Rules for Mathematical Expressions

This topic summarizes the rules for defining and applying mathematical expressions using the Math Expression Builder (these rules apply to all data formats including Channel, Grid and Voxel). These rules include operator precedence, locations, and working with Dummy (placeholder) values.

Operator Precedence

By definition, operators are symbols used to compare left hand and right hand variables or operands in expressions. In math tools, the standard programming hierarchy of operands is observed.

In the following list, each operator is shown in decreasing order of precedence. For some operators, there is also a left-to-right order for evaluating them.

Precedence	Operator	Definition	Location
1	,	Parentheses	Common Keys
2	F()	Function
3		Logical NOT operator	Frequent Tab
4		Exponent	Common Keys
5	,, evaluated left to right	Division, multiplication, modular division	Common Keys
6	, evaluated left to right	Plus, minus	Common Keys
7	,,, evaluated left to right	Greater than, greater than or equal to, less than, less than or equal to	Frequent Tab
8	, evaluated left to right	Equal to, not equal to	Frequent Tab
9		Logical AND operator	Frequent Tab
10		Logical OR operator	Frequent Tab
11		True/false operator used with the statement preceding it. If/Then/Else Statement	Frequent Tab

Rules for Using Dummy (Placeholder) Values

In the binary arithmetic and logical operations stated below, if a term on either side of the operation is undefined or if the operation yields an undefined value, the outcome is undefined and hence set to Dummy. For example, division by 0 is not defined, hence the outcome will be Dummy.

Binary arithmetic:   ,
				,
				,

Binary logical: ,  , ,

The operators ,
			  are cognisant of  the Dummy in order to be able to perform operations such as:

A = (B==DUMMY), which will set A to 1 if B is Dummy, and 0 if it is not.