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Lecture Notes: Relational Algebra – A quick tutorial to adapt SQL queries into relational algebra; Relational – A graphic implementation of the relational algebra; Query Optimization This paper is an introduction into the use of the relational algebra in optimizing queries, and includes numerous citations for more in-depth study.
Conjunctive queries without distinguished variables are called boolean conjunctive queries.Conjunctive queries where all variables are distinguished (and no variables are bound) are called equi-join queries, [1] because they are the equivalent, in the relational calculus, of the equi-join queries in the relational algebra (when selecting all columns of the result).
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 result of the query is the set of tuples X 1 to X n that make the DRC formula true. This language uses the same operators as tuple calculus, the logical connectives ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables.
The result of query rewriting may not be at the same abstraction level or application programming interface (API) as the original set of queries (though often is). For example, the input queries may be in relational algebra or SQL, and the rewritten queries may be closer to the physical representation of the data, e.g. array operations.
A view can be defined by an expression using the operators of the relational algebra or the relational calculus. Such an expression operates on one or more relations and when evaluated yields another relation. The result is sometimes referred to as a "derived" relation when the operands are relations assigned to database variables.
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
A relation algebra (L, ∧, ∨, −, 0, 1, •, I, ˘) is an algebraic structure equipped with the Boolean operations of conjunction x∧y, disjunction x∨y, and negation x −, the Boolean constants 0 and 1, the relational operations of composition x•y and converse x˘, and the relational constant I, such that these operations and constants satisfy certain equations constituting an ...