{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(u, v)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "var('u v')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def W(x):\n", " if x < -1:\n", " return RDF(0)\n", " return RDF(lambert_w(RDF(x)/RDF(e))+1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(W, (x,-2,5), aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def h(u,v):\n", " return sinh(tan(u))*sinh(tan(v))-1" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = 0.99*pi/2" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gakQSTCCQAACuRyQh1nh3AQDiwtSpo/S7363VU0+drZUrq0yPgwRHIAEA4saECd+RJG3e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\ngQQAABDm/wcG2YJQh/pqDQAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "implicit_plot(h, (u,-a,a), (v,-a,a), plot_points=400, fill=True, fillcolor='yellow')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def g(u,v):\n", " return 4*W(-sinh(tan(u))*sinh(tan(v)))^2 * cos(u)^2 * cos(v)^2" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph = plot3d(g, (u,-a,a), (v,-a,a), plot_points=200)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph += plot3d(lambda u,v: 0.001, (u,-a,a), (v,-a,a), color='yellow')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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j7pgd3FG8Grw7woUHWT8SO6hloWCxbNv2INpfjhO37Zhl9VlWf3k5fP/7N4/1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\nrAaDDZoWU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