*this Algebraix Data product goes beyond the Relational Model and is based on a new Algebra of Data, which is directly derived from classical set theory.*

**Date:**

Robin Bloor has recently published a whitepaper which analyzes a new BI product from Algebraix Data, named A

^{2}DB.

**DOING THE MATH: The Algebraic DataBase: What it is, how it works, why we need it**

**Executive Summary**

Algebraix Data recently introduced a highly unusual BI database product, named A^{2}DB. The
database is the realization of a new and highly versatile Algebra of Data, which is directly
derived from classical set theory. As far as we can tell, it is valid, viable and versatile. As this
white paper will explain, this unique algebra is the foundation of the A^{2}DB database, and is
the reason for all of the positive characteristics of the product. This new algebra subsumes the
relational algebra created by Tedd Codd in the 1970s, and hence is able to replace it.
Detailed explanations of how and why A^{2}DB provides the capabilities it does are found in
this paper. The following is a list of the benefits that A^{2}DB delivers or claims to deliver:

- Low hardware costs. A
^{2}DB runs on commodity x86 hardware. - Scalability: A
^{2}DB scales well (roughly linearly) within SMP environments and, in such environments, will accommodate data growth without performance issues arising. - Extremely low operational overhead: A
^{2}DB is self-managing in many ways that other databases are not. - Database design effort reduces almost to zero: A
^{2}DB is extremely forgiving in respect of database design. Any design that is consistent in respect of data is a viable starting point. The algebraic nature of the database compensates for imperfect data design. - Improved performance and accelerating performance: A
^{2}DB delivers high performance; and, uniquely among database products, the performance improves with usage. It is particularly suited to BI applications in the 1- 2 terabyte arena where performance has been an issue for other database products.

**The Algebraic Model of Data**

The Algebraic Model of Data that sits beneath Algebraix's A2DB does not force data into twodimensional tables. Instead it represents data using the more familiar mathematical structure of sets. This turns out to be a more flexible structure for data. To get a sense of this algebra, you need to understand four simple ideas:

1. The couplet

2. The extended set

3. The clan

4. The derived clan

Here the paper:

**DOING THE MATH**: The Algebraic DataBase: What it is, how it works, why we need it