When you define a complicated function, you will often want to let some of the arguments of the function be "optional". If you do not give those arguments explicitly, you ...

There are many situations where you want to write a particular algebraic expression in the simplest possible form. Although it is difficult to know exactly what one means in ...

You can give Solve a list of simultaneous equations to solve. Solve can find explicit solutions for a large class of simultaneous polynomial equations. Here is a simple ...

When you give a list of equations to Solve, it assumes that you want all the equations to be satisfied simultaneously. It is also possible to give Solve more complicated ...

As discussed in "The Structure of Graphics and Sound", Mathematica includes a full graphics programming language. In this language, you can set up many different kinds of ...

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 ...

Particularly when you write procedural programs in Mathematica, you will often need to modify the value of a particular variable repeatedly. You can always do this by ...

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.