Luca Sonaglioni

A new number theory Book II rel. Luca Sonaglioni

At the end of 1990 I was a student, and I was studying applications of computers for solving electromagnetic problems with finite elements system. In that period I asked myself if it was possible to build up a 3d number to simplify the calculus. In the summer of 2014 I got the idea that is exposed in chapter I. This method permits to treat numbers with more than 2 dimensions. The core of the idea is the definitions of the sum and of the product for 3d numbers; next we will see we can built up a similar, multi dimensions algebra, very close to the standard 2d complex algebra. The product rule and the sum rule can be extended to more dimensions. This algebra is commutative but not distributive so, for the study of many (3-n)d problems it needs to have a computational approach instead of an analytical approach. The book analyze the basis of the algebra. At the end, out of the theme, is proposed a generalized de-convolution algorithm that, I suppose, it's a news.