**Defined in theory: Scalar-quantities****Source code: scalar-quantities.lisp****Also defined in:**Kif-numbers, Physical-quantities, Unary-scalar-functions, Basic-matrix-algebra, Tensor-quantities

**Documentation:*** defines the specialization of the quantity multiplication operator * for scalar-quantities. The operator enforces the relationship between the physical-dimensions of the operands and the product. The operator is defined in terms of the number multiplication operator * and the magnitudes of quantities for a particular unit. Scalar-Quantities excluding all the zero-scalars form an abelian group with respect to this operator and the identity-scalar

*<1>*. This operator distributes over the + operator for scalar-quantities,

providing a field behavior with restrictions.

(Abelian-Group (Kappa (?X) (And (Scalar-Quantity ?X) (Forall (?Dim) (=> (Physical-Dimension ?Dim) (/= (The-Zero-Scalar-For-Dimension ?Dim) ?X))))) * 1) (=> (And (Scalar-Quantity ?X) (Scalar-Quantity ?Y)) (<=> (* ?X ?Y ?Z) (And (Scalar-Quantity ?Z) (Forall (?U ?U1 ?U2) (=> (And (Unit-Of-Measure ?U) (Compatible-Quantities ?X ?U) (Unit-Of-Measure ?U1) (Compatible-Quantities ?Y ?U1) (Unit-Of-Measure ?U1) (= (Quantity.Dimension ?U2) (* (Quantity.Dimension ?U) (Quantity.Dimension ?U1)))) (= (* (Magnitude ?X ?U1) (Magnitude ?Y ?U2)) (Magnitude ?Z ?U)))))))