Wolfram Mathematica

Wolfram Mathematica is a technical computing system providing an integrated environment for mathematics, computation, analysis and visualisation, with tools spanning image processing, geometry, machine learning, data mining, statistics, symbolic algebra and numerical methods. Its defining characteristic, sustained over several decades, is the unification of symbolic and numerical computation in one coherent language. Mathematica manipulates mathematical expressions as exact symbolic objects — differentiating, integrating, solving equations and simplifying algebraically to produce closed-form answers — and then evaluates them numerically to arbitrary precision when required. Most computational tools do one or the other; doing both in the same notebook is what makes the system suited to research and engineering work where the analytical form of a result matters as much as its value.

The Wolfram Language underpinning it is exceptionally broad, with tens of thousands of built-in functions covering calculus, linear algebra, differential equations, number theory, discrete mathematics, optimisation, signal and image processing, graph theory, geometry, probability and statistics. Machine learning and neural network functionality is built in at a high level, so classifiers and predictors can be trained in a single expression. Visualisation is a particular strength, producing publication-quality two- and three-dimensional plots, interactive manipulations and animations with minimal code. The notebook interface interleaves executable code, formatted mathematics, text, graphics and interactive controls in one document, which makes it as much a medium for communicating and teaching as for computing. Curated data is integrated directly from the Wolfram Knowledgebase, giving access to chemical, geographic, astronomical, financial, linguistic and scientific datasets without sourcing them separately. Import and export handle a very wide range of formats, and connectivity covers databases, APIs, external languages and deployment to the cloud. Mathematica is used across academic research, engineering, finance, education and industrial R&D. Pricing starts from around USD 335 with a free trial and no free version, and substantially discounted academic and student licences are available.