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genkuroki/2017-06-17-192450sagemath.ipynb

Created June 19, 2017 12:30
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2017-06-17-192450sagemath.ipynb SageMath Integration Example
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2017-06-17-192450sagemath.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"#SageMath"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\pi + \\pi a - \\pi \\sqrt{a^{2} + a}</script></html>"
]
},
"execution_count": 23,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"var('x, a')\n",
"assume(a>0)\n",
"f(x)=sqrt(x*(1-x))/(x+a)\n",
"#show(integral(f(x),x))\n",
"show(integrate(f(x),x,0,1))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(a + b\\right)} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right) - 2 \\, \\sqrt{a b} \\arcsin\\left(-\\frac{\\sqrt{a^{2} - 2 \\, a b + b^{2}}}{a - b}\\right)</script></html>"
]
},
"execution_count": 24,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"var('x,a,b')\n",
"assume(a<b)\n",
"f(x)=sqrt((x-a)*(b-x))/x\n",
"#show(integral(f(x),x))\n",
"show(integrate(f(x),x,a,b))"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath (stable)",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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