MuPAD

by SciFace

MuPAD Pro is a full-fledged computer algebra system for symbolic and numeric computing. Beside the common features of all MuPAD versions, MuPAD Pro for Windows offers some highlights ? especially a user-friendly interface ? for doing mathematics as easy as possible with the conviences of mouse and keyboard.

• Notebook Concept
  A Notebook is the basic part of MuPAD Pro. It combines mathematical computations, advanced text processing and inline graphics in one document. In a Notebook you can re-edit and re-evaluate existing MuPAD expressions.
  Multiple independent Notebooks can be opened at once, and Notebooks can be exported to RTF, plain text and HTML documents.
   
• Source code editor
  MuPAD Pro for Windows includes a source code editor for writing user-defined procedures with syntax coloring and bookmark management.
   
• Source Code Debugger
  A powerful tool for step-by-step execution of MuPAD procedures. It displays used variables and allows evaluation of arbitrary expressions during debugging.
   
• Interactive Graphics Tools News in 3.0
  The Virtual Camera (VCam) for 2D and 3D visualizations of functions, curves, surfaces and many other mathematical objects.
   
• Hypertext Online Help
  Extensive documentation of all MuPAD commands with user definable links and bookmarks using a Help Browser with fast and comfortable search functions.
   
• OLE 2 Support
  MuPAD Notebooks and VCam Graphics can be embedded into other OLE applications like Microsoft Word or Excel. On the other hand, Excel sheets can be embedded into a MuPAD Pro Notebook.
   
• Other goodies
  Extras Menu ? a user definable menu with commonly used MuPAD commands.
  Command Bar ? a graphical tool bar with commonly used MuPAD commands.
  Drag and Drop support.

General Capabilities and Features

• Multi-precision arithmetic
• Symbolic computation and expression manipulation
• User-definable data structures
• Procedural, object-oriented and functional programming
• Dynamic linking of external binary code
• Extensive online hypertext documentation
• Interactive 2D- and 3D-graphics tool

Extensive Mathematics Capabilities

• 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:
  • 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
• Assumptions and Properties:
  • Attach properties to identifiers
  • Check mathematical properties of identifiers and expressions
• 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:
  • 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:
  • Define, edit, and plot; find shortest paths or maximal flows
• 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.
• Library source included