Relational algebra

7480: 7471: 11856: 11866: 7405: 1394: 11876: 11277: 7577:. The secondary goal is to try to form common subexpressions within a single query, or if there is more than one query being evaluated at the same time, in all of those queries. The rationale behind the second goal is that it is enough to compute common subexpressions once, and the results can be used in all queries that contain that subexpression. 9130: 2544: 8884: 8694:

Selection commutes with projection if and only if the fields referenced in the selection condition are a subset of the fields in the projection. Performing selection before projection may be useful if the operand is a cross product or join. In other cases, if the selection condition is relatively

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There is nothing in relational algebra introduced so far that would allow computations on the data domains (other than evaluation of propositional expressions involving equality). For example, it is not possible using only the algebra introduced so far to write an expression that would multiply the

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over the set difference, intersection, and union operators. The following three rules are used to push selection below set operations in the expression tree. For the set difference and the intersection operators, it is possible to apply the selection operator to just one of the operands following

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Whereas the result of a join (or inner join) consists of tuples formed by combining matching tuples in the two operands, an outer join contains those tuples and additionally some tuples formed by extending an unmatched tuple in one of the operands by "fill" values for each of the attributes of the

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The natural join is arguably one of the most important operators since it is the relational counterpart of the logical AND operator. Note that if the same variable appears in each of two predicates that are connected by AND, then that variable stands for the same thing and both appearances must

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that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express complex queries that transform multiple input relations (whose data are stored in the database) into a

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keyword allows one to specify the predicate used to filter the rows. It is important to note: forming the flattened Cartesian product then filtering the rows is conceptually correct, but an implementation would use more sophisticated data structures to speed up the join query.

7541:, estimate their cost, and pick the plan with the lowest estimated cost. If queries are represented by operators from relational algebra, the query optimizer can enumerate possible query plans by rewriting the initial query using the algebraic properties of these operators. 9881:

Successive renames of a variable can be collapsed into a single rename. Rename operations which have no variables in common can be arbitrarily reordered with respect to one another, which can be exploited to make successive renames adjacent so that they can be collapsed.

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In the prior example, T would represent a table such that every Student (because Student is the unique key / attribute of the Completed table) is combined with every given Task. So Eugene, for instance, would have two rows, Eugene → Database1 and Eugene → Database2 in T.

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Rules about selection operators play the most important role in query optimization. Selection is an operator that very effectively decreases the number of rows in its operand, so if the selections in an expression tree are moved towards the leaves, the internal

9313: 7363: 6401: 5900: 1915: 1057: 8684: 8454: 9432: 8905: 8076:. Considering the definition of join, this is the most likely case. If the cross product is not followed by a selection operator, we can try to push down a selection from higher levels of the expression tree using the other selection rules. 7899: 4453:

contains all the tasks of the Database project, then the result of the division above contains exactly the students who have completed both of the tasks in the Database project. More formally the semantics of the division is defined as

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expensive to compute, moving selection outside the projection may reduce the number of tuples which must be tested (since projection may produce fewer tuples due to the elimination of duplicates resulting from omitted fields).

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is equivalent to a union of selections. These identities can be used to merge selections so that fewer selections need to be evaluated, or to split them so that the component selections may be moved or optimized separately.

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EG: First, let's pretend that "Completed" has a third attribute called "grade". It's unwanted baggage here, so we must project it off always. In fact in this step we can drop "Task" from R as well; the multiply puts it back

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numbers from two columns, e.g. a unit price with a quantity to obtain a total price. Practical query languages have such facilities, e.g. the SQL SELECT allows arithmetic operations to define new columns in the result

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are grouping attributes, which function like a "group by" clause in SQL. Then there are an arbitrary number of aggregation functions applied to individual attributes. The operation is applied to an arbitrary relation

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in SQL. In order to make subsequent selection operations on the resulting table meaningful, a semantic meaning needs to be assigned to nulls; in Codd's approach the propositional logic used by the selection is

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In order to combine tuples from two relations where the combination condition is not simply the equality of shared attributes it is convenient to have a more general form of join operator, which is the

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which list models of cars and boats and their respective prices. Suppose a customer wants to buy a car and a boat, but she does not want to spend more money for the boat than for the car. The

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that are included with most relational database systems. These operations are Sum, Count, Average, Maximum and Minimum. In relational algebra the aggregation operation over a schema (

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combines all employees with their departments. This works because the foreign key holds between attributes with the same name. If this is not the case such as in the foreign key from

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produces the flattened pairs of rows which satisfy the predicate. When using a condition where the attributes are equal, for example Price, then the condition may be specified as

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and several useful theorems about the relational algebra do not hold in the SQL counterpart (arguably to the detriment of optimisers and/or users). The SQL table model is a bag (

8131: 3765: 756: 6864: 11466: 8345: 9125:{\displaystyle \pi _{a_{1},\ldots ,a_{n}}(\pi _{b_{1},\ldots ,b_{m}}(R))=\pi _{a_{1},\ldots ,a_{n}}(R){\text{ where }}\{a_{1},\ldots ,a_{n}\}\subseteq \{b_{1},\ldots ,b_{m}\}} 8335:

the transformation. This can be beneficial where one of the operands is small, and the overhead of evaluating the selection operator outweighs the benefits of using a smaller

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Furthermore, computing various functions on a column, like the summing up of its elements, is also not possible using the relational algebra introduced so far. There are five

1135: 7102:. The grouping attributes are optional, and if they are not supplied, the aggregation functions are applied across the entire relation to which the operation is applied. 3313: 11449: 9324: 5329:

In practice the classical relational algebra described above is extended with various operations such as outer joins, aggregate functions and even transitive closure.

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Given this, the antijoin is sometimes called the anti-semijoin, and the antijoin operator is sometimes written as semijoin symbol with a bar above it, instead of ▷.

3269:-join as well, as this can be achieved by selection from the result of a natural join (which degenerates to Cartesian product when there are no shared attributes). 986: 962: 7786: 2539:{\displaystyle P=\sigma _{c_{1}=x_{1},\ldots ,c_{m}=x_{m}}(R\times T)=\sigma _{c_{1}=x_{1}}(\sigma _{c_{2}=x_{2}}(\ldots \sigma _{c_{m}=x_{m}}(R\times T)\ldots ))} 11461: 10933: 8879:{\displaystyle \pi _{a_{1},\ldots ,a_{n}}(\sigma _{A}(R))=\sigma _{A}(\pi _{a_{1},\ldots ,a_{n}}(R)){\text{ where fields in }}A\subseteq \{a_{1},\ldots ,a_{n}\}} 8029: 3785: 3595: 3417: 3397: 3377: 3353: 3333: 2570: 1159: 10124: 7388: 234:

where we commonly interpret m to be the number of rows in a table and n to be the number of columns. All entries in each column have the same type.

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This paper is an introduction into the use of the relational algebra in optimizing queries, and includes numerous citations for more in-depth study.

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For the Cartesian product to be defined, the two relations involved must have disjoint headers—that is, they must not have a common attribute name.

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into equivalent expression trees, where the average size of the relations yielded by subexpressions in the tree is smaller than it was before the

599:{\displaystyle R\times S:=\{(r_{1},r_{2},\dots ,r_{n},s_{1},s_{2},\dots ,s_{m})|(r_{1},r_{2},\dots ,r_{n})\in R,(s_{1},s_{2},\dots ,s_{m})\in S\}} 10550:

was created, and this pioneering work has been acclaimed by many authorities as having shown the way to make Codd's idea into a useful language.

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theory in the sense that tuples are considered to be "shallow" for the purposes of the operation. That is, the Cartesian product of a set of

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Other more advanced operators can also be included, where the inclusion or exclusion of certain operators gives rise to a family of algebras.

