A.3.3.CC:4.2 - Express compatible combinations

Start with the product of the separate value sets. Write the conditions selecting the combinations admitted by the model. In a finite problem this may be a table of allowed tuples. In an algebraic description it may use equalities, inequalities or other predicates.

In A.19 terms, CS = product_i ValueSet(Scale_i) is the CharacteristicSpace. A constraint predicate P selects a subset Q = {q in CS : P(q)} used as the represented configuration set. A point in CS supplies a value for every selected slot; membership in Q additionally satisfies the constraints. The same method can be used in ordinary mathematical notation without creating a separate FPF record.

Explain what each condition represents. Fixed distance, conserved stock, nonpenetration and an imposed operating limit can all constrain the calculation, but changing each condition changes a different premise. Keep a condition imposed by the intended use recognizable so that revising a preference does not appear to alter a physical law.

When time or an external parameter changes which combinations are admitted, make that dependence recoverable, for example Q(t; p). A moving wall changes a position constraint even before its interaction law is known.

Place restrictions on rates, operations or transitions with those relations. The car constraint in :5.4 limits instantaneous velocity; it leaves the corresponding configuration variables available. A.3.3 uses both kinds of restriction when constructing allowed continuations.