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# Aggregate Product function extends SQL

, 19 Feb 2015 CPOL
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Technique to extend capability of standard SQL by adding the Aggregate Product Function

## Preamble

The suggested solution extends the capability of Structured Query Language (SQL) by adding the Aggregate Product function. Entire 'pure SQL' solution is encapsulated into a single query, portable to any SQL backed databases, for example, Microsoft Access or SQL Server.

## 1. Underlying Math Transforms

Fig.1. SQL Aggregate Product function based on this underlying Math transfom

Standard SQL contains several aggregate functions (Sum, Count, Min, Max, etc.) with noticeable absence of aggregate Product. As a reminder, Product function P of multiple arguments (X1, X2,...XN) is defined as:

N
P(Xi)=X1*X2*...XN .................................................(1)
i=1

Database engine cannot perform the aggregate product calculation directly, but it can calculate sums. Simple mathematical transforms provide a workaround enabling to compute the product P by using the standard built-in mathematical Log(), Exp() and SQL aggregated Sum() functions; the core technique is illustrated by mathematical formulas (2) and (3):

Log(X1*X2*... XN)= Log(X1)+Log(X2)+...Log(XN) ......................(2),

N           N
P(Xi)= Exp(SUM(Log(Xi))) ............................................(3)
i=1         i=1

The last formula (3) could be translated into SQL statement in a rather straightforward manner, enabling the calculation of aggregate Product by means of standard built-in SQL functions.

## 2. Programming Technique: Math-to-SQL Translation

This simple yet practical example will demonstrate the SQL programming technique enabling to calculate the Product of all positive numbers {2, 4, 5, 7, 8} stored in a Microsoft Access Table1. Based on the precondition that there are no any negative values, a simple SQL query can do the job of calculating Product (SQL 1):

SELECT Exp(Sum(Log([Num]))) AS P FROM Table1

The statement could be modified with IIf() conditional operator added in order to handle zeros(SQL 2):

SELECT Exp(Sum(IIf([Num]=0,0,Log([Num]))))*IIf(Min([Num])=0,0,1) AS P
FROM Table1

The solution has been implemented/tested in Microsoft Access 2003/2007; it is also portable to any other SQL-backed Database. For detailed discussion of this SQL technique, please refer to the online article [1], published by the author and included in the reference section.

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 President Infosoft International Inc United States
Dr. A. Bell is a full-stack software developer (Win/Web/Mobile). He holds PhD in EE/IT, published 300+ articles, authored 37 inventions and is credited for 10+ Enterprise level projects; currently focused on HTML5/CSS3, Javascript/jQuery, .NET/WPF/C#, Android/Angular.js, 'Big Data', AI, IoT. Alex participated in App Innovation Contests (AIC 2102/2013) with multiple winning submissions. Sample projects/pubs:

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 Re: generalization to the level of a semigroup? DrABELL21-Feb-15 10:36 DrABELL 21-Feb-15 10:36
 My vote of 5 Scott Burkow20-Feb-13 7:31 Scott Burkow 20-Feb-13 7:31
 Re: My vote of 5 DrABELL20-Feb-13 18:46 DrABELL 20-Feb-13 18:46
 Re: My vote of 5 Scott Burkow21-Feb-13 8:21 Scott Burkow 21-Feb-13 8:21
 Re: My vote of 5 DrABELL21-Feb-13 11:39 DrABELL 21-Feb-13 11:39
 Re: My vote of 5 Scott Burkow22-Feb-13 5:56 Scott Burkow 22-Feb-13 5:56
 Re: My vote of 5 DrABELL22-Feb-13 7:44 DrABELL 22-Feb-13 7:44
 Re: My vote of 5 Scott Burkow22-Feb-13 8:40 Scott Burkow 22-Feb-13 8:40
 Reason for my vote of 5 Excellent example of using a little ... MacMaverick23-Mar-11 1:51 MacMaverick 23-Mar-11 1:51
 Re: Many thanks! Kind regards/wishes, Alex DrABELL23-Mar-11 3:57 DrABELL 23-Mar-11 3:57
 Reason for my vote of 5 Simple & unusual A.J.Wegierski14-Mar-11 19:52 A.J.Wegierski 14-Mar-11 19:52
 Re: Many thanks! DrABELL15-Mar-11 3:33 DrABELL 15-Mar-11 3:33
 Short URL to the article: http://exm.nr/PrdSQL DrABELL4-Jan-11 9:37 DrABELL 4-Jan-11 9:37
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