Finding singular values and norms of matrices. The singular values of a matrix m are the square roots of the eigenvalues of m.m^*, where * denotes Hermitian transpose. The ...

Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...

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 ...

Now that we have introduced the basic features of patterns in Mathematica, we can use them to give a more or less complete example. We will show how you could define your own ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

In many kinds of numerical computations, it is convenient to introduce approximate functions. Approximate functions can be thought of as generalizations of ordinary ...

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

In addition to the interfaces of Import and Export, Mathematica 8 comes with an autoloading mechanism that simplifies the registration of formats used by the Import and ...

Other tutorials have discussed explicit loading of Mathematica packages using <<package and Needs[package]. Sometimes, however, you may want to set Mathematica up so that it ...

Two ways to set up automatic numbering in a Mathematica notebook. These cells are in DisplayFormulaNumbered style. DisplayFormulaNumbered style is available in the default ...