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The Open Computer Algebra System
MuPAD Pro 3 is a full-fledged computer algebra system with a rich set of features including extensive mathematics capabilities for symbolic and numeric computation and a Virtual Camera (VCam) toolkit for visualization, animation, and interactive manipulation of 2D and 3D plots and other mathematical objects.
Developed at the University of Paderborn in Germany, MuPAD Pro is intended for an extremely broad range of users. Its domains and categories are similar to object-oriented classes that allow overriding and overloading methods and operators, inheritance, and generic algorithms. The MuPAD language has a Pascal-like syntax and allows imperative, functional, and object-oriented programming. A comfortable notebook interface includes an integrated source-level debugger, a profiler, and hypertext help, along with the graphics visualization toolkit.
MuPAD worksheets provide examples on how MuPAD Pro can be used in teaching and training students. They are available as HTML files and as Notebooks, .mnb files that can be used interactively with MuPAD Pro for Windows.
Use MuPAD Pro 3 to develop real-world solutions and applications.
| • | Use convenient keyboard and mouse commands to solve numeric and symbolic equations. |
| • | Understand implicit assumptions often made by other computer algebra systems. |
| • | Visually depict complicated functions in two and three dimensions. |
| • | Write programs to solve complex problems using a familiar, high-level language. |
| • | Debug your programs at the source code level, for speed and convenience. |
| • | Save time by incorporating MuPAD programs written elsewhere. |
New features
| • | Newly implemented renderers for 2D and 3D plots offer animations, lighting, improved interactive manipulation, and more |
| • | Uses OpenGL® to produce stunning 3D plots |
| • | New plot attributes allow interactive fine-tuning of graphics |
| • | Animations can be saved as AVI files |
| • | Contains Scilab for fast numerical computations |
| • | Transparency in 3D plots |
General
| • | Notebook interface for interactive calculations |
| • | Symbolic computation and expression manipulation |
| • | Multiprecision arithmetic |
| • | Export to HTML, RTF, plain text, and MS Word |
| • | Completely redesigned interactive 2D and 3D graphics tool |
| • | Extensive online hypertext documentation with fast search functions |
| • | Procedural, object-oriented, and functional programming |
| • | User-definable data structures |
| • | Integrated source-level debugger |
| • | Dynamic linking of external binary code |
Notebook Interface for Interactive Calculations
| • | New, more powerful Simplify command allows fine-tuning |
| • | Improved ODE capability |
| • | New Graph library for graph theory |
| • | New special functions |
| • | Expanded linear algebra library |
| • | Expanded number theory capability |
| • | Extensive library of statistics functions |
| • | Extensive numeric library |
| • | Library for combinatorics |
| • | Combines text, calculations, and graphics in a single document |
| • | Open multiple notebooks at the same time |
| • | 2D graphical output of mathematical formulae |
| • | Built-in rich text editor for writing notebooks |
| • | Built-in text editor with syntax coloring and bookmark management for writing user-defined procedures |
| • | Support for OLE 2 embedding |
| • | Support for drag and drop |
| • | User-definable command menu |
Interactive Graphics Tool
| • | New Virtual Camera (VCam) user interface |
| • | Completely redesigned VCam toolkit for visualization of 2D and 3D plots |
| • | New, advanced algorithms for plotting functions, implicit functions, curves, and surfaces |
| • | Transparency in 3D plots |
| • | Extensive new plot library of object types |
| • | Interactive manipulation of hundreds of plot properties |
| • | Creation of animations of 2D and 3D graphics |
| • | Produce 3D plots with OpenGL® |
| • | 3D Viewer features shading, zooming, clipping planes, rotating, point requests, perspective control of scenes, and animations |
| • | New graphics command toolbar |
| • | User-definable color functions |
| • | New graphics tutorial |
| • | Export to many formats including popular raster formats, AVI, EPS, WMF, and SVG |
Integrated Source-level Debugger
| • | Mouse-driven interface |
| • | Conditional breakpoints |
| • | Step-by-step execution |
| • | Display of call stack |
| • | Evaluation of arbitrary expressions during execution |
| • | Library source included |
| • | New, more powerful Simplify tool allows fine-tuning. Specify time, designate a rule-base, obtain lists of rules applied and intermediate expressions computed |
| • | Solve: Equations and systems of equations; inequalities; ordinary and partial differential equations; linear recurrence relations; linear congruences; polynomial diophantine equations; equations over standard domains (integer; real; complex); equations over abstract algebraic structures |
| • | Calculus: Limits; integration; differentiation; series expansions; integral transforms; differential operators; orthogonal polynomials; piecewise defined functions |
| • | Linear Algebra: Extended linear algebra library includes Pascal and Vandermonde matrices and their inverses, Toepliz matrices, and linear Toepliz and Vandermonde system solutions, in addition to matrices over arbitrary coefficient rings; determinants; eigenvalues; eigenvectors; canonical forms; divergence; gradient; curl |