11103: 11062: 11035: 11004: 10909: 7686: 10603: 10346: 10235: 8460: 7905: 11900: 11859: 2292:{\displaystyle T=\rho _{x_{1}/c_{1},\ldots ,x_{m}/c_{m}}(S)=\rho _{x_{1}/c_{1}}(\rho _{x_{2}/c_{2}}(\ldots \rho _{x_{m}/c_{m}}(S)\ldots ))} 7775:

of simpler conditions is equivalent to a sequence of selections with those same individual conditions, and selection whose condition is a

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Three outer join operators are defined: left outer join, right outer join, and full outer join. (The word "outer" is sometimes omitted.)

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intended for use in teaching relational database theory, and its query language also draws on ISBL's ideas. Rel is an implementation of

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accept two relations as input and combine them into a single output relation. For example, taking all tuples found in either relation (

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is defined in terms of set union and set difference, the two relations involved in set intersection must also be union-compatible.

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The full outer join can be simulated using the left and right outer joins (and hence the natural join and set union) as follows:

131: 11879: 11585: 11299: 10715: 633: 245: 11836: 8315:{\displaystyle \sigma _{A}(R\times P)=\sigma _{B\wedge C\wedge D}(R\times P)=\sigma _{D}(\sigma _{B}(R)\times \sigma _{C}(P))} 7183:

Although relational algebra seems powerful enough for most practical purposes, there are some simple and natural operators on

11483: 7430: 917: 853: 239: 106:), extending the tuples of the first relation with tuples in the second relation matching certain conditions, and so forth. 11775: 3108: 3053: 9577:{\displaystyle \pi _{A}(\{\langle A=a,B=b\rangle \})\cap \pi _{A}(\{\langle A=a,B=b'\rangle \})=\{\langle A=a\rangle \}} 5752:). Then the left outer join can be described in terms of the natural join (and hence using basic operators) as follows: 50: 11339: 1200: 11905: 11801: 11520: 9308:{\displaystyle \pi _{a_{1},\ldots ,a_{n}}(R\cup P)=\pi _{a_{1},\ldots ,a_{n}}(R)\cup \pi _{a_{1},\ldots ,a_{n}}(P).\,} 5910:

The right outer join (⟖) behaves almost identically to the left outer join, but the roles of the tables are switched.

1076: 7358:{\displaystyle \forall x\forall y\forall z\left((x,y)\in R^{+}\wedge (y,z)\in R^{+}\Rightarrow (x,z)\in R^{+}\right)} 6396:{\displaystyle (R\bowtie S)\cup (\{(\omega ,\dots ,\omega )\}\times (S-\pi _{s_{1},s_{2},\dots ,s_{n}}(R\bowtie S)))} 5895:{\displaystyle (R\bowtie S)\cup ((R-\pi _{r_{1},r_{2},\dots ,r_{n}}(R\bowtie S))\times \{(\omega ,\dots ,\omega )\})} 11724: 11714: 11490: 9850:{\displaystyle \pi _{A}(\{\langle A=a,B=b\rangle \})\setminus \pi _{A}(\{\langle A=a,B=b'\rangle \})=\emptyset \,,} 9714:{\displaystyle \pi _{A}(\{\langle A=a,B=b\rangle \}\setminus \{\langle A=a,B=b'\rangle \})=\{\langle A=a\rangle \}} 8031:

rows. Therefore, it is important to decrease the size of both operands before applying the cross product operator.

1910:{\displaystyle R\bowtie S=\left\{r\cup s\ \vert \ r\in R\ \land \ s\in S\ \land \ {\mathit {Fun}}(r\cup s)\right\}} 1784:

then these columns must be renamed before taking the natural join. Such a join is sometimes also referred to as an

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Since we can simulate the natural join with the basic operators it follows that this also holds for the semijoin.

1052:{\displaystyle \sigma _{{\text{isFriend = true}}\,\lor \,{\text{isBusinessContact = true}}}({\text{addressBook}})} 11910: 11811: 11544: 10956: 10775: 10689: 7537:

which attempts to determine the most efficient way to execute a given query. Query optimizers enumerate possible

1407: 8679:{\displaystyle \sigma _{A}(R\cap P)=\sigma _{A}(R)\cap \sigma _{A}(P)=\sigma _{A}(R)\cap P=R\cap \sigma _{A}(P)} 1009:

To obtain a listing of all friends or business associates in an address book, the selection might be written as

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The first query language to be based on Codd's algebra was Alpha, developed by Dr. Codd himself. Subsequently,

7415: 6253:). Then, as with the left outer join, the right outer join can be simulated using the natural join as follows: 1709: 1740:

of the logical AND). In particular, natural join allows the combination of relations that are associated by a

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Projection is idempotent, so that a series of (valid) projections is equivalent to the outermost projection.

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Note, however, that a computer language that supports the natural join and selection operators does not need

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In the case where the relations have the same attributes (union-compatible), antijoin is the same as minus.

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that is equal on their common attribute names. The difference from a natural join is that other columns of

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other operand. Outer joins are not considered part of the classical relational algebra discussed so far.

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accept a single relation as input. Examples include operators to filter certain attributes (columns) or

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The cardinality of the Cartesian product is the product of the cardinalities of its factors, that is, |

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Projection does not distribute over intersection and set difference. Counterexamples are given by:

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Relational algebra received little attention outside of pure mathematics until the publication of

76:. Queries over relational databases often likewise return tabular data represented as relations. 11765: 11734: 11683: 11515: 11407: 11362: 11138: 10975: 10927: 10814:, the join symbol is ⨝ (U+2A1D), and the bowtie symbol, occasionally used instead, is ⋈ (U+22C8). 10700: 10573:. Bmg is an implementation of relational algebra in Ruby which closely follows the principles of 10551: 9427:{\displaystyle \pi _{A}(\{\langle A=a,B=b\rangle \}\cap \{\langle A=a,B=b'\rangle \})=\emptyset } 7574: 7188: 6832: 1433: 99: 11575: 3292: 11641: 11495: 11259: 11099: 11058: 11052: 11031: 11025: 11000: 10915: 10905: 10790: 10684: 5355:, which we do not define, to be used for the fill values; in practice this corresponds to the 1705:

Note that neither the employee named Mary nor the Production department appear in the result.

759: 344:-tuples (whereas basic set theory would have prescribed a set of 2-tuples, each containing an 321: 292: 251: 10994: 7894:{\displaystyle \sigma _{A\land B}(R)=\sigma _{A}(\sigma _{B}(R))=\sigma _{B}(\sigma _{A}(R))} 923: 11831: 11678: 11668: 11636: 11247: 11128: 10965: 10770: 10760: 10735: 10589: 8034:

This can be effectively done if the cross product is followed by a selection operator, e.g.

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that are equal on their common attribute names, in addition (loosely speaking) to tuples in

311: 122: 31: 7137:). To find the highest balance of all accounts regardless of branch, we could simply write 971: 947: 11739: 11709: 11663: 11444: 11157: 11125:

Proceedings of the 6th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages

7534: 3677:{\displaystyle R\ltimes S=\{t:t\in R\land \exists s\in S(\operatorname {Fun} (t\cup s))\}} 1725: 1447: 1090: 863: 647: 95: 38: 1059:. The result would be a relation containing every attribute of every unique record where 11379:

DES – An educational tool for working with Relational Algebra and other formal languages

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The simulation of this operation in the fundamental operations is therefore as follows:

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have no common attributes, then the natural join becomes exactly the Cartesian product.

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The simulation of the division with the basic operations is as follows. We assume that

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are relations. The result of this operation consists of all combinations of tuples in

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since 1999, and it had vendor-specific extensions in this direction well before that.

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The main application of relational algebra is to provide a theoretical foundation for

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is a theorem for relational algebra on sets, but not for relational algebra on bags.

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was a short-lived industry-strength relational DBMS that followed the ISBL example.

