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@Hasenpfote
Created June 25, 2021 11:25
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "63f7945a",
"metadata": {},
"outputs": [],
"source": [
"import sympy as sp\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import display\n",
"from IPython.display import Math\n",
"%matplotlib inline \n",
"#sp.init_printing()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d1500d71",
"metadata": {},
"outputs": [],
"source": [
"def broadcast(func):\n",
" return lambda *args: np.broadcast_arrays(func(*args), *args)[0]\n",
"\n",
"def plot(func, orders, points, label):\n",
" evalfunc = sp.lambdify(x, func, modules=['numpy'])\n",
" order_to_evaltaylor = {}\n",
" for order in orders:\n",
" taylor = sp.series(func, n=order+1).removeO()\n",
" evaltaylor = sp.lambdify(x, taylor, modules=['numpy'])\n",
" if taylor.is_constant():\n",
" evaltaylor = broadcast(evaltaylor)\n",
" order_to_evaltaylor[order] = evaltaylor\n",
" # plot\n",
" fig, ax = plt.subplots()\n",
" ax.plot(points, evalfunc(points), 'b', label=label)\n",
" order_to_str = {'1':'st', '2':'nd', '3':'rd'}\n",
" for order, evaltaylor in sorted(order_to_evaltaylor.items()):\n",
" ax.plot(points, evaltaylor(points), label='{}{} order'.format(order, order_to_str.get(str(order), 'th')))\n",
" #ax.set_title(title)\n",
" ax.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0, fontsize=18)\n",
" ax.grid()\n",
" ax.spines['top'].set_visible(False)\n",
" ax.spines['right'].set_visible(False)\n",
" #plt.show()\n",
"\n",
"x = sp.Symbol('x', real=True)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "75d32418",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\sin{\\left(x \\right)}}{x}=1 - \\frac{x^{2}}{6} + \\frac{x^{4}}{120} - \\frac{x^{6}}{5040} + \\frac{x^{8}}{362880} + O\\left(x^{9}\\right)$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expr = sp.sin(x) / x\n",
"orders = [1,2,4,6,8]\n",
"points = np.linspace(-5.5, 5.5, 50)\n",
"plot(expr, orders=orders, points=points, label='${}$'.format(sp.latex(expr)))\n",
"display(Math('${}={}$'.format(sp.latex(expr), sp.latex(sp.series(expr, n=max(orders) + 1)))))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5a38e6a0",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{x}{\\sin{\\left(x \\right)}}=1 + \\frac{x^{2}}{6} + \\frac{7 x^{4}}{360} + \\frac{31 x^{6}}{15120} + \\frac{127 x^{8}}{604800} + O\\left(x^{9}\\right)$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expr = x / sp.sin(x)\n",
"orders = [1,2,4,6,8]\n",
"points = np.linspace(-5.5, 5.5, 50)\n",
"plot(expr, orders=orders, points=points, label='${}$'.format(sp.latex(expr)))\n",
"display(Math('${}={}$'.format(sp.latex(expr), sp.latex(sp.series(expr, n=max(orders) + 1)))))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "07c62e79",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{x \\cos{\\left(x \\right)}}{\\sin^{3}{\\left(x \\right)}} - \\frac{1}{\\sin^{2}{\\left(x \\right)}}=- \\frac{1}{3} - \\frac{2 x^{2}}{15} - \\frac{2 x^{4}}{63} - \\frac{4 x^{6}}{675} - \\frac{2 x^{8}}{2079} + O\\left(x^{9}\\right)$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expr = - 1 / sp.sin(x) ** 2 + x * sp.cos(x) / sp.sin(x) ** 3\n",
"orders = [1,2,4,6,8]\n",
"points = np.linspace(-5.5, 5.5, 50)\n",
"plot(expr, orders=orders, points=points, label='${}$'.format(sp.latex(expr)))\n",
"display(Math('${}={}$'.format(sp.latex(expr), sp.latex(sp.series(expr, n=max(orders) + 1)))))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "372d98be",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\cos{\\left(x \\right)} - \\frac{\\sin{\\left(x \\right)}}{x}}{x^{2}}=- \\frac{1}{3} + \\frac{x^{2}}{30} - \\frac{x^{4}}{840} + \\frac{x^{6}}{45360} - \\frac{x^{8}}{3991680} + O\\left(x^{9}\\right)$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expr = (sp.cos(x) - sp.sin(x) / x) / x ** 2\n",
"orders = [1,2,4,6,8]\n",
"points = np.linspace(-5.5, 5.5, 50)\n",
"plot(expr, orders=orders, points=points, label='${}$'.format(sp.latex(expr)))\n",
"display(Math('${}={}$'.format(sp.latex(expr), sp.latex(sp.series(expr, n=max(orders) + 1)))))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "107eff8a",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - \\frac{x}{\\sin^{3}{\\left(x \\right)}} + \\frac{\\cos{\\left(x \\right)}}{\\sin^{2}{\\left(x \\right)}}=- \\frac{2}{3} - \\frac{x^{2}}{5} - \\frac{17 x^{4}}{420} - \\frac{29 x^{6}}{4200} - \\frac{1181 x^{8}}{1108800} + O\\left(x^{9}\\right)$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"expr = sp.cos(x) / sp.sin(x) ** 2 - x / sp.sin(x) ** 3\n",
"orders = [1,2,4,6,8]\n",
"points = np.linspace(-5.5, 5.5, 50)\n",
"plot(expr, orders=orders, points=points, label='${}$'.format(sp.latex(expr)))\n",
"display(Math('${}={}$'.format(sp.latex(expr), sp.latex(sp.series(expr, n=max(orders) + 1)))))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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