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Merge pull request #9 from mbujosab/main
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mbujosab committed Dec 30, 2023
2 parents 9568bfb + 8433197 commit 95b8b74
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166 changes: 14 additions & 152 deletions LeccProb05-1.ipynb
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"$\\begin{pmatrix}2,& 2,& 2,& 2,\\end{pmatrix}$"
"$\\begin{pmatrix}1,& 1,& 1,& 1,\\end{pmatrix}$"
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"text/plain": [
"Vector([2, 2, 2, 2])"
"Vector([1, 1, 1, 1])"
]
},
"execution_count": 33,
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"$\\begin{pmatrix}2,& 3,& 2,& 3,\\end{pmatrix}$"
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"Vector([2, 3, 2, 3])"
"Vector([3, 2, 1, 2])"
]
},
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"## Espacio euclideo de probabilidad\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Ejemplo de la demostración en el libro sobre la *construcción de subespacios independientes e isomorfos*.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(u0, u1, w0, w1, w2)"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R1=symbols('u:2')\n",
"R2=symbols('w:3')\n",
"lista=R1+R2\n",
"lista"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(u0, w0), (u0, w1), (u0, w2), (u1, w0), (u1, w1), (u1, w2)]"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B = [x for x in aspa((R1,R2)) ]\n",
"B"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
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"text/html": [
"<p style=\"text-align:center;\">$\\left[ \\begin{array}{ccccc}1&0&1&0&0\\\\1&0&0&1&0\\\\1&0&0&0&1\\\\0&1&1&0&0\\\\0&1&0&1&0\\\\0&1&0&0&1\\\\ \\end{array} \\right]$</p>"
],
"text/latex": [
"$\\left[ \\begin{array}{ccccc}1&0&1&0&0\\\\1&0&0&1&0\\\\1&0&0&0&1\\\\0&1&1&0&0\\\\0&1&0&1&0\\\\0&1&0&0&1\\\\ \\end{array} \\right]$"
],
"text/plain": [
"Matrix([Vector([1, 1, 1, 0, 0, 0]), Vector([0, 0, 0, 1, 1, 1]), Vector([1, 0, 0, 1, 0, 0]), Vector([0, 1, 0, 0, 1, 0]), Vector([0, 0, 1, 0, 0, 1])])"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M = Matrix([ [ int(i in w) for i in lista ] for w in B]).ccol({len(R1),len(R1+R2)})\n",
"fmp = [fracc(3,4),fracc(1,4),fracc(1,2),fracc(1,4),fracc(1,4)]\n",
"M = Matrix([VAI(M[i],fmp[i]) for i in range(M.n)])\n",
"M"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"prodH = lambda u,w: VAI([u[i]*w[i] for i in range(u.n)],u.prb*w.prb)\n",
"productoH = lambda x,n: VAI(V1(n),1) if not x else prodH(x[0], productoH(x[1:], n) )"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3/8, 3/16, 3/16, 1/8, 1/16, 1/16]\n"
]
},
{
"data": {
"text/latex": [
"$\\displaystyle 1$"
],
"text/plain": [
"1"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = M.m\n",
"Q = [x for x in aspa([M[:2],M[2:]]) ]\n",
"baseC = Sistema([v for v in [productoH(s,n) for s in Q] if v.no_es_nulo()])\n",
"print([(baseC[i]).prb for i in range(len(baseC))])\n",
"sum([(baseC[i]).prb for i in range(len(baseC))])"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"class SampleSpace(Matrix):\n",
" def __init__(self, data, Prb=0):\n",
" super().__init__(data)\n",
" self.lista = [ VA(i,Prb) for i in self.lista ]"
]
}
],
"metadata": {
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