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In MathProg the model is described in terms of sets, parameters,
variables, constraints, and objectives, which are called *model
objects*.

The user introduces particular model objects using the language statements. Each model object is provided with a symbolic name that uniquely identifies the object and is intended for referencing purposes.

Model objects, including sets, can be multidimensional arrays built
over indexing sets. Formally, *n*-dimensional array *A* is the
mapping:
$$\begin{equation}A:\Delta\rightarrow\Xi,\tag{4}\end{equation}$$
where $\Delta\subseteq S_1\times S_2\times\dots\times S_n$ is a
subset of the Cartesian product of indexing sets, $\Xi$ is a set of
the array members. In MathProg the set $\Delta$ is called
*subscript domain*. Its members are $n$-tuples
$(i_1,i_2,\dots,i_n)$, where $i_1\in S_1, i_2\in S_2$,
$\dots, i_n\in S_n$.

If *n* = 0, the Cartesian product above has exactly one element
(namely, 0-tuple), so it is convenient to think scalar objects as
0-dimensional arrays which have one member.

The type of array members is determined by the type of corresponding model object as follows:

Model objectArray memberSet Elemental plain set Parameter Number or symbol Variable Elemental variable Constraint Elemental constraint Objective Elemental objective

In order to refer to a particular object member the object should be
provided with subscripts. For example, if *a* is 2-dimensional
parameter built over
$I\times J$,
a reference to its particular
member can be written as *a*[*i*, *j*], where
$i\in I$ and $j\in J$.
It is understood that scalar objects being 0-dimensional need no
subscripts.