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## Dimension Checking in QUDT

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There are a lot of services that an engineer or scientist could ask of a system of units; many of these go by the name *dimensional analysis*. Whole books have been written on the subject; we can barely scratch the surface of this topic here (therefore, see the Further Reading section at the conclusion of the book). We will illustrate enough of the QUDT ontology to show how it can support certain basic operations in dimensional analysis.

The basic idea of dimensional analysis is that a quantity has a signature that tells how it relates to basic quantities like length, time, and mass. QUDT defines eight base quantities of this sort, but in this exposition, we will focus on these three. A compound quantity has a signature in these basic quantities. For example, the compound quantity velocity is defined as a ratio between distance and time; this means that its signature in terms of length, time, and mass is length/time. The signature can be written as a vector, with one vector component for each base unit, and the magnitude of the vector in that component being the exponent of the base quantity in the formula for the compound quantity. If we write our vectors in the order [le....