CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

InterpolatingFunction[domain, table] represents an approximate function whose values are found by interpolation.

e_1 || e_2 || ... is the logical OR function. It evaluates its arguments in order, giving True immediately if any of them are True, and False if they are all False.

Converting between strings, boxes, and expressions. Here is a simple expression. This gives the InputForm of the expression as a string.

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 ...

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 ...

MonitorLM gives information on the total number of licenses available and checked out, the fully qualified domain name and username of those who have them checked out, and so ...

Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...