In SBML Level 3 as well as Level 2, rules are separated into three subclasses for the benefit of model analysis software. The three subclasses are based on the following three different possible functional forms (where x is a variable, f is some arbitrary function returning a numerical result, V is a vector of variables that does not include x, and W is a vector of variables that may include x):
Algebraic:left-hand side is zero0 = f(W)
Assignment:left-hand side is a scalar:x = f(V)
Rate:left-hand side is a rate-of-change:dx/dt = f(W)
In their general form given above, there is little to distinguish between assignment and algebraic rules. They are treated as separate cases for the following reasons: The approach taken to covering these cases in SBML is to define an abstract Rule structure containing a subelement, "math", to hold the right-hand side expression, then to derive subtypes of Rule that add attributes to distinguish the cases of algebraic, assignment and rate rules. The "math" subelement must contain a MathML expression defining the mathematical formula of the rule. This MathML formula must return a numerical value. The formula can be an arbitrary expression referencing the variables and other entities in an SBML model. Each of the three subclasses of Rule (AssignmentRule, AlgebraicRule, RateRule) inherit the the "math" subelement and other fields from SBase. The AssignmentRule and RateRule classes add an additional attribute, "variable". See the definitions of AssignmentRule, AlgebraicRule and RateRule for details about the structure and interpretation of each one.