Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

Numerical sums and products. This gives a numerical approximation to ∑_(i=1)^∞((1)/(i^3+i!)). There is no exact result for this sum, so Mathematica leaves it in a symbolic ...

Functions relating real numbers and integers. Extracting integer and fractional parts. IntegerPart[x] and FractionalPart[x] can be thought of as extracting digits to the left ...

One of the important features of Mathematica is its ability to give you exact, symbolic, results for computations. There are, however, computations where it is just ...

When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...

Most mathematical functions in Mathematica are set up to apply themselves separately to each element in a list. This is true in particular of all functions that carry the ...

When Mathematica plots a graph for you, it has to make many choices. It has to work out what the scales should be, where the function should be sampled, how the axes should ...

Mathematica supports an extremely wide range of mathematical notation, although often it does not assign a predefined meaning to it. Thus, for example, you can enter an ...

Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.

Much of what Mathematica does revolves around manipulating structured expressions. But you can also use Mathematica as a system for handling unstructured strings of text. ...