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set name alias domain , attrib , $\dots$ , attrib ; |
name is the symbolic name of the set;
alias is an optional string literal which specifies the alias of the set;
domain is an optional indexing expression which specifies the subscript domain of the set;
attrib, $\dots$, attrib are optional attributes of the set. (Commae preceding attributes may be omitted.)
Optional attributes:
specifies dimension of n-tuples, which the set consists of;
specifies a superset which restricts the set or all its members (elemental sets) to be within this superset;
specifies an elemental set assigned to the set or its members;
specifies an elemental set assigned to the set or its members whenever no appropriate data are available in the data section.
Examples
set V; set E within V cross V; set step{s in 1..maxiter} dimen 2 := if s = 1 then E else step[s-1] union setof{k in V, (i,k) in step[s-1], (k,j) in step[s-1]}(i,j); set A{i in I, j in J}, within B[i+1] cross C[j-1], within D diff E, default {('abc',123), (321,'cba')};
The set statement declares a set. If the subscript domain is not specified, the set is a simple set, otherwise it is an array of elemental sets.
The dimen
attribute specifies dimension of n-tuples, which
the set (if it is a simple set) or its members (if the set is an array
of elemental sets) consist of, where n must be unsigned integer from
1 to 20. At most one dimen
attribute can be specified. If the
dimen
attribute is not specified, dimension of n-tuples is
implicitly determined by other attributes (for example, if there is a
set expression that follows :=
or the keyword default
, the
dimension of n-tuples of the corresponding elemental set is used).
If no dimension information is available, dimen 1
is assumed.
The within
attribute specifies a set expression whose resultant
value is a superset used to restrict the set (if it is a simple set) or
its members (if the set is an array of elemental sets) to be within this
superset. Arbitrary number of within
attributes may be specified
in the same set statement.
The assign (:=
) attribute specifies a set expression used to
evaluate elemental set(s) assigned to the set (if it is a simple set) or
its members (if the set is an array of elemental sets). If the assign
attribute is specified, the set is computable and therefore needs
no data to be provided in the data section. If the assign attribute is
not specified, the set must be provided with data in the data section.
At most one assign or default
attribute can be specified for the
same set.
The default
attribute specifies a set expression used to
evaluate elemental set(s) assigned to the set (if it is a simple set) or
its members (if the set is an array of elemental sets) whenever
no appropriate data are available in the data section. If neither assign
nor default
attribute is specified, missing data will cause an
error.
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