# Set Expressions¶

Set expressions are a convenient way to build sets from other sets or locations. For the following examples we will assume that these objects are available in the scene:

• A
• B
• C
• D
• E

Set memberships in this imaginary scene are as follows.

set1 set2 set3 set4
A B C B C D C D E E

The following operators are currently supported

Operator Behaviour
| Union, unites two sets
& Intersection, intersects two sets
- Difference, removes elements from sets

## Simple Examples¶

SetExpression Objects in resulting set
set1 A B C
set1 | set2 A B C D
set1 & set2 B C
set1 - set2 A
set1 - C A B

The last example illustrates the use of objects in set expressions. Gaffer will interpret them as a set with the specified object as its sole member. Gaffer will also conveniently interpret space separated lists of sets and objects as a set that contains all the elements in the list (think of it as Gaffer inserting the | for you).

SetExpression Objects in resulting set
set1 set2 A B C D
set1 D A B C D

Note that you can build sets on-the-fly to be used in the expression by using these space separated list of sets and objects.

SetExpression Objects in resulting set
set1 | (D E) A B C D E
set1 & (A B D) A B
set1 - (B C) A

## Operator Precedence¶

Operations in the expression are executed in the following order: difference before intersection before union. The following examples demonstrate this in action.

SetExpression Objects in resulting set
set1 | set3 & set4 A B C E
set1 - set2 | set4 A E
set1 - set3 & set2 B

Parenthesis can be used to explicitly change the order of evaluation. The following examples use the same sets and operations as before, and demonstrate the effect of changing the evaluation order.

SetExpression Objects in resulting set
(set1 | set3) & set4 E
set1 - (set2 | set4) A
set1 - (set3 & set2) A B