A common operation in analyzing various kinds of data is to find the discrete Fourier transform (or spectrum) of a list of values. The idea is typically to pick out ...

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...

Front end tokens let you perform kernel commands that would normally be done using the menus. Front end tokens are particularly convenient for writing programs to manipulate ...

Function Names as Expressions Applying Functions Repeatedly Applying Functions to Lists and Other Expressions

In an expression like f[x], the 'function name' f is itself an expression, and you can treat it as you would any other expression. You can replace names of functions using ...

Defining Functions Functions as Procedures Manipulating Options

In many kinds of calculations, you may find yourself typing the same input to Mathematica over and over again. You can save yourself a lot of typing by defining a function ...

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 ...

When you make a function definition using :=, the value of the function is recomputed every time you ask for it. In some kinds of calculations, you may end up asking for the ...

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...