Function SCALAR-QUANTITIES-OF-DIMENSION

• Defined in theory: Scalar-quantities
• Source code: scalar-quantities.lisp

Slots on this function:

Documentation:

Scalar-Quantities are partitioned into classes of uniform dimension. All instances of one of these classes have the same physical dimension. Each of these classes form a linear order with respect to the < relation. Length scalars, time scalars, and mass scalars are examples of scalar subclasses.

Instance-Of: Function

Arity: 2

Domain: Physical-dimension

Range: Class

Other Related Axioms:

(Forall (?D)
        (=> (Physical-Dimension ?D)
            (Abelian-Group (Scalar-Quantities-Of-Dimension ?D)
                           +
                           (The-Zero-Scalar-For-Dimension ?D))))

(<- (Scalar-Quantities-Of-Dimension ?Dimension)
    (If (Physical-Dimension ?Dimension)
        (Kappa (?Q)
               (And (Scalar-Quantity ?Q)
                    (= (Quantity.Dimension ?Q) ?Dimension)))))

(=> (= (Scalar-Quantities-Of-Dimension ?Dimension) ?Class)
    (Linear-Order ?Class <))

(=> (= (The-Zero-Scalar-For-Dimension ?Dimension) ?Zero-Scalar)
    (Identity-Element-For ?Zero-Scalar
                          +
                          (Scalar-Quantities-Of-Dimension ?Dimension)))