This tutorial covers advanced features of the Manipulate command. It assumes that you have read "Introduction to Manipulate" and thus have a good idea what the command is for ...

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 ...

Symbolic Computation Values for Symbols Transforming Algebraic Expressions

Structural Operations on Polynomials Finding the Structure of a Polynomial Polynomial Orderings

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 ...

For many kinds of practical calculations, the only operations you will need to perform on polynomials are essentially structural ones. If you do more advanced algebra with ...

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 ...

Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful constructs for doing this. Applying functions of one ...

In an expression like f[{a,b,c}] you are giving a list as the argument to a function. Often you need instead to apply a function directly to the elements of a list, rather ...