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The left semijoin (⋉ and ⋊) is a joining similar to the natural join and written as

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s occur in the Name and EmpId attributes of the resulting relation where tuples in

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that are equal on their common attribute names. For an example consider the tables

838: 11345: 5932:. The result of the right outer join is the set of all combinations of tuples in 1978:

The natural join can be simulated with Codd's primitives as follows. Assume that

1187:{\displaystyle \rho _{\text{isBusinessContact / isFriend}}({\text{addressBook}})} 11600: 11580: 10562: 10224:{\displaystyle \rho _{a/b}(R\setminus P)=\rho _{a/b}(R)\setminus \rho _{a/b}(P)} 7606: 7404: 6442:. The result of the full outer join is the set of all combinations of tuples in 5395:. The result of the left outer join is the set of all combinations of tuples in 2315:

Then we take the Cartesian product and select the tuples that are to be joined:

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must have at least one common attribute, but if this constraint is omitted, and

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in 1970. Codd proposed such an algebra as a basis for database query languages.

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It can be proved using the fact that there is no relational algebra expression

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to this set. It is usually required that the attribute names in the header of

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Pireal – An experimental educational tool for working with Relational Algebra

1470:. The result of the natural join is the set of all combinations of tuples in 758:

is a set of attribute names. The result of such projection is defined as the

10947: 7609:(the order selections are applied in has no effect on the eventual result). 4601:

on its unique attribute names and construct all combinations with tuples in

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does not map any attribute to multiple values). It is usually required that

1440: 284: 265: 11357: 10103:{\displaystyle \rho _{a/b}(\rho _{c/d}(R))=\rho _{c/d}(\rho _{a/b}(R))\,\!} 2951:{\displaystyle {Car\bowtie Boat \atop \scriptstyle CarPrice\geq BoatPrice}} 1439:"⋈" redirects here. For the band sometimes represented by this symbol, see 310:—that is, the two relations must have the same set of attributes. Because 11389: 11386:(open-source software available as an online service without registration) 11133: 11120: 10970: 10951: 837:

projection to eliminate duplicate data is obtained by the addition of the

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In addition, the Cartesian product is defined differently from the one in

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that are equal on their common attribute names, in addition to tuples in

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that are equal on their common attribute names, in addition to tuples in

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To rename the "isFriend" attribute to "isBusinessContact" in a relation,

989: 830: 102:), removing tuples from the first relation found in the second relation ( 1791:

More formally the semantics of the natural join are defined as follows:

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is their join as shown above, projected on all but the common attribute

10876: 10863: 10850: 10837: 10824: 10811: 10785: 7756:{\displaystyle \sigma _{A}\sigma _{B}(R)=\sigma _{B}\sigma _{A}(R)\,\!} 3590:

More formally the semantics of the semijoin can be defined as follows:

11205: 10667:{\displaystyle (R\cup S)\setminus T=(R\setminus T)\cup (S\setminus T)} 10588:

is loosely based on a relational algebra, though the operands in SQL (

10446:{\displaystyle \rho _{a/b}(R\cap P)=\rho _{a/b}(R)\cap \rho _{a/b}(P)} 10335:{\displaystyle \rho _{a/b}(R\cup P)=\rho _{a/b}(R)\cup \rho _{a/b}(P)} 8536:{\displaystyle \sigma _{A}(R\cup P)=\sigma _{A}(R)\cup \sigma _{A}(P)} 7981:{\displaystyle \sigma _{A\lor B}(R)=\sigma _{A}(R)\cup \sigma _{B}(R)} 1744:. For example, in the above example a foreign key probably holds from 1736:

always be substituted by the same value (this is a consequence of the

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Rename is distributive over set difference, union, and intersection.

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which have no common values in common attribute names with tuples in

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which have no common values in common attribute names with tuples in

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which have no common values in common attribute names with tuples in

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which have no common values in common attribute names with tuples in

11348:- An introduction to how database systems process relational algebra 4554:

because otherwise the result of the operation will always be empty.

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The semijoin can be simulated using the natural join as follows. If

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In SQL implementations, joining on a predicate is usually called an

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external links, and converting useful links where appropriate into

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that cannot be expressed by relational algebra. One of them is the

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Finally we take a projection to get rid of the renamed attributes:

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Database: Principles, Programming, and Performance, Second Edition

10827:, the ltimes symbol is ⋉ (U+22C9). The rtimes symbol is ⋊ (U+22CA) 8095:

using the split rules about complex selection conditions, so that

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Cross product is the costliest operator to evaluate. If the input

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Here are a set of rules that can be used in such transformations.

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in effect combines the results of the left and right outer joins.

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So if we now take the projection on the attribute names unique to

3865:{\displaystyle R\ltimes S=\Pi _{a_{1},\ldots ,a_{n}}(R\bowtie S).} 993: 763: 91: 11183:"Databases, Types, and the Relational model: The Third Manifesto" 11565: 10547: 5347:

The operators defined in this section assume the existence of a

4291:, for which it holds that all their combinations with tuples in 11403: 11358:

Relational – A graphic implementation of the relational algebra

11354:– A quick tutorial to adapt SQL queries into relational algebra 1432:"Natural join" redirects here. For the SQL implementation, see 49:

for modeling data and defining queries on it with well founded

11270: 10780: 10585: 9978:{\displaystyle \rho _{a/b}(\rho _{b/c}(R))=\rho _{a/c}(R)\,\!} 7398: 3258:

is the equality operator (=) then this join is also called an

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Relational Algebra System for Oracle and Microsoft SQL Server

10531:{\displaystyle (A\times B)\cup (A\times C)=A\times (B\cup C)} 1149:

attribute. This is simply used to rename the attribute of a

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Silberschatz, Abraham; Henry F. Korth; S. Sudarshan (2020).

7675:{\displaystyle \sigma _{A}(R)=\sigma _{A}\sigma _{A}(R)\,\!} 6480: 5962: 5425: 5203: 5106: 4828: 4786:

we have the possible combinations that "could have" been in

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The division (÷) is a binary operation that is written as

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are disjoint, that is, do not contain a common attribute.

227:{\displaystyle S=\{(s_{j1},s_{j2},...s_{jn})|j\in 1...m\}} 128:

Relational algebra operates on homogeneous sets of tuples

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SQL and Relational Theory: How to Write Accurate SQL Code

72:. Relational databases store tabular data represented as 10952:"A Relational Model of Data for Large Shared Data Banks" 7569:

The primary goal of the query optimizer is to transform

6241:)} be the singleton relation on the attributes that are 5740:)} be the singleton relation on the attributes that are 11295: 3877:

In Codd's 1970 paper, semijoin is called restriction.

2890: 299:, but adds additional constraints to these operators. 11234:"The relational model of data and cylindric algebras" 10606: 10470: 10349: 10238: 10127: 9992: 9891: 9730: 9596: 9443: 9327: 9153: 8908: 8704: 8550: 8463: 8348: 8186: 8101: 8040: 8014: 7908: 7789: 7689: 7618: 7236: 6867: 6262: 5761: 5138:

So what remains to be done is take the projection of

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on its unique attribute names and subtract those in

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down to just the attribute(s) in question (Student)

3153:{\displaystyle {R\ \bowtie \ S \atop a\ \theta \ v}} 3098:{\displaystyle {R\ \bowtie \ S \atop a\ \theta \ b}} 79:

