Cartesian product

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cartesian product

[kär′tē·zhan ′präd·əkt]
In reference to the product of P and Q, the set P × Q of all pairs (p,q), where p belongs to P and q belongs to Q.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Cartesian product

(After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set

A x B = a, b) | a in A, b in .

I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.

If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.

See also tuple.
This article is provided by FOLDOC - Free Online Dictionary of Computing (
References in periodicals archive ?
Figures 3(a), 3(b), and 3(c) illustrate two directed graphs and their Cartesian product, respectively.
Among the class of nontrivial Cartesian products several infinite families of EOD-graphs have been found.
We are interested in the cartesian product of codes in the Hamming graphs H(n, q) and H(n', q').
Then, the Cartesian product of [[psi].sub.K] and [[OMEGA].sub.L] is obtained as follows;
Zerovnik, "Roman domination number of the cartesian products of paths and cycles," Electronic Journal of Combinatorics, vol.
The pattern required to convert the transactor and transactand functions is actually an extension of the 'Cartesian product' pattern shown in table 1, which has been formalized as: R [subset or equal to] X x Y.
Moreover, Cartesian products, projections, selections, unions, and differences of induced subobjects satisfy all the abstract properties that are axiomatized by relational calculus (15; 16).
Another possible extension is to functions bandlimited to the Cartesian product of two (or more) balls.
In this section, we define the theoretical annotated temporal algebra and provide definitions for compaction, intersection, union, selection, difference, cartesian product, projection, and join on annotated relations.
To this end we study the following algorithm inspired by a similar, though more complex, algorithm of Monfroy and Rety [1999] defined on a Cartesian product of component partial orderings.
Furthermore, among the structural, set-theoretic relationships it is often desirable to identify the Cartesian product of some of the sets--an action that can be crucial in preventing certain kinds of representations from growing exponentially in size.
This is done by maximizing the number of cartesian products and joins with two operators as children.