Genius Manual

Jiř Lebl

   Oklahoma State University

    <jirka@5z.com>

Kai Willadsen

   University of Queensland, Australia

    <kaiw@itee.uq.edu.au>

   Copyright © 1997-2016 Jiř (George) Lebl

   Copyright © 2004 Kai Willadsen

   Manual for the Genius Math Tool.

   Permission is granted to copy, distribute and/or modify this
   document under the terms of the GNU Free Documentation License
   (GFDL), Version 1.1 or any later version published by the Free
   Software Foundation with no Invariant Sections, no Front-Cover
   Texts, and no Back-Cover Texts. You can find a copy of the GFDL
   at this link or in the file COPYING-DOCS distributed with this
   manual.

   This manual is part of a collection of GNOME manuals
   distributed under the GFDL. If you want to distribute this
   manual separately from the collection, you can do so by adding
   a copy of the license to the manual, as described in section 6
   of the license.

   Many of the names used by companies to distinguish their
   products and services are claimed as trademarks. Where those
   names appear in any GNOME documentation, and the members of the
   GNOME Documentation Project are made aware of those trademarks,
   then the names are in capital letters or initial capital
   letters.

   DOCUMENT AND MODIFIED VERSIONS OF THE DOCUMENT ARE PROVIDED
   UNDER THE TERMS OF THE GNU FREE DOCUMENTATION LICENSE WITH THE
   FURTHER UNDERSTANDING THAT:

    1. DOCUMENT IS PROVIDED ON AN "AS IS" BASIS, WITHOUT WARRANTY
       OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
       WITHOUT LIMITATION, WARRANTIES THAT THE DOCUMENT OR
       MODIFIED VERSION OF THE DOCUMENT IS FREE OF DEFECTS
       MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE OR
       NON-INFRINGING. THE ENTIRE RISK AS TO THE QUALITY,
       ACCURACY, AND PERFORMANCE OF THE DOCUMENT OR MODIFIED
       VERSION OF THE DOCUMENT IS WITH YOU. SHOULD ANY DOCUMENT OR
       MODIFIED VERSION PROVE DEFECTIVE IN ANY RESPECT, YOU (NOT
       THE INITIAL WRITER, AUTHOR OR ANY CONTRIBUTOR) ASSUME THE
       COST OF ANY NECESSARY SERVICING, REPAIR OR CORRECTION. THIS
       DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL PART OF
       THIS LICENSE. NO USE OF ANY DOCUMENT OR MODIFIED VERSION OF
       THE DOCUMENT IS AUTHORIZED HEREUNDER EXCEPT UNDER THIS
       DISCLAIMER; AND
    2. UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, WHETHER
       IN TORT (INCLUDING NEGLIGENCE), CONTRACT, OR OTHERWISE,
       SHALL THE AUTHOR, INITIAL WRITER, ANY CONTRIBUTOR, OR ANY
       DISTRIBUTOR OF THE DOCUMENT OR MODIFIED VERSION OF THE
       DOCUMENT, OR ANY SUPPLIER OF ANY OF SUCH PARTIES, BE LIABLE
       TO ANY PERSON FOR ANY DIRECT, INDIRECT, SPECIAL,
       INCIDENTAL, OR CONSEQUENTIAL DAMAGES OF ANY CHARACTER
       INCLUDING, WITHOUT LIMITATION, DAMAGES FOR LOSS OF
       GOODWILL, WORK STOPPAGE, COMPUTER FAILURE OR MALFUNCTION,
       OR ANY AND ALL OTHER DAMAGES OR LOSSES ARISING OUT OF OR
       RELATING TO USE OF THE DOCUMENT AND MODIFIED VERSIONS OF
       THE DOCUMENT, EVEN IF SUCH PARTY SHALL HAVE BEEN INFORMED
       OF THE POSSIBILITY OF SUCH DAMAGES.