The main purpose of relational algebra is to define

11784: 11753: 11697: 11624: 11553: 11437: 6789: 5364:, although we elide those details in this article. 237:Five primitive operators of Codd's algebra are the 11342:Free software to convert relational algebra to SQL 10666: 10600:), rather than a set. For example, the expression 10530: 10445: 10334: 10223: 10102: 9977: 9849: 9713: 9576: 9426: 9307: 9124: 8878: 8678: 8535: 8448: 8314: 8125: 8068: 8023: 7980: 7893: 7755: 7674: 7395:Use of algebraic properties for query optimization 7357: 7045: 6395: 5894: 5686:s occur in the resulting relation where tuples in 3864: 3779: 3759: 3710: 3676: 3411: 3391: 3371: 3347: 3327: 3307: 3152: 3097: 2950: 2691: 2538: 2291: 1909: 1372: 1320: 1260: 1186: 1129: 1051: 980: 956: 932: 894: 814: 750: 704: 598: 226: 11290:may not follow Knowledge's policies or guidelines 10099: 9974: 7752: 7671: 1261:{\displaystyle \rho _{x(A_{1},\ldots ,A_{n})}(R)} 7593:(yielded by subexpressions) will likely shrink. 3419:do not appear. For example, consider the tables 2066:. In a first step the common attribute names in 2042:. Furthermore, assume that the attribute names 5038:then we have the restrictions of the tuples in 4804:need to have identical attribute names/headers. 3917:that is equal on their common attribute names. 10461:Cartesian product is distributive over union. 8177:are possibly empty. Then the following holds: 7767:Breaking up selections with complex conditions 5042:for which not all combinations with tuples in 3050:-join is a binary operator that is written as 11415: 11346:Lecture Videos: Relational Algebra Processing 4091:The antijoin is formally defined as follows: 705:{\displaystyle \Pi _{a_{1},\ldots ,a_{n}}(R)} 84:single output relation (the query results). 8: 11158:"Edgar F. Codd - A.M. Turing Award Laureate" 10866:, the Right outer join symbol is ⟖ (U+27D6). 9831: 9828: 9799: 9796: 9774: 9771: 9747: 9744: 9708: 9705: 9693: 9690: 9681: 9678: 9649: 9646: 9640: 9637: 9613: 9610: 9571: 9568: 9556: 9553: 9544: 9541: 9512: 9509: 9487: 9484: 9460: 9457: 9412: 9409: 9380: 9377: 9371: 9368: 9344: 9341: 9119: 9087: 9081: 9049: 8873: 8841: 6819:keyword. In database theory, this is called 6308: 6284: 5886: 5862: 3671: 3611: 1832: 1367: 1335: 1315: 1283: 829:standard the "default projection" returns a 809: 777: 593: 381: 221: 141: 10879:, the Full Outer join symbol is ⟗ (U+27D7). 10853:, the Left outer join symbol is ⟕ (U+27D5). 7433:. Unsourced material may be challenged and 4822:) // This gives us a "what's missing" list. 1401:It has been suggested that this section be 11422: 11408: 11400: 11121:"Universality of data retrieval languages" 11119:Aho, Alfred V.; Jeffrey D. Ullman (1979). 10996:Principles of Distributed Database Systems 10932:: CS1 maint: location missing publisher ( 10904:(Seventh ed.). New York. p. 56. 4534:} is the set of attribute names unique to 302:For set union and set difference, the two 11326:Learn how and when to remove this message 11251: 11132: 11057:. O'Reilly Media, Inc. pp. 133–135. 10993:M. Tamer Özsu; Patrick Valduriez (2011). 10969: 10605: 10469: 10424: 10420: 10394: 10390: 10358: 10354: 10348: 10313: 10309: 10283: 10279: 10247: 10243: 10237: 10202: 10198: 10172: 10168: 10136: 10132: 10126: 10098: 10076: 10072: 10055: 10051: 10022: 10018: 10001: 9997: 9991: 9973: 9954: 9950: 9921: 9917: 9900: 9896: 9890: 9843: 9787: 9735: 9729: 9601: 9595: 9500: 9448: 9442: 9332: 9326: 9304: 9284: 9265: 9260: 9236: 9217: 9212: 9182: 9163: 9158: 9152: 9113: 9094: 9075: 9056: 9044: 9027: 9008: 9003: 8976: 8957: 8952: 8937: 8918: 8913: 8907: 8867: 8848: 8830: 8810: 8791: 8786: 8773: 8748: 8733: 8714: 8709: 8703: 8661: 8627: 8605: 8583: 8555: 8549: 8518: 8496: 8468: 8462: 8425: 8403: 8381: 8353: 8347: 8294: 8272: 8259: 8219: 8191: 8185: 8100: 8045: 8039: 8013: 7963: 7941: 7913: 7907: 7873: 7860: 7835: 7822: 7794: 7788: 7751: 7736: 7726: 7704: 7694: 7688: 7670: 7655: 7645: 7623: 7617: 7453:Learn how and when to remove this message 7344: 7313: 7282: 7235: 7015: 7010: 7000: 6973: 6968: 6958: 6937: 6932: 6922: 6917: 6904: 6885: 6872: 6866: 6364: 6345: 6332: 6327: 6261: 5833: 5814: 5801: 5796: 5760: 4206:is as in the definition of natural join. 3836: 3817: 3812: 3794: 3772: 3751: 3732: 3726: 3718:is as in the definition of natural join. 3691: 3597: 3404: 3384: 3364: 3359:. The result is the set of all tuples in 3340: 3320: 3294: 3112: 3110: 3057: 3055: 2862: 2860: 2672: 2653: 2640: 2621: 2608: 2589: 2584: 2572: 2504: 2491: 2486: 2468: 2455: 2450: 2435: 2422: 2417: 2387: 2374: 2355: 2342: 2337: 2325: 2263: 2254: 2248: 2243: 2225: 2216: 2210: 2205: 2190: 2181: 2175: 2170: 2146: 2137: 2131: 2112: 2103: 2097: 2092: 2080: 1875: 1874: 1801: 1361: 1342: 1333: 1309: 1290: 1281: 1238: 1219: 1208: 1202: 1176: 1167: 1161: 1145:attribute in all tuples is renamed to an 1108: 1104: 1098: 1041: 1031: 1030: 1026: 1021: 1020: 1014: 973: 949: 925: 877: 871: 803: 784: 775: 742: 723: 717: 685: 666: 661: 655: 578: 559: 546: 521: 502: 489: 477: 468: 449: 436: 423: 404: 391: 367: 204: 192: 167: 151: 133: 68:for such databases, chief among which is 7105:Let's assume that we have a table named 6596: 6561: 6484: 6078: 6043: 5966: 5541: 5506: 5429: 5265: 5244: 5207: 5110: 4978: 4899: 4832: 4677: 4412: 4386: 4311: 4209:The antijoin can also be defined as the 4036: 4001: 3935: 3535: 3500: 3434: 3208:-join is defined only if the headers of 2854: 2811: 2768: 1613: 1570: 1493: 11239:Journal of Computer and System Sciences 11098:(2nd ed.). Pearson Prentice Hall. 10892: 10803: 10655: 10637: 10622: 10191: 10152: 9780: 9643: 8440: 8396: 8365: 7227:and satisfies the following condition: 3711:{\displaystyle \operatorname {Fun} (r)} 1373:{\displaystyle \{A_{1},\ldots ,A_{n}\}} 1321:{\displaystyle \{a_{1},\ldots ,a_{n}\}} 815:{\displaystyle \{a_{1},\ldots ,a_{n}\}} 10999:(3rd ed.). Springer. p. 46. 