How CAL Evaluates Expressions (CAL Command)

CAL evaluates expressions according to standard mathematical rules of precedence:

• Expressions in parentheses first, starting with the innermost set
• Operators in standard order: exponents first, multiplication and division second, and addition and subtraction last
• Operators of equal precedence from left to right

Numeric Expressions

Numeric expressions are real integer numbers and functions combined with the operators in the following table.

Numeric operators
Operator	Operation
( )	Groups expressions
^	Indicates exponentiation
* , /	Multiplies, divides
+, -	Adds, subtracts

The following are examples of numeric expressions:

3

3 + 0.6

(5.8^2) + PI

Vector Expressions

A vector expression is a collection of points, vectors, numbers, and functions combined with the operators in the following table.

Vector operators
Operator	Operation
( )	Groups expressions
&	Determines the vector product of vectors (as a vector) [a,b,c]&[x,y,z] = [ (b*z) - (c*y) , (c*x) - (a*z) , (a*y) - (b*x) ]
*	Determines the scalar product of vectors (as a real number) [a,b,c]*[x,y,z] = ax + by + cz
*, /	Multiplies, divides a vector by a real number a*[x,y,z] = [a*x,a*y,a*z]
+ , -	Adds, subtracts vectors (points) [a,b,c] + [x,y,z] = [a+x,b+y,c+z]

The following are examples of vector expressions:

A+[1,2,3] provides the point located [1,2,3] units relative to point A.

The expression

[2<45<45] + [2<45<0] - [1.02, 3.5, 2]

adds two points and subtracts a third point. The first two points are expressed in spherical coordinates.