# How-CAL-Evaluates-Expressions-CAL-Command

How CAL Evaluates Expressions (CAL Command)

# 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,
• 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

+, –

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]

+ , –

[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.

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