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Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far less faithful to the ...
Relational algebra is a branch of mathematics that studies the manipulation and analysis of data in relational databases. It defines a set of operations, such as selection, projection, join, and union, that can be applied to relations or sets of tuples. Learn more about the concepts and notation of relational algebra on Wikipedia, including the rename operation that changes the attribute name ...
The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization of query optimization, which is finding more efficient ...
In computer science, domain relational calculus ( DRC) is a calculus that was introduced by Michel Lacroix and Alain Pirotte as a declarative database query language for the relational data model. [ 1] In DRC, queries have the form: where each X i is either a domain variable or constant, and denotes a DRC formula.
Relation (database) In database theory, a relation, as originally defined by E. F. Codd, [ 1] is a set of tuples (d 1 ,d 2 ,...,d n ), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a ...
Codd's theorem. Codd's theorem states that relational algebra and the domain-independent relational calculus queries, two well-known foundational query languages for the relational model, are precisely equivalent in expressive power. That is, a database query can be formulated in one language if and only if it can be expressed in the other.
The relational model ( RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, [ 1][ 2] where all data is represented in terms of tuples, grouped into relations. A database organized in terms of the relational model is a ...
e. Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.