Mathematica provides many options for customizing and annotating plots. Legends can be added to plots and customized with many of the same methods used to customize other ...

NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot ...

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

Functions like Read and Write handle ordinary printable text. But in dealing with external data files or devices it is sometimes necessary to go to a lower level, and work ...

Modules in Mathematica allow you to treat the names of variables as local. Sometimes, however, you want the names to be global, but values to be local. You can do this in ...

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 ...

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 ...