# Introduction

Shows

- an overview of what Euler is,
- what files Euler consists of and how it is installed,
- how to run the demo,
- how to get on-line help.

## Overview

The idea of EULER is a system with the following features

- Interactive evaluation of numerical expressions with real or complex values, vectors and matrices, including use of variables.
- Built-in functions that can take vectors as input and are then evaluated for each element of the vector or matrix.
- Matrix functions.
- Interval arithmetic for result verification.
- Exact scalar product.
- Statistical functions and random numbers.
- Optimization.
- 2D- and 3D-plots.
- A built-in programming language with parameters and local variables.
- An online help.
- A tracing feature for the programming language.
- Possibility to read and write raw numerical data or even binary data from and to files.

Most version are in a notebook style. You can edit old commands and execute them again. Moreover, you can add text to every command. The notebook supports a color scheme to distinguish between commands, text and output.

EULER is an ideal tool for the tasks such as

- Inspecting and discussing functions of one real or complex variable.
- Viewing surfaces in parameter representation.
- Linear algebra and eigenvalue computation.
- Testing numerical algorithms.
- Statistical evaluations and Monte Carlo simulations.
- Solving differential equations numerically.
- Computing polynomials.
- Studying interval arithmetic.
- Examining and generating sound files.

## Files and Installation

EULER consists of the following files at least

- The program code and the on-line help.
- euler.cfg (is loaded after the start of the program)
- util.e (in turn loaded from euler.cfg)
- Several other *.E files, which are loaded from euler.cfg.

Note that there might be a command in euler.cfg to switch directory, so the program files need not be in the same directory. There are some additional files, which help using the program

- demo.e (a demo file, see the demo section)
- Other *.e files, which contain sample applications.
- The Notebook files *.en, which contain sample notebooks.

You should name your EULER program files *.e.

To exit EULER issue the command

        > quit

or close the EULER window.

## The Demo

The best way to get a good introduction into EULER is to run the demo. To do that issue the command

        >load demo

Do not enter the prompt ">" and press the Return key. Of course, the file DEMO must be in the active directory. This is usually the progs directory and shoudl be set up automatically. There is also an automatic, non-interactive demo, which you might load with

        >load autodemo

You can learn to program EULER by studying the demo file, of course.

If you are using a notebook version, you should start by loading the welcome.en notebook.

## Online EULER Help

You can select Help from the menu bar or press the F1 key to see the help text. Also

        >help function

will show the help text of a function (see "programming EULER"). For user defined functions, this is a very good way to remember their purpose and give some documentation to the user.

For builtin functions and commands, the help command will display the help text from help.txt. This file is loaded at the start of EULER and is ASCII readable. The format is simple and you are welcome to extend this file with your own comments. It does also contain help for brackets, as in

        >help (

There is also this documentation, which explains how all these commands are supposed to work together.