"thebe-remove-input-init"
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]
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},
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"outputs": [],
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"source": [
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"x, y, z = sym.symbols('x, y, z')\n",
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"H = sym.Function('H')\n",
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"function_correct = H(x,y,z)\n",
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"function_answer = 0\n",
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"H = None"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"function = "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {
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"tags": [
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"thebe-remove-input-init"
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]
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "bf9cdc4356624837a034f353336aeb2a",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Button(description='Check answer', style=ButtonStyle())"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "8052642635a74e9b966db4bbc3ee54ac",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Output()"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"check_answer(\"function\",function_correct, check_equation)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "mude",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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