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 ...

If you type in an expression like 0/0, Mathematica prints a message, and returns the result Indeterminate. An expression like 0/0 is an example of an indeterminate numerical ...

Mathematica provides various options for labeling three-dimensional graphics. Some of these options are directly analogous to those for two-dimensional graphics, discussed in ...

Ways to label two-dimensional plots. Here is a plot, using the default Axes->True. Setting Frame->True generates a frame with axes, and removes tick marks from the ordinary ...

Whenever machine-precision numbers appear in a calculation, the whole calculation is typically done in machine precision. Mathematica will then give machine-precision numbers ...

Introduction to MathLink How MathLink Is Used Installing Existing MathLink-Compatible Programs

Matrix inversion. Here is a simple 2×2 matrix. This gives the inverse of m. In producing this formula, Mathematica implicitly assumes that the determinant ad-bc is nonzero.

Finding memory usage. Particularly for symbolic computations, memory is usually the primary resource which limits the size of computations you can do. If a computation runs ...