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Mathematica - Functionality and Application Packs
Mathematica can be used as:
- a numerical and symbolic calculator
- support of standard mathematical notation for input and output
- a visualisation (2D and 3D) and sound generation system for functions and data
- a high-level programming language to create small or large programs
- a modelling and data analysis environment
- a system for representing knowledge in mathematical and technical fields
- a control language for external programs and processes
- a high-level shell for file, text, and data manipulation
- tailoring for specific applications
- a way to create interactive documents that mix text and animated graphics with active formulas
In addition, it offers many add-in packages ready to be used (some free of charge).
Standard Add-on Applications (free of charge)
Additional Applications from Wolfram Research (chargeable)
Additional Applications from Third Party developers (chargeable)
Standard Add-on Packages (free of charge)
Most versions of Mathematica also includes a collection of standard add-on packages that define many additional functions in areas such as: Algebra, Calculus, Discrete and numerical mathematics, Graphics and Geometry, Linear Algebra, Number theory, Numerical Mathematics, Statistics and Miscellaneous.
Algebra Package
Algebra packages extend the capability of working with polynomials. There are functions for solving polynomial inequalities, counting and isolating roots of polynomials, and representing polynomials in terms of symmetric and remainder parts. This package also provides functions for manipulating quercitrons and elements of Galois fields.
Calculus package
Mathematica has extensive built-in support for calculus, including integration, differentiation, differential equation solving and limits. The calculus package extends this functionality by providing functions for finding complete integrals of differential equations, computing Pade approximation, and doing vector operations in various three-dimensional co-ordinate systems. The package VariationalMethods is useful for solving for a function extreminising a definite integral functional, a problem that appears in many areas of physics and engineering.
Discrete Mathematics Packages
Discrete Mathematics is concerned with enumerable mathematical structures, such as are studied in combinations, graph theory, and computational geometry. The DiscreteMath packages include Combinatorica, which extends Mathematica by over 200 functions in combinatorics and graph theory. It includes functions for constructing graphs and other combinatorial objects, computing invariants of these objects, and finally displaying them. ComputationalGeometry, which provides several important geometric functions useful in nonparametric data analysis, and RSolve, for solving recurrence equations.
Graphics and Geometry Packages
The Graphics package offer log, polar, error, scatter, vector field, surface of revolution, three-dimensional contour, and implicit plots. Functions include maps of visualising complex functions of complex numbers, and bar and pie charts for visualising data. The Geometry packages provides functions giving the characteristics of regular polygons and polyhedral and rotation in two and three dimensions.
Linear Algebra Packages
The LinearAlgebra portion of the standard add-on packages provide functions for producing orthonormal vectors, solving tridiagonal matrix equations, computing the LU factorisation or Cholesky decomposition of a matrix, and other sorts of matrix manipulation.
Number Theory Packages
Functions relevant to number theory are PrimePi, EulerPhi, MoebiusMu and DivisorSigma. The NumberTheory packages broaden this set of functions. There are packages for providing primality, exploring the elliptic curve method for integer factorisation, and finding primitive elements of multiple algebraic extensions of rational. There are functions for approximating real numbers by rationals and approximating polynomials with real roots by polynomials with integer coefficients.
Numerical Mathematics Packages
This package provides fitting functions (polynomial, spline, trigonometric), numerical versions of some of the kernel functions (ND, NLimit, NResidue, NSeries), numerical integration functions (CauchyPrincipalValue, ListIntegrate, NIntegrate, InterpolationsFunction), support for numerical solution of differential equations (BesselZeros, Butcher, OrderStar), alternatives to FindRoot using interpolation or interval methods, functions for approximating by a ratio of polynomials, and pedagogical functions for exploring floating-point arithmetic and numerical quadrature.
Statistics Package
Continuous and discrete univariate and multivariate statistical distributions are supported. There are packages offering descriptive statistics for univariate and multivariate data, data manipulation and smoothing , and classical hypothesis testing and confidence interval estimation. Both linear and non-linear regression functions permit users to take advantage of an extensive collection of diagnostics.
Miscellaneous Packages
The package grouped under Miscellaneous offer a diverse set of functions that are not easily categorised. There are functions for exploring the audio capabilities of Mathematica via waveform modulation and musical scales. Other functions provide calendar dates, chemical element data, physical constants, unit conversions, geodetic measurements and world plots.
Additional Applications from Wolfram Research
Whether you're an engineer, financial analyst, researcher, or student or you just happen to like exploring science and technology, check here before you delve into your next project. It's likely that a team of experts in your field has created software to help you work smarter.
Giving you direct access to Mathematica's powerful programming language and expansive collection of computational commands, each application package or MathLink product provides an incredibly rich and flexible working environment.
Mathematica Applications from Wolfram Research
Mathematica Applications from Third-Party Developers
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