Cellular automata provide a convenient way to represent many kinds of systems in which the values of cells in an array are updated in discrete steps according to a local ...

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

Every new version of Mathematica contains many new features. But careful design from the outset has allowed nearly total compatibility to be maintained between all versions. ...

Mathematica has a general mechanism for handling messages generated during computations. Many built-in Mathematica functions use this mechanism to produce error and warning ...

The precise details of the naming of files differ from one computer system to another. Nevertheless, Mathematica provides some fairly general mechanisms that work on all ...

Cluster analysis is an unsupervised learning technique used for classification of data. Data elements are partitioned into groups called clusters that represent proximate ...

Database connection pools are a common way to improve the performance of database operations. They can be useful because creating a new connection can easily take several ...

This example shows how to use a private database to store Mathematica commands and query the data from Java and Mathematica. If you find that the examples in this section do ...

Programming OpenCL in Mathematica is simple since the user need not write C wrapper code—which can be quite verbose, difficult to understand, and hard to debug. Using ...