How to define a MultidimensionalNumberSpace?
In ISO 15926-5 you can find two rather esoteric entity types, the ClassOfMultidimensionalObject and the MultidimensionalObject. These are discussed in a separate topic. In this topic I'll try to give an explanation of one of the derivatives, the MultidimensionalNumberSpace.
Part 2 defines:
EXAMPLE R3, the space defined as being all the triples of real numbers (e.g. <1.0, 2.1, 5.4>), is a MultidimensionalNumberSpace.
SUBTYPE OF (number_space, multidimensional_object);
Let's use the (adapted) diagram below as reference:
The adaptation, whereby the non-applicable attributes are being left out, shows that the esoteric character disappears. For details see here.
Let us first focus on the ClassOfMultidimensionalObject, attribute by attribute.
The rdf:object of this attribute is a set of instances of RoleAndDomain that indicate what the role actually is and what subtype of Thing is the object. If the multidimensional object is the input in a function (so a ClassOfFunctional Mapping), then each role is the same as its parameter name in that function.
If any of the Roles could exist 0, 1, or more times for an instance of MultidimensionalObject, then that shall be expressed by a list of instances of Cardinality. If one or more such cardinalities apply, all cardinalities shall be defined. (no example comes to my mind)
and then of the MultidimensionalProperty:
Here the 1:? multidimensional properties that are part of the multidimensional property space, where that cardinality is determined by the "cardinalities" attribute of the classifying ClassOfMultidimensionalObject.
Let us now focus on the MultidimensionalNumberSpace that defines the ultimate limits of the values that any member Multidimensional Number may have:
MultidimensionalNumberSpace defines the limits of any member MultidimensionalNumber
In template format this looks like this:
An official template looks like this: