Connecting to a subsidiary program via MathLink. This starts a subsidiary Mathematica process on the computer system used here. Here is a packet representing the first input ...

Converting to and from character codes. Mathematica assigns every character that can appear in a string a unique character code. This code is used internally as a way to ...

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 ...

Converting between strings, boxes, and expressions. Here is a simple expression. This gives the InputForm of the expression as a string.

Within a standard interactive session, you can create "subsessions" or dialogs using the Mathematica command Dialog. Dialogs are often useful if you want to interact with ...

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

There are a number of important interactions in Mathematica between evaluation and pattern matching. The first observation is that pattern matching is usually done on ...

When you ask for the square root s of a number a, you are effectively asking for the solution to the equation s^2a. This equation, however, in general has two different ...

If you have an equation like 2x==0, it is perfectly clear that the only possible solution is x->0. However, if you have an equation like ax==0, things are not so clear. If a ...

Mathematica provides built-in support for both programmatic and interactive image processing, fully integrated with Mathematica's powerful mathematical and algorithmic ...