10925: 8069:{\displaystyle \sigma _{A}(R\times P)} 7531:Relational database management systems 5375:The left outer join (⟕) is written as 11395:Translating SQL to Relational Algebra 11384:RelaX - Relational Algebra Calculator 7387:SQL however officially supports such 7380:as a variable argument that produces 7191:of a binary relation. Given a domain 6716:In the resulting relation, tuples in 6156:In the resulting relation, tuples in 5647:In the resulting relation, tuples in 1405:out into another article titled 895:{\displaystyle \sigma _{\varphi }(R)} 7: 11390:RA: A Relational Algebra Interpreter 10840:, the Antijoin symbol is ▷ (U+25B7). 7431:adding citations to reliable sources 7073:, is one of the original attributes 4456: 4215: 2564: 2317: 2072: 1793: 992:). This selection selects all those 332:-tuples yields a set of "flattened" 11875: 11096:Database systems: the complete book 8157:that contains attributes from both 8126:{\displaystyle A=B\wedge C\wedge D} 6469:For an example consider the tables 5414:For an example consider the tables 3920:For an example consider the tables 3760:{\displaystyle a_{1},\ldots ,a_{n}} 1712:. For example, the composition of 751:{\displaystyle a_{1},\ldots ,a_{n}} 9840: 9421: 7249: 7243: 7237: 6783:Operations for domain computations 6422:The full outer join is written as 6249:(those that are not attributes of 6229:be the attributes of the relation 5748:(those that are not attributes of 5728:be the attributes of the relation 4573:are the attribute names unique to 3809: 3632: 3113: 3058: 2863: 2581: 2038:are the attribute names unique to 2018:are the attribute names unique to 1994:are the attribute names common to 975: 658: 25: 11352:Lecture Notes: Relational Algebra 11340:RAT Relational Algebra Translator 7771:A selection whose condition is a 7555:the internal nodes are operators, 6466:in their common attribute names. 5951:For example, consider the tables 4279:to the attribute names unique to 1137:where the result is identical to 11874: 11864: 11855: 11854: 11275: 11030:. Morgan Kaufmann. p. 120. 8079:In the above case the condition 7521:first and joins the result with 7509:first and joins the result with 7478: 7469: 7403: 6462:that have no matching tuples in 6454:that have no matching tuples in 5944:that have no matching tuples in 5407:that have no matching tuples in 5362:extended to a three-valued logic 1708:This can also be used to define 1392: 11865: 10716:Projection (relational algebra) 9864:is assumed to be distinct from 4597:. In the first step we project 634:Projection (relational algebra) 94:(rows) from an input relation. 53:. The theory was introduced by 10661: 10649: 10643: 10631: 10619: 10607: 10525: 10513: 10501: 10489: 10483: 10471: 10440: 10434: 10410: 10404: 10380: 10368: 10329: 10323: 10299: 10293: 10269: 10257: 10218: 10212: 10188: 10182: 10158: 10146: 10095: 10092: 10086: 10065: 10041: 10038: 10032: 10011: 9970: 9964: 9940: 9937: 9931: 9910: 9834: 9793: 9777: 9741: 9684: 9607: 9547: 9506: 9490: 9454: 9415: 9338: 9298: 9292: 9250: 9244: 9202: 9190: 9041: 9035: 8993: 8990: 8984: 8945: 8827: 8824: 8818: 8779: 8763: 8760: 8754: 8741: 8673: 8667: 8639: 8633: 8617: 8611: 8595: 8589: 8573: 8561: 8530: 8524: 8508: 8502: 8486: 8474: 8437: 8431: 8415: 8409: 8393: 8387: 8371: 8359: 8309: 8306: 8300: 8284: 8278: 8265: 8249: 8237: 8209: 8197: 8145:contains attributes only from 8137:contains attributes only from 8083:is broken up in to conditions 8063: 8051: 8008:rows, the result will contain 7975: 7969: 7953: 7947: 7931: 7925: 7888: 7885: 7879: 7866: 7850: 7847: 7841: 7828: 7812: 7806: 7748: 7742: 7716: 7710: 7667: 7661: 7635: 7629: 7334: 7322: 7319: 7303: 7291: 7272: 7260: 7040: 7034: 7026: 7006: 6984: 6964: 6948: 6928: 6390: 6387: 6384: 6372: 6314: 6305: 6287: 6281: 6275: 6263: 5889: 5883: 5865: 5856: 5853: 5841: 5783: 5780: 5774: 5762: 3856: 3844: 3705: 3699: 3668: 3665: 3653: 3644: 3379:for which there is a tuple in 2686: 2680: 2533: 2530: 2524: 2512: 2476: 2443: 2407: 2395: 2286: 2283: 2277: 2271: 2233: 2198: 2160: 2154: 1899: 1887: 1255: 1249: 1244: 1212: 1181: 1173: 1130:{\displaystyle \rho _{a/b}(R)} 1124: 1118: 1046: 1038: 889: 883: 854:Selection (relational algebra) 699: 693: 584: 539: 527: 482: 478: 474: 384: 205: 201: 144: 27:Theory of relational databases 1: 7155:Grouping is often written as 7093:The attributes preceding the 6175:Since there are no tuples in 5666:Since there are no tuples in 4796:EG: Again with projections — 4751:In the next step we subtract 4213:of the semijoin, as follows: 3885:The antijoin (▷), written as 1760:and then the natural join of 1384:Joins and join-like operators 11253:10.1016/0022-0000(84)90077-1 11181:C. J. Date and Hugh Darwen. 9136:Projection and set operators 7565:subtrees are subexpressions. 5959:and their right outer join: 5422:and their left outer join: 5339:Join (SQL) § Outer join 1948:(in the mathematical sense) 1728:, the join is precisely the 1169:isBusinessContact / isFriend 283:The relational algebra uses 11901:Database management systems 11431:Database management systems 10584:Even the query language of 10565:proposed a language called 8895:Basic projection properties 8832: where fields in 8326:Selection and set operators 7992:Selection and cross product 7499:R(A, B) ⋈ S(B, C) ⋈ T(A, C) 7111:Account_Number, Branch_Name 7109:with three columns, namely 6477:and their full outer join: 4593:are the attribute names of 3767:are the attribute names of 3046:-join (or theta-join). The 1077:Rename (relational algebra) 11927: 11837:Object–relational database 7597:Basic selection properties 7215:is the smallest subset of 5336: 3308:{\displaystyle R\ltimes S} 1438: 1431: 1074: 920:and the logical operators 851: 833:instead of a set, and the 825:Note: when implemented in 770:are restricted to the set 762:that is obtained when all 631: 352:-tuple). More formally, 29: 11850: 11812:Federated database system 11545:Blockchain-based database 10957:Communications of the ACM 10776:Tuple relational calculus 10690:D4 (programming language) 7547:can be represented as a 7207:. The transitive closure 6858:) is written as follows: 4550:are a subset of those of 4287:but not in the header of 4283:, i.e., in the header of 3184:is a value constant, and 1408:Join (relational algebra) 10902:Database system concepts 10711:Projection (mathematics) 10692:(an implementation of D) 10114:Rename and set operators 8690:Selection and projection 5913:The right outer join of 1955:is a function (that is, 1710:composition of relations 1486:and their natural join: 1153:or the relation itself. 