{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The symbolic mess\n", "=========\n", "\n", "The symbolic ring (`SR`) is not fitted to answer mathemtical questions like equality, existence, etc.\n", "\n", "Every elements in the symbolic ring are expression with no defined semantics... as a consequence we end up with many errors." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "1 - functions are not well defined objects\n", "---------------------------------------------" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "Category of objects" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp.category()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeta(5).is_real()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(pi/7).is_real()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "x, y = SR.var('x,y')\n", "assume(x, 'real')\n", "assume(y, 'real')\n", "assume(x > 0)\n", "assume(y > 0)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "x^log(y) == y^log(x)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x^log(y) == y^log(x)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(x^log(y) == y^log(x))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "2 - silently and unpredictably mixes exact and unexact numbers\n", "-------------------------------------------------------------------" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pi - 3.14159265358979324\n" ] } ], "source": [ "a = pi - 3.641592653589793238 + 1/2\n", "print a" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "pi - 3.14159265358979324" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(a == 0)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "3 - $\\pi$ and $e$ are rationals\n", "-------------------------------" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "6701487259*pi == 21053343141" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "6701487259 * pi == 21053343141" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(6701487259 * pi == 21053343141)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ "161260336*e == 438351041" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "161260336 * e == 438351041" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(161260336 * e == 438351041)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.1.beta3", "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": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }