# Number - Addition (or Sum, Sigma) or Total

The addition of all numbers in a set is called a total.

Sum can be use as:

It can follow the full syntax of the analytic function and in this way create Function - (Moving|Rolling|Running) Calculation

It's a binary function.

## Associative Property

An addition has an associative property and groups to the left (i.e., is left-associative). 1 + 2 + 3 is equivalent to (1 + 2 ) + 3

Example in Javascript

console.log(1 + 2 + 3); // 6
console.log((1 + 2) + 3); // 6
console.log(1 + "2" + 3); // 123
console.log((1 + "2") + 3); // 123


## Different Methods

The two arithmetic operations work on different types of operands and require different functions.

## Sigma

The symbol “sigma” is the Greek capital S and is a shortcut for “the sum of”.

• sum of x:

## Analytic / Aggregate

The data come from the sample schema SH and the two next statements retrieve the same result.

### Aggregate (Group By)

select distinct CUST_LAST_NAME, sum(AMOUNT_SOLD)
from
SH.CUSTOMERS CUST,
SH.SALES SALES
where  ( CUST.CUST_ID = SALES.CUST_ID ) AND
( CUST_LAST_NAME like 'Aa%' or CUST_LAST_NAME like 'Ab%' or CUST_LAST_NAME like 'Ac%' )
group by CUST_LAST_NAME
order by CUST_LAST_NAME asc


### Analytic / Window (Over )

select distinct CUST_LAST_NAME, sum(AMOUNT_SOLD)  over (order by CUST_LAST_NAME)
from
SH.CUSTOMERS CUST,
SH.SALES SALES
where  ( CUST.CUST_ID = SALES.CUST_ID ) AND
( CUST_LAST_NAME like 'Aa%' or CUST_LAST_NAME like 'Ab%' or CUST_LAST_NAME like 'Ac%' )
order by CUST_LAST_NAME asc


### Analytic and Aggregate Statement

select
distinct CUST_LAST_NAME,
sum(AMOUNT_SOLD) ,
sum(sum(AMOUNT_SOLD) over () -- Grand Total. You must give the two times the SUM function. Otherwise you get a ORA-00979.
from
SH.CUSTOMERS CUST,
SH.SALES SALES
where  ( CUST.CUST_ID = SALES.CUST_ID ) AND
( CUST_LAST_NAME like 'Aa%' or CUST_LAST_NAME like 'Ab%' or CUST_LAST_NAME like 'Ac%' )
group by CUST_LAST_NAME
order by CUST_LAST_NAME asc


## Identity

The identity function for addition (+) is $$x+0 = x$$