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	Dr. Dobb's \| Relational Algebra & Metakit \| December 1, 2004
		Relational algebra and Relational calculus are the foundation of the Structured Query Language (SQL).
		Relational algebra begins with a base relation, which is simply the initial view, sometimes called a "table" in relational databases.
		Relational algebra and calculus are the foundation of modern relational databases.
	www.ddj.com /184405933 (0 words)

	Relational algebra Encyclopedia
		Relational algebra, an offshoot of first-order logic, is a set of relations closed under operators.
		Relation algebra in pure mathematics is an algebraic structure, relevant to mathematical logic and set theory.
		Because a relation is interpreted as the extension of some predicate, each operator of a relational algebra has a counterpart in predicate calculus.
	www.hallencyclopedia.com /topic/Relational_algebra.html (3532 words)

	RAFE: A Relational Algebra Front-End for RDBMS (Site not responding. Last check: )
		Relational Algebra is a popular set-oriented notation for specifying queries under the relational model and is frequently mentioned in database courses to illustrate the basic relational database operations.
		Relational Algebra is one of the formal query languages associated with the Relational Data Model.
		A relational schema is the definition of the form of the "table of information" and consists of a name and a set of attributes that define the data types of each "column" of the relation.
	www.cs.niu.edu /midwestconf/mh.htm (3178 words)

	Relational algebra
		The relational algebra is a set of operations that manipulate relations as they are defined in the relational model and as such describes part of the data manipulation aspect of this data model.
		Because of their algebraic properties these operations are often used in database query optimization as an intermediate representation of a query to which certain rewrite rules can be applied to obtain a more efficient version of the query.
		The exact set of operations may differ per definition and also depends on whether the unlabeled relational model (that uses mathematical relations) or the labeled relational model (that used the labeled generalization of mathematical relations) is used.
	www.fact-index.com /r/re/relational_algebra.html (1292 words)

	Building queries with Relational Algebra
		The fundamental operations of the relational algebra are simple operations involving one or two relations as their operands.
		Since the operations of the relational algebra are quite simple, many intermediate results might have to be produced before the final result is reached.
		For most relational algebra operations, the order of execution does not matter, which means that the same result can be reached by forming and combining intermediate results in different ways.
	www.cs.helsinki.fi /u/laine/tkpv/algebra/buildingqueries.html (0 words)

	RxPress_Article
		Relational algebra does not follow Boolean logic, where conditions are either true or false.
		Since search operations are passed directly to the database and they base their searches on relational algebra, this means the AR System is based on relational algebra.
		Remember that according to relational algebra, a NULL value within an operation will cause the result of the operation to be NULL.
	www.remedy.com /customers/dht/archive/RxPress_V8_I1_2000_B.htm (1071 words)

	MORE ON RELATIONAL ALGEBRA VS. CALCULUS
		EM's question on your site today about the differences between relational algebra and relational calculus, Suzanne W.Dietrich in her book "Understanding Relational Database Query Languages" says this at the beginning of chapter 2: "Relational algebra is a procedural query language that applies specific operators to a relation [...]".
		At the beginning of chapter 3 she writes: "Relational calculus is a declarative query language and indicates the properties of the data [...] instead of the procedural paradigm of relational algebra [...]".
		She goes on to describe the tuple relational calculus (TRC) - where variables range over the tuples of a relation - and the domain relational calculus (DRC), where the variables range over the domain of an attribute.
	www.dbdebunk.com /page/page/1897740.htm (483 words)

	Relational Algebra
		The union of two relations is formed by adding the tuples of the two relations to create a third relation.
		The difference of two relations is a third relation containing tuples that occurs in the first relation but not in the second relation.
		The intersection of two relations is a third relation containing the tuples that appear in both relations.
	www.emunix.emich.edu /~khailany/files/database-lan.html (640 words)

	relational from FOLDOC
		The main operations of the relational algebra are the set operations (such as union, intersection, and cartesian product), selection (keeping only some lines of a table) and the projection (keeping only some columns).
		A relational database allows the definition of data structures, storage and retrieval operations and integrity constraints.
		SQL is a standard language for talking to a database built on the relational model (a "relational database").
	www.foldoc.org /?query=relational (784 words)

	The Third Manifesto
		ISBN 0 321 39942 0 Argues that relational database management systems never were fully alive in the first place, since they do not implement the relational model, as handed down by DrCodd, just something quite a lot like it.
		The idea is then that a relation is a predicate, rows in a table are tuples of objects that satisfy that predicate.
		Relational math can describe the logic of the data it provides to you, but it isn't strong enough to describe the storage space upon which it is implemented.
	c2.com /cgi/wiki?TheThirdManifesto (1851 words)

	The Myth of relational algebra (was Re: Clean Object Class Design -- What is it?)
		Often this myth is explained with relational algebra and the possibility to optimize queries in an RDBMS.
		Relational algebra gives you the possibility to transform a query in order to optimize it.
		Relational algebra is used to transform the query to use the index.
	www.orafaq.com /usenet/comp.databases.theory/2001/09/07/0075.htm (687 words)

	relational from FOLDOC
		The main operations of the relational algebra are the set operations (such as union, intersection, and cartesian product), selection (keeping only some lines of a table) and the projection (keeping only some columns).
		A relational database allows the definition of data structures, storage and retrieval operations and integrity constraints.
		SQL is a standard language for talking to a database built on the relational model (a "relational database").
	foldoc.org /?relational (784 words)