1033:isBusinessContact = true 123:relational model of data 30:Not to be confused with 11258:(For relationship with 10721:Projection (set theory) 9877:Basic rename properties 3178:{<, ≤, =, ≠, >, ≥ 933:{\displaystyle \wedge } 360:is defined as follows: 11842:Transaction processing 11797:Database normalization 11740:Query rewriting system 10668: 10532: 10447: 10336: 10225: 10104: 9979: 9851: 9715: 9578: 9428: 9309: 9126: 8880: 8680: 8537: 8450: 8316: 8127: 8070: 8025: 7982: 7895: 7757: 7676: 7359: 7195:, let binary relation 7047: 6397: 5896: 4542:is the restriction of 3866: 3781: 3761: 3712: 3678: 3413: 3393: 3373: 3349: 3329: 3309: 3154: 3099: 2952: 2693: 2540: 2293: 1911: 1446:Natural join (⨝) is a 1374: 1322: 1262: 1188: 1131: 1053: 982: 958: 934: 896: 816: 752: 706: 600: 328:-tuples with a set of 228: 45:is a theory that uses 11817:Referential integrity 11232:; Lipski, W. (1984). 11134:10.1145/567752.567763 10971:10.1145/362384.362685 10746:Relation construction 10669: 10533: 10448: 10337: 10226: 10105: 9980: 9852: 9716: 9579: 9429: 9310: 9127: 8881: 8681: 8538: 8451: 8317: 8153:contains the part of 8128: 8071: 8026: 7983: 7896: 7758: 7677: 7360: 7048: 6398: 5897: 3867: 3782: 3762: 3713: 3679: 3414: 3394: 3374: 3350: 3330: 3310: 3254:In case the operator 3204:. The result of the 3168:are attribute names, 3155: 3100: 2953: 2694: 2541: 2294: 1912: 1375: 1323: 1263: 1189: 1132: 1054: 983: 981:{\displaystyle \neg } 959: 957:{\displaystyle \lor } 935: 910:propositional formula 897: 860:generalized selection 817: 753: 707: 601: 229: 11807:Distributed database 11296:improve this article 11084:Hector Garcia-Molina 10741:Relation composition 10706:Object-role modeling 10604: 10468: 10347: 10236: 10125: 9990: 9889: 9728: 9594: 9441: 9325: 9151: 8906: 8702: 8548: 8461: 8346: 8184: 8099: 8038: 8012: 7906: 7787: 7687: 7616: 7427:improve this section 7234: 6865: 6260: 5759: 4165:, there is no tuple 3928:and their antijoin: 3793: 3771: 3725: 3690: 3596: 3427:and their semijoin: 3403: 3383: 3363: 3339: 3319: 3293: 3109: 3054: 2859: 2571: 2324: 2079: 1800: 1450:that is written as ( 1332: 1280: 1201: 1160: 1097: 1013: 972: 948: 924: 870: 774: 716: 654: 366: 132: 62:relational databases 47:algebraic structures 11827:Relational calculus 11705:Concurrency control 11308:footnote references 11206:"Bmg documentation" 11051:C. J. Date (2011). 10766:Theory of relations 10756:Relational database 10751:Relational calculus 10731:Relation (database) 10579:The Third Manifesto 7513:, the second joins 6833:aggregate functions 6821:extended projection 6605: 6566: 6489: 6087: 6048: 5971: 5550: 5511: 5434: 5296: 5293: 5290: 5273: 5270: 5249: 5218: 5115: 5003: 4998: 4995: 4986: 4983: 4908: 4837: 4682: 4421: 4391: 4316: 4231: − 4045: 4006: 3940: 3909:for which there is 3544: 3505: 3439: 3174:relational operator 2958: 2816: 2773: 2741:) on the predicate 1941:that is true for a 1622: 1575: 1498: 1276:and the attributes 11906:Relational algebra 11822:Relational algebra 11766:Query optimization 11571:Armstrong's axioms 11363:Query Optimization 11260:cylindric algebras 10701:Logic of relatives 10664: 10592:) are not exactly 10552:Business System 12 10528: 10443: 10332: 10221: 10100: 9975: 9847: 9711: 9574: 9424: 9305: 9122: 8876: 8676: 8533: 8446: 8312: 8123: 8066: 8024:{\displaystyle NM} 8021: 7978: 7891: 7753: 7672: 7501:; the first joins 7355: 7189:transitive closure 7179:Transitive closure 7043: 6597: 6562: 6485: 6393: 6079: 6044: 5967: 5892: 5542: 5507: 5430: 5294: 5291: 5274: 5271: 5266: 5245: 5208: 5111: 4999: 4996: 4987: 4984: 4979: 4900: 4833: 4678: 4413: 4387: 4312: 4037: 4002: 3936: 3862: 3777: 3757: 3708: 3674: 3536: 3501: 3435: 3409: 3389: 3369: 3345: 3325: 3305: 3150: 3095: 2948: 2945: 2855: 2812: 2769: 2757:or alternatively ( 2719:-join and equijoin 2689: 2536: 2289: 1907: 1614: 1571: 1494: 1434:Natural join (SQL) 1370: 1318: 1258: 1197:There is also the 1184: 1127: 1049: 978: 954: 930: 916:as allowed in the 892: 812: 748: 702: 596: 224: 43:relational algebra 11888: 11887: 11496:Wide-column store 11491:Document-oriented 11336: 11335: 11328: 11105:978-0-13-187325-4 11088:Jeffrey D. Ullman 11064:978-1-4493-1974-8 11037:978-1-55860-438-4 11006:978-1-4419-8833-1 10911:978-0-07-802215-9 10685:Cartesian product 10457:Product and union 9047: 9046: where 8833: 7463: 7462: 7455: 7033: 6912: 6713: 6712: 6706: 6705: 6593: 6592: 6558: 6557: 6153: 6152: 6146: 6145: 6075: 6074: 6040: 6039: 5644: 5643: 5637: 5636: 5538: 5537: 5503: 5502: 5325:Common extensions 5321: 5320: 5314: 5313: 5262: 5261: 5241: 5240: 5135: 5134: 5128: 5127: 5029: 5028: 5022: 5021: 4975: 4974: 4896: 4895: 4748: 4747: 4741: 4740: 4516: 4515: 4446: 4445: 4439: 4438: 4409: 4408: 4383: 4382: 4254: 4253: 4088: 4087: 4081: 4080: 4033: 4032: 3998: 3997: 3780:{\displaystyle R} 3587: 3586: 3580: 3579: 3532: 3531: 3497: 3496: 3412:{\displaystyle S} 3392:{\displaystyle S} 3372:{\displaystyle R} 3348:{\displaystyle S} 3328:{\displaystyle R} 3148: 3143: 3137: 3126: 3120: 3093: 3088: 3082: 3071: 3065: 3038: 3037: 3031: 3030: 2946: 2851: 2850: 2808: 2807: 2713: 2712: 2560: 2559: 2313: 2312: 1931: 1930: 1873: 1867: 1855: 1849: 1837: 1831: 1702: 1701: 1695: 1694: 