When a programmer deals with mathematics, one of the most common routines added to his/her math library is matrix inversion. The following code implements a very efficient in-situ matrix inversion (meaning that no memory is allocated for another matrix to hold the result; the inverse of the matrix is built gradually in the matrix itself!). The code is based on an algorithm published in Numerical Recipes.

The Monty Hall is a famous problem, which can be stated as follows: 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

The answer is counter-intuitive; yes, it is advantageous to switch. In fact, if you switch, you have doubled your chances to win. The theory may be difficult to grasp at first, so a computer simulation should verify the answer. 

Today I stumbled on an program I had written years ago. During a hot summer I used to spend my time solving Sudoku puzzles at the beach - which is quite fun if you are in a must-not-work mode. Of course, very soon I found myself on my laptop, writing a program for creating and solving Sudoku puzzles. The algorithm for the creation of new puzzles is interesting, although probably not the most efficient, and surely someone else has thought it before me. In any case, I am sharing:

Following the article on how to create dynamic pages in Joomla! by inserting PHP code in the content, there is another case that I have encountered countless times; the content of the article does not need to change very often and it is systematic in the sense that it could be handled by a computer program. But how can you access the contents of a Joomla article and modify it?

I have been involved lately in a soon-to-be-huge project about accounting, invoices, etc.

When printing some invoices I noticed some inconsistencies in the sums; one or two cents difference with respect to the result I obtain when checking the numbers by hand. A little digging and the problem was isolated; it was the Math.Round() function.

Joomla! is a very popular CMS (Content Management System) which allows you to build websites and powerful online applications. In fact, the lines that you read right now belong to a Joomla! website.

Although the CMS is dynamic, I have found that, oddly, the articles (i.e. the content) is rather static. Of course you can include videos, or a gallery of images in the article, but what about the actual text? How can you change it dynamically?