On most computer systems, Mathematica can produce not only graphics but also sound. Mathematica treats graphics and sound in a closely analogous way. For example, just as you ...

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 ...

Spheroidal functions. The radial spheroidal functions SpheroidalS1[n,m, γ,z] and SpheroidalS2[n,m,γ,z] and angular spheroidal functions SpheroidalPS[n,m,γ,z] and ...

Invisible characters. In the input there is an invisible comma between the 1 and 2. Here there is an invisible space between the x and y, interpreted as multiplication.

For ordinary polynomials, Factor and Expand give the most important forms. For rational expressions, there are many different forms that can be useful. Different kinds of ...

The hierarchy of levels at which options can be set. Here is a notebook containing three cells. This is what happens when the setting CellFrame->True is made specifically for ...

This constructs the sum ∑_(i=1)^7 (x^i)/(i) . You can leave out the lower limit if it is equal to 1. This makes i increase in steps of 2, so that only odd-numbered values are ...

One of the important features of Mathematica is that it can do symbolic, as well as numerical calculations. This means that it can handle algebraic formulas as well as ...

The built-in functions of Mathematica implement a very large number of algorithms from computer science and mathematics. Some of these algorithms are fairly old, but the vast ...

When you make a sequence of definitions in Mathematica, some may be more general than others. Mathematica follows the principle of trying to put more general definitions ...