1610: 1609: 1567: 1566: 1425: 1424: 1420: 1179: 1170: 1065:isBusinessContact 1063:is true or where 1044: 1034: 1024: 912:that consists of 306:involved must be 293:Cartesian product 255:(also called the 252:Cartesian product 16:(Redirected from 11918: 11911:Relational model 11878: 11877: 11868: 11867: 11858: 11857: 11832:Relational model 11802:Database storage 11679:Stored procedure 11424: 11417: 11410: 11401: 11331: 11324: 11320: 11317: 11311: 11279: 11278: 11271: 11257: 11255: 11216: 11215: 11213: 11212: 11202: 11196: 11195: 11193: 11192: 11187: 11178: 11172: 11171: 11169: 11168: 11162:amturing.acm.org 11153: 11147: 11146: 11136: 11116: 11110: 11109: 11080: 11069: 11068: 11048: 11042: 11041: 11022:Elizabeth O'Neil 11020:Patrick O'Neil; 11017: 11011: 11010: 10990: 10984: 10983: 10973: 10944: 10938: 10937: 10931: 10923: 10897: 10880: 10873: 10867: 10860: 10854: 10847: 10841: 10834: 10828: 10821: 10815: 10808: 10771:Triadic relation 10761:Relational model 10736:Relation algebra 10673: 10671: 10670: 10665: 10537: 10535: 10534: 10529: 10452: 10450: 10449: 10444: 10433: 10432: 10428: 10403: 10402: 10398: 10367: 10366: 10362: 10341: 10339: 10338: 10333: 10322: 10321: 10317: 10292: 10291: 10287: 10256: 10255: 10251: 10230: 10228: 10227: 10222: 10211: 10210: 10206: 10181: 10180: 10176: 10145: 10144: 10140: 10109: 10107: 10106: 10101: 10085: 10084: 10080: 10064: 10063: 10059: 10031: 10030: 10026: 10010: 10009: 10005: 9984: 9982: 9981: 9976: 9963: 9962: 9958: 9930: 9929: 9925: 9909: 9908: 9904: 9856: 9854: 9853: 9848: 9827: 9792: 9791: 9740: 9739: 9720: 9718: 9717: 9712: 9677: 9606: 9605: 9583: 9581: 9580: 9575: 9540: 9505: 9504: 9453: 9452: 9433: 9431: 9430: 9425: 9408: 9337: 9336: 9314: 9312: 9311: 9306: 9291: 9290: 9289: 9288: 9270: 9269: 9243: 9242: 9241: 9240: 9222: 9221: 9189: 9188: 9187: 9186: 9168: 9167: 9144:over set union. 9131: 9129: 9128: 9123: 9118: 9117: 9099: 9098: 9080: 9079: 9061: 9060: 9048: 9045: 9034: 9033: 9032: 9031: 9013: 9012: 8983: 8982: 8981: 8980: 8962: 8961: 8944: 8943: 8942: 8941: 8923: 8922: 8885: 8883: 8882: 8877: 8872: 8871: 8853: 8852: 8834: 8831: 8817: 8816: 8815: 8814: 8796: 8795: 8778: 8777: 8753: 8752: 8740: 8739: 8738: 8737: 8719: 8718: 8685: 8683: 8682: 8677: 8666: 8665: 8632: 8631: 8610: 8609: 8588: 8587: 8560: 8559: 8542: 8540: 8539: 8534: 8523: 8522: 8501: 8500: 8473: 8472: 8455: 8453: 8452: 8447: 8430: 8429: 8408: 8407: 8386: 8385: 8358: 8357: 8321: 8319: 8318: 8313: 8299: 8298: 8277: 8276: 8264: 8263: 8236: 8235: 8196: 8195: 8132: 8130: 8129: 8124: 8075: 8073: 8072: 8067: 8050: 8049: 8030: 8028: 8027: 8022: 7987: 7985: 7984: 7979: 7968: 7967: 7946: 7945: 7924: 7923: 7900: 7898: 7897: 7892: 7878: 7877: 7865: 7864: 7840: 7839: 7827: 7826: 7805: 7804: 7762: 7760: 7759: 7754: 7741: 7740: 7731: 7730: 7709: 7708: 7699: 7698: 7681: 7679: 7678: 7673: 7660: 7659: 7650: 7649: 7628: 7627: 7571:expression trees 7533:often include a 7524: 7520: 7516: 7512: 7508: 7504: 7500: 7482: 7473: 7458: 7451: 7447: 7444: 7438: 7407: 7399: 7389:fixpoint queries 7364: 7362: 7361: 7356: 7354: 7350: 7349: 7348: 7318: 7317: 7287: 7286: 7174: 7168: 7159: 7151: 7145: 7136: 7130: 7121: 7116: 7112: 7108: 7052: 7050: 7049: 7044: 7031: 7030: 7029: 7025: 7021: 7020: 7019: 7005: 7004: 6983: 6979: 6978: 6977: 6963: 6962: 6947: 6943: 6942: 6941: 6927: 6926: 6910: 6909: 6908: 6890: 6889: 6877: 6876: 6818: 6814: 6813: 6810: 6807: 6804: 6801: 6798: 6795: 6792: 6606: 6567: 6490: 6481: 6402: 6400: 6399: 6394: 6371: 6370: 6369: 6368: 6350: 6349: 6337: 6336: 6245:to the relation 6088: 6049: 5972: 5963: 5906:Right outer join 5901: 5899: 5898: 5893: 5840: 5839: 5838: 5837: 5819: 5818: 5806: 5805: 5744:to the relation 5551: 5512: 5435: 5426: 5297: 5289: 5250: 5219: 5204: 5116: 5107: 5046:were present in 5004: 4909: 4838: 4829: 4790:, but weren't. 4683: 4674: 4510: 4501: 4457: 4422: 4392: 4317: 4308: 4248: 4239: 4216: 4205: 4186: 4136: 4115:∧ ¬∃ 4046: 4007: 3941: 3932: 3871: 3869: 3868: 3863: 3843: 3842: 3841: 3840: 3822: 3821: 3786: 3784: 3783: 3778: 3766: 3764: 3763: 3758: 3756: 3755: 3737: 3736: 3717: 3715: 3714: 3709: 3683: 3681: 3680: 3675: 3545: 3506: 3440: 3431: 3418: 3416: 3415: 3410: 3398: 3396: 3395: 3390: 3378: 3376: 3375: 3370: 3354: 3352: 3351: 3346: 3334: 3332: 3331: 3326: 3314: 3312: 3311: 3306: 3179: 3159: 3157: 3156: 3151: 3149: 3147: 3141: 3135: 3130: 3124: 3118: 3104: 3102: 3101: 3096: 3094: 3092: 3086: 3080: 3075: 3069: 3063: 2959: 2957: 2955: 2954: 2949: 2947: 2889: 2817: 2774: 2765: 2723:Consider tables 2707: 2698: 2696: 2695: 2690: 2679: 2678: 2677: 2676: 2658: 2657: 2645: 2644: 2626: 2625: 2613: 2612: 2594: 2593: 2565: 2554: 2545: 2543: 2542: 2537: 2511: 2510: 2509: 2508: 2496: 2495: 2475: 2474: 2473: 2472: 2460: 2459: 2442: 2441: 2440: 2439: 2427: 2426: 2394: 2393: 2392: 2391: 2379: 2378: 2360: 2359: 2347: 2346: 2318: 2307: 2298: 2296: 2295: 2290: 2270: 2269: 2268: 2267: 2258: 2253: 2252: 2232: 2231: 2230: 2229: 2220: 2215: 2214: 2197: 2196: 2195: 2194: 2185: 2180: 2179: 2153: 2152: 2151: 2150: 2141: 2136: 2135: 2117: 2116: 2107: 2102: 2101: 2073: 2070:can be renamed: 1925: 1916: 1914: 1913: 1908: 1906: 1902: 1886: 1885: 1871: 1865: 1853: 1847: 1835: 1829: 1794: 1623: 1576: 1563:Human Resources 1499: 1490: 1416: 1396: 1395: 1388: 1379: 1377: 1376: 1371: 1366: 1365: 1347: 1346: 1327: 1325: 1324: 1319: 1314: 1313: 1295: 1294: 1268:notation, where 1267: 1265: 1264: 1259: 1248: 1247: 1243: 1242: 1224: 1223: 1193: 1191: 1190: 1185: 1180: 1177: 1172: 1171: 1168: 1141:except that the 1136: 1134: 1133: 1128: 1117: 1116: 1112: 1066: 1062: 1058: 1056: 1055: 1050: 1045: 1042: 1037: 1036: 1035: 1032: 1025: 1022: 1005: 987: 985: 984: 979: 963: 961: 960: 955: 939: 937: 936: 931: 918:normal selection 907: 901: 899: 898: 893: 882: 881: 841: 836: 821: 819: 818: 813: 808: 807: 789: 788: 757: 755: 754: 749: 747: 746: 728: 727: 711: 709: 708: 703: 692: 691: 690: 