2.8 Operations for Relations

rel1 * rel2

The operator * evaluates to the product of the two relations rel1 and rel2 if both have the same degree.

rel * trans
trans * rel

The operator * evaluates to the product of the relation rel and the transformation trans in the given order provided both have the same degree (see chapter Transformations).

rel * perm
perm * rel

The operator * evaluates to the product of the relation rel and the permutation perm in the given order provided both have the same degree (see chapter "Permutations").

list * rel
rel * list

The operator * evaluates to the list of products of the elements in list with the relation rel. That means that the value is a new list new such that new[i] = list[i] * rel or new[i] = rel * list[i], respectively.

i ^ rel

The operator ^ evaluates to the set of successors <i>^<rel> of the positive integer i under the relation rel if i is smaller than or equal to the degree of rel.

set ^ rel

The operator ^ evaluates to the image or the set set under the relation rel which is defined as the union of the sets of successors of the elements of set.

rel ^ 0

The operator ^ evaluates to the identity relation on n points if rel is a relation on n points (see IdentityRelation).

rel ^ i

For a positive integer i the operator ^ evaluates to the i-th power of the relation rel which is defined in the usual way as the i-fold product of rel by itself.

rel ^ -1

The operator ^ evaluates to the inverse of the relation rel. The inverse of a relation R subseteq {1, ..., n} x {1, ..., n} is given by {(y, x) | (x, y) in R}. Note that, in general, the product of a binary relation and its inverse is not equal to the identity relation. Neither is it in general equal to the product of the inverse and the binary relation.

   
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