**Last modified:***Friday, 1 July 1994***Source code: scalar-quantities.lisp****List of other known theories**

The term 'scalar' is often equated with the field of real numbers. In this theory we extend that notion to quantities in general, which are associated with dimensions and units. Scalar quantities are quantities whose magnitude is a real number, such as 'the length of rod a'. The normal operators for real arithmetic such as + and *, and the relation<, are extended to the case of scalar quantities (i.e., to consider dimensions and units). Scalar-Quantities are disjoint from vectors quantities, and scalar functions.

- (c) 1993, 1994 Greg R. Olsen and Thomas R. Gruber

**See-Also:**The EngMath paper on line

Physical-Quantities

Tensor-QuantitiesUnary-Scalar-FunctionsVt-Design

Scalar-Quantity

*+ExptRecipScalar-Quantities-Of-DimensionThe-Zero-Scalar-For-Dimension

Identity-Scalar

**The following constants were used from included theories:**

**<***defined as a***relation***in theory***Kif-Numbers****<***defined as a***relation***in theory***Physical-Quantities****Abelian-Group***defined as a***relation***in theory***Abstract-Algebra****Arity***defined as a***function***in theory***Frame-Ontology****Class***defined as a***class***in theory***Frame-Ontology****Compatible-Quantities***defined as a***relation***in theory***Physical-Quantities****Constant-Quantity***defined as a***class***in theory***Physical-Quantities****Documentation***defined as a***relation***in theory***Frame-Ontology****Domain***defined as a***relation***in theory***Frame-Ontology****Function***defined as a***class***in theory***Kif-Relations****Identity-Dimension***defined as a***object***in theory***Physical-Quantities****Identity-Element-For***defined as a***relation***in theory***Abstract-Algebra****Linear-Order***defined as a***relation***in theory***Abstract-Algebra****Magnitude***defined as a***function***in theory***Physical-Quantities****Partial-Order***defined as a***relation***in theory***Abstract-Algebra****Physical-Dimension***defined as a***class***in theory***Physical-Quantities****Quantity.Dimension***defined as a***function***in theory***Physical-Quantities****Range***defined as a***relation***in theory***Frame-Ontology****Real-Number***defined as a***class***in theory***Kif-Numbers****Subclass-Of***defined as a***relation***in theory***Frame-Ontology****Superclass-Of***defined as a***relation***in theory***Frame-Ontology****Unit-Of-Measure***defined as a***class***in theory***Physical-Quantities****Zero-Quantity***defined as a***class***in theory***Physical-Quantities**

**All constants that were mentioned were defined.**

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