Mathematica provides a uniquely powerful interactive environment for building up arbitrarily complex computations, under convenient interactive or programmatic control.

Using the objects described in "Introduction to Patterns", you can set up patterns for many kinds of expressions. In all cases, you must remember that the patterns must ...

The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to ...

Mathematica allows any front end command to be executed programmatically from within the kernel by sending an appropriate front end token. There are tokens for all standard ...

Mathematica allows you to use special notation for many common operators. For example, although internally Mathematica represents a sum of two terms as Plus[x,y], you can ...

Mathematica treats equations as logical statements. If you type in an equation like x^2+3x==2, Mathematica interprets this as a logical statement which asserts that x^2+3x is ...

TargetFunctions is an option for functions such as ComplexExpand that specifies what functions to attempt to generate in the output.

Mathematica usually pays no attention to whether variables like x stand for real or complex numbers. Sometimes, however, you may want to make transformations which are ...

Finding the structure of polynomials written in expanded form. Here is a polynomial in two variables. This is the polynomial in expanded form.

Just as Mathematica allows you to define how expressions should be evaluated, so also it allows you to define how expressions should be formatted for output. The basic idea ...