Mathematica

TL;DR

• A general-purpose computational software platform used across scientific and engineering fields.
• Performs complex symbolic computations and produces a wide range of visualizations and interactive documents.
• Includes features such as parallel computing and a large library of algorithms and data structures.

Definition

Mathematica is a powerful computational software platform developed by Wolfram Research, used in many fields including scientific and engineering computing, and for creating interactive technical applications and web-based documents.

Explanation

Mathematica provides capabilities for complex symbolic computation, enabling manipulation and simplification of algebraic equations and expressions. It also offers extensive visualization and plotting functions (for example, scatter plots, bar charts, histograms, and contour plots), along with support for parallel computing, a large library of algorithms and data structures, and tools for creating interactive documents and web applications.

Examples

Symbolic computation example

Given the equation $x^2 + 2x + 1 = 0$ the following Mathematica command solves for x:

Solve[x^2 + 2x + 1 == 0, x]

The output of this code would be {x -> -1 - Sqrt[2], x -> -1 + Sqrt[2]}, which shows that the solutions to the equation are x = -1 - sqrt(2) and x = -1 + sqrt(2).

Plotting example

For the data points {(1,2), (3,4), (5,6), (7,8)}, Mathematica can create a scatter plot with:

ListPlot[{{1,2}, {3,4}, {5,6}, {7,8}}, PlotStyle -> PointSize[0.05]]

This generates a scatter plot with each point represented by a small dot; the plot can be customized (point size, title, axis labels, etc.).

Use cases

• Scientific computing
• Engineering computing
• Creating interactive technical applications
• Creating web-based documents

Related terms

• Wolfram Research
• Symbolic computation
• Parallel computing
• ListPlot