and what is needed is to represent or code the data in X and Y, and the function, by means of the data sets A and B, respectively. Functions α and β are chosen where α : A → X and β : B → Y
and a function f : A → B is defined to be a representation or function for φ on the code sets A and B if, for all a∈A, the following equation holds: φα(a) = βf(a)
This equation is depicted by the commutative diagram shown in the figure.
Equations and commutative diagrams of this form play an important role in relating different levels of abstraction, and are used to formulate the correctness of data-type implementations, compilers, and machine architectures. As equations grow in complexity, commutative diagrams become essential. See also computable algebra.
"commutative diagram." A Dictionary of Computing. . Encyclopedia.com. (October 21, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/commutative-diagram
"commutative diagram." A Dictionary of Computing. . Retrieved October 21, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/commutative-diagram
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.