| • | Numerics: Solve equations and systems of equations; polynomial roots; integration; ODEs; functional calculus for matrices; eigenvalues; eigenvectors; singular value decomposition; FFT; polynomial interpolation; splines; optimization problems. Extended library when the Scilab numerical system is connected to MuPAD Pro 3 |
| • | Special Functions: New special functions include Airy and Whittaker functions, the KummerU confluent hypergeometric function, and the surd function |
| • | Assumptions and Properties: Attach properties to identifiers (properties are integers; reals; intervals; residue classes; relations); check mathematical properties of identifiers |
| • | Set Theory: Union; Intersection; Cartesian product; power set |
| • | Polynomials: Over arbitrary rings; sparse representation; gcd; factorization; Groebner bases |
| • | Linear Optimization: Solve; minimize; maximize; plot linear and mixed-integer programs |
| • | Number Theory: Now includes Cornacchia's algorithm along with continued fractions; factorization using elliptic curves; Jacobi and Legendre symbol; Euler phi; Euler totient; Mangoldt's; Moebius and Carmichael functions; modular and primitive roots |
| • | Combinatorics: Bell, Catalan, and Stirling numbers; compositions; partitions of numbers; powerset; permutations of lists; subsets; generators |
| • | Statistics: Bravais-Pearson and Fechner correlation; continuous and discrete distributions; chi square, normal, and T distribution; arithmetic; geometric; harmonic and quadratic mean; linear and non-linear regression; standard and mean deviation; variance, covariance, kurtosis, and k-th moment; random number generators; quartiles; cumulative and probability densities for 16 types of parametrized distributions; goodness-of-fit tests; box plot representations of statistical samples |
| • | Networks and Graphs: A new, more general Graph library replaces the Version 2.5 Network library and contains over 60 functions for creating, modifying, and visualizing graphs; computing the maximal flow, minimal cost flow, shortest path, and more |
| • | Lindenmayer Systems: Define and draw fractals by means of context-free grammars |
| • | Algebraic Structures: Symmetric groups; polynomial rings; matrix rings and groups; product rings; algebraic field extensions; finite fields; and quotient fields. User-created domains extend these structures |
MuPAD Pro 3 is a general-purpose computer algebra system for symbolic and numeric computation. It was designed as a tool for handling gigabytes of data efficiently.
MuPAD is structured around a kernel implemented in C and C++. The kernel consists of five elements:
• The arithmetic, which handles numbers of arbitrary lengths.
• The parser, which reads and checks the user's input.
• The evaluator, which evaluates and simplifies input data.
• The memory allocation management unit, or MAMMUT, which handles all system data and provides the interface between the kernel and the hardware. The MAMMUT is platform-dependent.
• The built-in functions, which are frequently-used functions for manipulating arithmetical expressions or polynomials. These user-accessible functions are implemented in the kernel for speed and efficiency.
The kernel's libraries contain the mathematical expertise of the MuPAD kernel. The libraries are written in a high-level MuPAD programming language and are platform-independent. Dynamic modules are similar to library packages. The modules are compiled machine code functions written in C/C++, the just like the built-in functions of the kernel.
The system also offers data types (graphical primitives such as points and polygons) and 2D and 3D plotting functions that work with the VCam graphics tool. With VCam, the perspective, scale, axes, colors, and other elements of plots can be defined. Plots can be manipulated interactively and translated into MuPAD input.
Like the MAMMUT, the graphical user interface is platform-dependent. The help tool for the system is organized as a hypertext system and comprises complete system documentation, including information about the MuPAD language and libraries.
MuPAD differs in three important ways from other computer algebra systems.
MuPAD Uses Object-Oriented Programming and User-Definable Data Types
In addition to working with basic data types, such as numbers, polynomials, strings, and sets, MuPAD users can use both predefined and user-defined "domains" for computation of series and matrices, solving of ordinary differential equations, development of special applications, and more. With domains, users can define their own data types, overload MuPAD functions and operators for new data types; control input and output of objects; hide or redefine internal evaluation and simplification rules; and use polymorphic algorithms. Predefined domains are provided by a MuPAD library and include Matrix, SquareMatrix, GaloisField, AlgebraicExtension, and others.
MuPAD Extends the Kernel with Dynamic Modules
Dynamic modules are similar to library packages, but are not written in the MuPAD programming language. Instead, they are compiled machine code functions written in C/C++, as are the built-in functions in the kernel. Dynamic modules can be unloaded (or removed from main memory) at any time and reloaded on demand. This means that MuPAD is a modular system that acts as a universal shell. Users can integrate various specialized software packages with the system to solve many kinds of mathematical problems.
MuPAD Has a Source Code Debugger
MuPAD is the only computer algebra system that has a source code debugger for use with user-defined procedures and domains written in the MuPAD language. Debuggers are common to modern programming language compilers. The debugger is Windows-based, mouse-driven, and interactive.
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