   Feedback

   To report a bug or make a suggestion regarding the Genius
   Mathematics Tool application or this manual, please visit the
   Genius Web page or email me at <jirka@5z.com>.
     __________________________________________________________

   Table of Contents
   1. Introduction
   2. Getting Started

        2.1. To Start Genius Mathematics Tool
        2.2. When You Start Genius

   3. Basic Usage

        3.1. Using the Work Area
        3.2. To Create a New Program
        3.3. To Open and Run a Program

   4. Plotting

        4.1. Line Plots
        4.2. Parametric Plots
        4.3. Slopefield Plots
        4.4. Vectorfield Plots
        4.5. Surface Plots

   5. GEL Basics

        5.1. Values

              5.1.1. Numbers
              5.1.2. Booleans
              5.1.3. Strings
              5.1.4. Null

        5.2. Using Variables

              5.2.1. Setting Variables
              5.2.2. Built-in Variables
              5.2.3. Previous Result Variable

        5.3. Using Functions

              5.3.1. Defining Functions
              5.3.2. Variable Argument Lists
              5.3.3. Passing Functions to Functions
              5.3.4. Operations on Functions

        5.4. Separator
        5.5. Comments
        5.6. Modular Evaluation
        5.7. List of GEL Operators

   6. Programming with GEL

        6.1. Conditionals
        6.2. Loops

              6.2.1. While Loops
              6.2.2. For Loops
              6.2.3. Foreach Loops
              6.2.4. Break and Continue

        6.3. Sums and Products
        6.4. Comparison Operators
        6.5. Global Variables and Scope of Variables
        6.6. Parameter variables
        6.7. Returning
        6.8. References
        6.9. Lvalues

   7. Advanced Programming with GEL

        7.1. Error Handling
        7.2. Toplevel Syntax
        7.3. Returning Functions
        7.4. True Local Variables
        7.5. GEL Startup Procedure
        7.6. Loading Programs

   8. Matrices in GEL

        8.1. Entering Matrices
        8.2. Conjugate Transpose and Transpose Operator
        8.3. Linear Algebra

   9. Polynomials in GEL

        9.1. Using Polynomials

   10. Set Theory in GEL

        10.1. Using Sets

   11. List of GEL functions

        11.1. Commands
        11.2. Basic
        11.3. Parameters
        11.4. Constants
        11.5. Numeric
        11.6. Trigonometry
        11.7. Number Theory
        11.8. Matrix Manipulation
        11.9. Linear Algebra
        11.10. Combinatorics
        11.11. Calculus
        11.12. Functions
        11.13. Equation Solving
        11.14. Statistics
        11.15. Polynomials
        11.16. Set Theory
        11.17. Commutative Algebra
        11.18. Miscellaneous
        11.19. Symbolic Operations
        11.20. Plotting

   12. Example Programs in GEL
   13. Settings

        13.1. Output
        13.2. Precision
        13.3. Terminal
        13.4. Memory

   14. About Genius Mathematics Tool

   List of Figures
   2-1. Genius Mathematics Tool Window
   4-1. Create Plot Window
   4-2. Plot Window
   4-3. Parametric Plot Tab
   4-4. Parametric Plot
   4-5. Surface Plot
     __________________________________________________________

Chapter 1. Introduction

   The Genius Mathematics Tool application is a general calculator
   for use as a desktop calculator, an educational tool in
   mathematics, and is useful even for research. The language used
   in Genius Mathematics Tool is designed to be ‘mathematical’ in
   the sense that it should be ‘what you mean is what you get’. Of
   course that is not an entirely attainable goal. Genius
   Mathematics Tool features rationals, arbitrary precision
   integers and multiple precision floats using the GMP library.
   It handles complex numbers using cartesian notation. It has
   good vector and matrix manipulation and can handle basic linear
   algebra. The programming language allows user defined
   functions, variables and modification of parameters.

   Genius Mathematics Tool comes in two versions. One version is
   the graphical GNOME version, which features an IDE style
   interface and the ability to plot functions of one or two
   variables. The command line version does not require GNOME, but
   of course does not implement any feature that requires the
   graphical interface.

   Parts of this manual describe the graphical version of the
   calculator, but the language is of course the same. The command
   line only version lacks the graphing capabilities and all other
   capabilities that require the graphical user interface.

   Generally, when some feature of the language (function,
   operator, etc...) is new in some version past 1.0.5, it is
   mentioned, but below 1.0.5 you would have to look at the NEWS
   file.
     __________________________________________________________

Chapter 2. Getting Started

2.1. To Start Genius Mathematics Tool

   You can start Genius Mathematics Tool in the following ways:

   Applications menu
          Depending on your operating system and version, the menu
          item for Genius Mathematics Tool could appear in a
          number of different places. It can be in the Education,
          Accessories, Office, Science, or similar submenu,
          depending on your particular setup. The menu item name
          you are looking for is Genius Math Tool. Once you locate
          this menu item click on it to start Genius Mathematics
          Tool.

   Run dialog
          Depending on your system installation the menu ite                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     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