{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 7.3, Release Date: 2016-08-04'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x |--> cos(x^3)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = cos(x^3)\n", "f" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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A3H23nD775JO6V0Kkz7ZtcjUhNADcdtUpdXXOntGgFBUxNEQraJWGnBzg6FGg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