Because application knowledge is often entered into a dynamic knowledge acquisition environment, again no pre-compilation dimensionality information would be available in order to handle units of measure statically. Having thus argued that keeping unit of measure information at numbers explicitly is not only a deplorable burden but may actually have advantages of its own, I will now turn to the representation of dim-numbers. This ought to be as efficient as possible with respect to space and computational time. Moreover, it ought to support easy consistency checks in additive and comparative operations as well as easy unit conversion in multiplicative operations. All authors in the field agree that the representation that is best suited for these tasks, is based on exponent vectors over elementary units of measure.
Elementary measures are e.g. length, time, and weight.
This is common usage among all approaches to dimensional analysis so far. Second, vectors have fixed length and can thus handle only a fixed number of elementary measures. Our approach to unit of measure representation reduces exponent vectors to a single rational number. Complex measures can the be represented as ratios by multiplying these prime numbers according to the underlying exponent vectors. Handling of these ratios in computations and comparisons is as easy as for vectors.