	[No title]
		The relational algebra is the part of the relational model concerned with the operators available for manipulation of relations.
		The relation instance of the result is the set of tuples from the operand relation instance, reduced to the attributes in the attribute list.
		A relation instance composed of tuples obtained as follows: each tuple from the relation instance of the first operand is paired with each tuple from the relation instance of the second operand and the concatenation of the two tuples is placed in the relation instance of the product result.
	www.it.jcu.edu.au /Subjects/cp1500/2002-1/Cns/lectureNotes/chapter7/chapter7b.html (1286 words)

	Lecture Notes: Relational Algebra
		The inner, lower-level operations of a relational DBMS are, or are similar to, relational algebra operations.
		Relations in relational algebra are seen as sets of tuples, so we can use basic set operations.
		If we assume that these relational algebra expressions are executed, inside a relational DBMS which uses relational algebra operations as its lower-level internal operations, different relational algebra expressions can take very different time (and memory) to execute.
	www.databasteknik.se /webbkursen/relalg-lecture (0 words)

	Relational Algebra (Site not responding. Last check: )
		Relational algebra is a notation for representing the types of operations which can be performed on relational databases.
		A relation is a set of k-tuples, for some k called the arity of the relation.
		A relational algebra is an algebraic language based on a small number of operators which operate on relations (tables).
	www.cs.wwc.edu /~aabyan/415/RelAlg.html (668 words)

	Intelligent Enterprise Magazine
		According to Chambers Twentieth Century Dictionary, an algebra is "any of a number of systems using symbols and involving reasoning about relationships and operations." More specifically, an algebra consists of a set of objects and a set of operators that satisfy certain axioms or laws (such as closure, commutativity, or associativity).
		In relational algebra, the objects are relations; the operations are things such as restriction, projection, and join, and there are several axioms or laws, including closure - the crucially important one.
		Relational comparisons provide a better basis for dealing with the kinds of problems that division was intended to solve -- but the relational model as originally defined by Codd didn't include such comparisons at all.7
	www.intelligententerprise.com /db_area/archives/1999/990501/online.shtml (2172 words)

	Relational algebra - Definition, explanation
		The natural join is arguably one of the most important operators since it allows the combination of relations that are associated by a foreign key.
		If we want to combine tuples from two relations where the combination condition is not simply the equality of shared columns then it is convenient to have a more general form of join operator, which is the θ-join.
		The result of the left outer join is the set of all combinations of tuples in R and S that are equal on their common attribute names, in addition to tuples in R that have no matching tuples in S.
	www.calsky.com /lexikon/en/txt/r/re/relational_algebra.php (2710 words)

	Chapter 7: Relational Calculus
		Relational algebra and calculus are equivalent in their expressive power.
		The original relational calculus has come to be known as the tuple calculus to distinguish with an alternative calculus -- domain oriented calculus.
		where R is a relation name, and each pair is of the form A:v, where A in turn is an attribute of R and v is either a domain variable or a literal.
	www.cse.scu.edu /~lseiter/97-98/coen178/ch7.html (1595 words)

	Oracle FAQ: Glossary of Terms - R
		The Relational Model is based on the principles of relational algebra.
		Relational Algebra consist of a collection of operators (like [SELECT], [PROJECT] and [JOIN]) that operate on a relation or relations.
		Since the application of a relational operation on a table always results in another table, a result set is a derived results table.
	www.orafaq.com /glossary/faqglosr.htm (1274 words)

	Relational Algebra
		Given a domain from each relation, join considers all possible pairs of tuples from the two relations, and if their values for the chosen domains are equal, it adds a tuple to the result containing all the attributes of both tuples (discarding the duplicate domain D2).
		The result is a relation of all workstation/printer attribute pairs that are in the same room.
		Relational algebra is an unambiguous notation (or formalism) for expressing queries.
	www.cs.rochester.edu /users/faculty/nelson/courses/csc_173/relations/algebra.html (1294 words)

	Dilip's Brief Introduction to Relational Databases
		The Select (no relation to the relational algebra operation) statement is probably the most widely used SQL statement, and it is used to retrieve data from a database.
		The relational model of databases provides a very simple way of looking at data structured into tables, and there are straightforward techniques, such as ER modeling (though we didn't map the ER to the relational model) to represent a world view from which to build a relational database.
		We looked at the set theoretic relational algebra that relational databases are based on, and considered the high-level SQL language for users to declaratively specify queries to retrieve information from databases.
	www.cs.unc.edu /Courses/wwwp-s98/members/barman/databaseLesson (2870 words)

	Relational Algebra
		The result of an intersection operation is the relation consisting of all rows that are in both of the relations.
		That is, the resultant relation contains only the columns asked for by the user, and is often referred to as a projection of the original relation.
		For each row in Relation A having attribute Aa, you look up the rows in Relation B where their attributes Aa have the same value as attribute Aa in A. The result would have duplicate, or redundant, columns for Aa.
	www.tcnj.edu /~letcher/databasestuff/RelationalAlgebra.html (531 words)

	Comp 3753: Relational Model
		Relational algebra operations fill in the gap between SQL and the database implementation.
		Relations are joined on pairs of attributes that have the same name: join attributes.
		Relational calculus has the same expressive power as the relational algebra.
	plato.acadiau.ca /COURSES/comp/amdenton/comp3753/relational.html (1764 words)

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