MuPAD - Demo

# ... Demos and examples

## Symbolic computation, Graphic, Modules, Test suites

The following examples are allmost taken from the hypertext demo that is distributed with the MuPAD system. Most examples are simple and are only intend to give a brief overview on the features of MuPAD. The following examples were computed with MuPAD release 1.2.2.

1. Basics: This chapter gives a first sight on basic features and data structures of the computer algebra system MuPAD.
   - Arithmetic
   - Working with symbolic objects
   - Strings
   - Data structures
   - Operator arithmetic
   - Manipulation of expressions
   - Programming language
   - Performance and profiling
   - Domains

2. Calculus: This chapter shows how algebraic problems and problems of higher analysis can be solved by symbolic computations in MuPAD.
   - Differentation and integration
   - Definite and indefinite summation
   - Series expansion and limit computation
   - Solving equations and systems of equations
   - Complex expressions - rectangular form

3. Graphics: MuPAD has an interactive graphic tool to create and manipulate 2D and 3D graphics. We're also working on a filmtool to animate them.
   - Graphic primitives
   - 2D-Graphics
   - 3D-Graphics

4. Polynomials: This chapter gives some examples how to operate on polynomials.
   - Arithmetic and manipulating
   - Factorisation of polynomials
   - Polynomials of Gaussian Integers

5. Orthogonal polynomials: This chapter gives some examples how to create orthogonal polynomials.
   - The library package orthpoly

6. Linear Algebra: MuPAD has a linear algebra library package. This chapter describes how to declare rings of matrices and how to operate on them.
   - The domain constructor Matrix
   - Manipulation of matrices
   - Standard arithmetic of matrices
   - The domain constructor SquareMatrix
   - The library package linalg
   - Solving systems of linear equations
   - Matrices over Gaussian Integers

7. Domains - User Defined Types: MuPAD has a flexible and object oriented type concept called domains. Users can define their own data structures/types and may overload standard operators like *, +, etc for them. The library package domains contains some predefined algebraic structures and also domain constructors.
   - The field Z/Z7
   - The abstract domain NUMERIC
   - The library package domains

8. Dynamic Modules: Dynamic Modules are binary code function libraries that can be loaded and also unloaded during a MuPAD session. Modules can be implemented by every MuPAD user and allows real extensions of the MuPAD system, without changing the kernel sources.
   - Introduction
   - How to use dynamic modules
   - How to create dynamic modules
   - Example of faster Sinus
   - The module slave

9. Gröbner Basis for Polynomial Ideals: MuPAD also has a groebner library package to solve systems of polynomial equations by computing gröbner basis of polynomial ideals.
   - Gröbner Basis for Polynomial Ideals
   - Solution of systems of polynomial equations

10. Further Examples: This chapter contains some nice examples of symbolic computations in MuPAD. Also refer to Release 1.2.2 to read about the new features.
    - Test suites and benchmarks (Wester's test suite, ...)
    - Continued Fractions Arithmetic

## Images of user interfaces

- On unix computer platforms MuPAD uses an OPENLOOK-like X11-interface, based on the XView programming toolkit:
  - the session interface - (8Kb)
  - the hypertext help system - (15Kb)
  - the debugger interface - (9Kb)
  - the graphic interface - (19Kb)
- For unix computer platforms we are also developing a Motif-version. It is in its beta test phase and will be available with the MuPAD version after 1.2.2. In the future this substitutes the XView version:
  - the session interface - (7Kb)
  - the hypertext help system - (20Kb)
  - the debugger interface - (10Kb)
  - the graphic interface - (14Kb)
- On Apple Macintosh computers the user interface differs according to the Apple style guide:
  - the session interface - (10Kb)
  - the hypertext help system - (16Kb)
  - the debugger interface - (9Kb)
  - the graphic interface - (22Kb)
- A first implementation (terminal version) of MuPAD for Windows-3.1 may be available in august 1995 (only for beta-testers).