{ "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": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "sin(x^2)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = sin(x^2)\n", "f(x)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WJXKfqip5OuvU8wwAEB4ug+sYGpzNmH1gh5WG5GSuNBBpb9cu4IUXZFuSzi3Z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\nDteVuFdVJfXrJ02Z4roS+GTCBHuGpUWpvt4+UGBHQ7QQGgAAnZo3Tzp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