{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"def f(x):\n",
" return x**2"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"16"
]
},
"execution_count": 3,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f(4)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"2+2"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"x"
]
},
"execution_count": 2,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"x"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"%display typeset"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 4,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"x"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"R.= QQ[]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"R"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 8,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f= x1^2*(x2*x5 + x3*x4);f"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"X= [0] + list(R.gens()); X"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"g= lambda i, j, k, l, m : X[i]^2*(X[j]*X[k] + X[l]*X[m])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 11,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"g(1, 2, 5, 3, 4)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"F= g(1, 2, 5, 4, 3) + g(2, 1, 3, 4, 5) + g(3, 1, 5, 2, 4) + g(4, 1, 2, 3, 5) + g(5, 1, 4, 2, 3)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"F"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"L= [F, F(X[2], X[1], X[3], X[4], X[5]), F(X[3], X[2], X[1], X[4], X[5]), F(X[4], X[2], X[3], X[1], X[5]) , F(X[5], X[2], X[3], X[4], X[1]), F(X[1], X[5], X[3], X[4], X[2]) ]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 15,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"len(L)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"S.= R[]"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"graal= prod([T - foo for foo in L])"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"c= graal.coefficients()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 21,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"c[6]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Some output was deleted.\n"
]
}
],
"source": [
"c[0]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 23,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"symmetrize(c[0])"
]
},
{
"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": "2.7.14"
}
},
"nbformat": 4,
"nbformat_minor": 0
}