# Theory SCALAR-QUANTITIES

## Theory documentation:

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.

## Cross Reference Report:

### Theories included by Scalar-Quantities:

`  Physical-Quantities`

### Theories that include Scalar-Quantities:

```  Tensor-Quantities
Unary-Scalar-Functions
Vt-Design```

### 1 class defined:

`    Scalar-Quantity`

### 6 functions defined:

```  *
+
Expt
Recip
Scalar-Quantities-Of-Dimension
The-Zero-Scalar-For-Dimension```

### 1 instance defined:

`  Identity-Scalar`

The following constants were used from included theories:

All constants that were mentioned were defined.

This document was generated using Ontolingua.
Formatting and translation code was written by
François Gerbaux and Tom Gruber