There are many detailed differences between different kinds of computer systems. But one of the important features of Mathematica is that it allows you to work and create ...

In most cases, you want the head f of a Mathematica expression like f[x] to be a single symbol. There are, however, some important applications of heads that are not symbols. ...

Basic vector operations. This is a vector in three dimensions. This gives a vector u in the direction opposite to v with twice the magnitude.

The general principle that Mathematica follows in evaluating expressions is to go on applying transformation rules until the expressions no longer change. This means, for ...

ByteCount[expr] gives the number of bytes used internally by Mathematica to store expr.

GradientFilter[image, r] gives an image corresponding to the magnitude of the gradient of image, computed using discrete derivatives of a Gaussian of pixel radius ...

ImageCooccurrence[image, n] gives the n*n cooccurrence matrix for image.ImageCooccurrence[image, n, ker] computes a cooccurrence matrix for arbitrary spatial relationships ...

Defining local constants. Module allows you to set up local variables, to which you can assign values and then change them. Often, however, all you really need are local ...

Mathematica supports state-of-the-art sound generation, providing both arbitrary waveform synthesis from functions and data, and symbolic note-based MIDI-style sound ...

Statistical visualization is used to understand how data is distributed and how that compares to other datasets and distributions. Histograms and smooth histograms both ...