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@jestinjoy
Created October 19, 2016 07:28
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Direct Product of Poset
{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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h9OnThISE2I/ouLi4sGjRIvtF8GKet99+mxdffNH++JlnnmHKlCkqbSJFjAqb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\nwiYiIiLi4lTYRERERFycCpuIiIiIi/t/PX5gNnXjOp4AAAAASUVORK5CYII=\n",
"text/plain": [
"Digraph on 4 vertices"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P = Posets.ChainPoset(2)\n",
"Q = Posets.ChainPoset(2)\n",
"R=P.product(Q)\n",
"R.hasse_diagram()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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3c/HiRbKzs4mJiWHNmjWVHqGNiYnhnXfeAYqm7xKuXOGJwQPIvHkT5wb3Pq1m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\n1N2N6PV6xowZw1tvvUVaWhqJiYn87W9/axUQk5KSeO211wgJCcHPz48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WLaKwsIAHI+7m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\nGISEhBjt1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Pzzz3fzJ6PeiOGJiIh6hbfeegtr1qwxes3X1xd79uzBu+++C4lEgj8/Mc+o\nLUvJZQ3sbG0RETSuw/ue/y4F2qM/ofjfyXBw6If33nsPOp0Ob7/9tjBm8+bNCAsLMzp1nPouhici\nIuoVYmNj8fzzz0OtVt/x3rJly+Dq6obnPvwcOt3/HpC593gOEh6biwCfYZ3eW6fTIeHDNXBzc8fS\npUvveN/e3h7r1q27/w9BVoG97YiIyCrc2hg4aeXLdzQO7khXGgMT3YozT0REZBXkcjmSk5OxebcS\nc155ExfKK+56TWm5Borlb2DzbiWSk5MZnKhLOPNERERWJSMjA/FLlqC6ugp/jIlE3Fw5ZGNGof/v\nh2w2NDVBVVSMLXszsE15EG5u7tjE4EQmYHgiIiKrU1dXh7Vr12J9UhLK1GpIpVJ4uradz6SproFe\nr4ePtzdeSEzE0qVL4ezsLHLF1JswPBERkdXSarUoKCiASqVCWVkZAMDHxwcymQwTJ06ErQnnQRHd\nxPBEREREZAJuGCciIiIyAcMTERERkQkYnoiIiIhMwPBEREREZAKGJyIiIiITMDwRERERmYDhiYiI\niMgEDE9EREREJvj/wxizowa3xg8AAAAASUVORK5CYII=\n",
"text/plain": [
"Digraph on 9 vertices"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P = Posets.ChainPoset(3)\n",
"Q = Posets.ChainPoset(3)\n",
"R=P.product(Q)\n",
"R.hasse_diagram()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 7.0",
"language": "",
"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": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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