4.5: Factorial Function

Mathematically, we define the factorial as a function on a non-negative integer as

$$n! = n(n − 1)(n − 2) \cdots 3 \cdot 2 \cdot 1 \label{factorial}$$
or the product of all of the numbers from itself down to 1. There are a number of ways to program this function as we will see. One way is

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function fact(n::Integer) 
  local prod=1
  for i=1:n
    prod *= i 
  end
  prod
end

function fact(n::Integer) 
  local prod=1
  for i=1:n
    prod *= i 
  end
  prod
end

uses a for loop and we will see the details of this in Chapter XXX. The for loop first assigns i the value 1 then executes the lines, then sets the value to 2, then executes the block, and so on until i is n. Since prod starts as 1, this multiplies prod by every integer between 1 and n, and thus is the factorial. The result in prod is returned. 

For example, we can call the factorial function with an example like

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factorial(10)

factorial(10)

Exercise

Try calling the factorial with a few other integers.  Include 0 and negative numbers as well.