689: 671: 670: 645: 605: 603: 602: 597: 583: 582: 564: 563: 551: 550: 526: 525: 507: 506: 494: 493: 481: 473: 472: 454: 453: 441: 440: 428: 427: 409: 408: 396: 395: 343: 312:set intersection 308:union-compatible 233: 231: 230: 225: 208: 200: 199: 175: 174: 159: 158: 96:Binary operators 32:Relation algebra 21: 18:Relational logic 11926: 11925: 11921: 11920: 11919: 11917: 11916: 11915: 11891: 11890: 11889: 11884: 11846: 11792:Database models 11780: 11749: 11735:Query optimizer 11710:Data dictionary 11693: 11664:Transaction log 11620: 11576:Codd's 12 rules 11549: 11479:Column-oriented 11445:Object-oriented 11433: 11428: 11332: 11321: 11315: 11312: 11293: 11284:This article's 11280: 11276: 11269: 11228: 11225: 11223:Further reading 11220: 11219: 11210: 11208: 11204: 11203: 11199: 11190: 11188: 11185: 11180: 11179: 11175: 11166: 11164: 11155: 11154: 11150: 11118: 11117: 11113: 11106: 11082: 11081: 11072: 11065: 11050: 11049: 11045: 11038: 11019: 11018: 11014: 11007: 10992: 10991: 10987: 10946: 10945: 10941: 10924: 10912: 10899: 10898: 10894: 10889: 10884: 10883: 10874: 10870: 10861: 10857: 10848: 10844: 10835: 10831: 10822: 10818: 10809: 10805: 10800: 10795: 10680: 10602: 10601: 10544: 10542:Implementations 10466: 10465: 10459: 10416: 10386: 10350: 10345: 10344: 10305: 10275: 10239: 10234: 10233: 10194: 10164: 10128: 10123: 10122: 10116: 10068: 10047: 10014: 9993: 9988: 9987: 9946: 9913: 9892: 9887: 9886: 9879: 9874: 9867: 9820: 9783: 9731: 9726: 9725: 9670: 9597: 9592: 9591: 9533: 9496: 9444: 9439: 9438: 9401: 9328: 9323: 9322: 9280: 9261: 9256: 9232: 9213: 9208: 9178: 9159: 9154: 9149: 9148: 9138: 9109: 9090: 9071: 9052: 9023: 9004: 8999: 8972: 8953: 8948: 8933: 8914: 8909: 8904: 8903: 8897: 8892: 8863: 8844: 8806: 8787: 8782: 8769: 8744: 8729: 8710: 8705: 8700: 8699: 8692: 8657: 8623: 8601: 8579: 8551: 8546: 8545: 8514: 8492: 8464: 8459: 8458: 8421: 8399: 8377: 8349: 8344: 8343: 8339:as an operand. 8328: 8290: 8268: 8255: 8215: 8187: 8182: 8181: 8097: 8096: 8041: 8036: 8035: 8010: 8009: 7994: 7959: 7937: 7909: 7904: 7903: 7869: 7856: 7831: 7818: 7790: 7785: 7784: 7769: 7732: 7722: 7700: 7690: 7685: 7684: 7651: 7641: 7619: 7614: 7613: 7599: 7586: 7535:query optimizer 7528: 7527: 7526: 7525: 7522: 7518: 7514: 7510: 7506: 7502: 7498: 7496: 7485: 7484: 7483: 7475: 7474: 7459: 7448: 7442: 7439: 7424: 7408: 7397: 7340: 7309: 7278: 7259: 7255: 7232: 7231: 7199:be a subset of 7181: 7172: 7170: 7166: 7160: 7157: 7149: 7147: 7143: 7134: 7132: 7128: 7122: 7119: 7114: 7110: 7106: 7081: 7064: 7011: 7009: 6996: 6969: 6967: 6954: 6933: 6931: 6918: 6913: 6900: 6881: 6868: 6863: 6862: 6857: 6848: 6841: 6829: 6816: 6811: 6808: 6805: 6802: 6799: 6796: 6793: 6790: 6785: 6714: 6417:full outer join 6409: 6407:Full outer join 6360: 6341: 6328: 6323: 6258: 6257: 6228: 6219: 6212: 6154: 5908: 5829: 5810: 5797: 5792: 5757: 5756: 5727: 5718: 5711: 5645: 5373: 5371:Left outer join 5341: 5335: 5327: 5322: 5295:desired result 5279: 5275: 5212: 5188: 5170: 5169: 5160: 5136: 5095: 5074: 5073: 5064: 5030: 4817: 4749: 4658: 4629: 4628: 4619: 4592: 4583: 4572: 4563: 4533: 4524: 4508: 4460: 4447: 4305: 4295:are present in 4265: 4246: 4219: 4192: 4173:that satisfies 4145: 4095: 4089: 3883: 3832: 3813: 3808: 3791: 3790: 3769: 3768: 3747: 3728: 3723: 3722: 3688: 3687: 3594: 3593: 3588: 3401: 3400: 3381: 3380: 3361: 3360: 3337: 3336: 3317: 3316: 3291: 3290: 3287: 3240: 3231: 3177: 3131: 3114: 3107: 3106: 3076: 3059: 3052: 3051: 3039: 2864: 2857: 2856: 2740: 2721: 2705: 2668: 2649: 2636: 2617: 2604: 2585: 2580: 2569: 2568: 2552: 2500: 2487: 2482: 2464: 2451: 2446: 2431: 2418: 2413: 2383: 2370: 2351: 2338: 2333: 2322: 2321: 2305: 2259: 2244: 2239: 2221: 2206: 2201: 2186: 2171: 2166: 2142: 2127: 2108: 2093: 2088: 2077: 2076: 2058:are neither in 2057: 2048: 2037: 2028: 2017: 2008: 1993: 1984: 1923: 1819: 1815: 1798: 1797: 1726:category theory 1703: 1448:binary operator 1444: 1437: 1430: 1421: 1397: 1393: 1386: 1357: 1338: 1330: 1329: 1328:are renamed to 1305: 1286: 1278: 1277: 1234: 1215: 1204: 1199: 1198: 1194:might be used. 1163: 1158: 1157: 1100: 1095: 1094: 1091:unary operation 1079: 1073: 1064: 1060: 1023:isFriend = true 1016: 1011: 1010: 1001: 970: 969: 946: 945: 922: 921: 903: 873: 868: 867: 864:unary operation 856: 850: 839: 834: 799: 780: 772: 771: 738: 719: 714: 713: 681: 662: 657: 652: 651: 648:unary operation 643: 636: 630: 574: 555: 542: 517: 498: 485: 464: 445: 432: 419: 400: 387: 364: 363: 333: 281: 188: 163: 147: 130: 129: 115: 88:Unary operators 66:query languages 64:, particularly 39:database theory 35: 28: 23: 22: 15: 12: 11: 5: 11924: 11922: 11914: 11913: 11908: 11903: 11893: 11892: 11886: 11885: 11883: 11882: 11872: 11862: 11851: 11848: 11847: 11845: 11844: 11839: 11834: 11829: 11824: 11819: 11814: 11809: 11804: 11799: 11794: 11788: 11786: 11785:Related topics 11782: 11781: 11779: 11778: 11773: 11768: 11763: 11761:Administration 11757: 11755: 11751: 11750: 11748: 11747: 11742: 11737: 11732: 11730:Query language 11727: 11722: 11717: 11712: 11707: 11701: 11699: 11695: 11694: 11692: 11691: 11686: 11681: 11676: 11671: 11666: 11661: 11656: 11651: 11650: 11649: 11644: 11639: 11628: 11626: 11622: 11621: 11619: 11618: 11613: 11608: 11603: 11598: 11593: 11588: 11583: 11578: 11573: 11568: 11563: 11557: 11555: 11551: 11550: 11548: 11547: 11542: 11537: 11536: 11535: 11525: 11524: 11523: 11513: 11508: 11503: 11498: 11493: 11488: 11487: 11486: 11476: 11471: 11470: 11469: 11464: 11454: 11453: 11452: 11441: 11439: 11435: 11434: 11429: 11427: 11426: 11419: 11412: 11404: 11398: 11397: 11392: 11387: 11381: 11376: 11371: 11366: 11360: 11355: 11349: 11343: 11334: 11333: 11288:external links 11283: 11281: 11274: 11268: 11267:External links 11265: 11264: 11263: 11230:Imieliński, T. 11224: 11221: 11218: 11217: 11197: 11173: 11148: 11111: 11104: 11092:Jennifer Widom 11070: 11063: 11043: 11036: 11012: 11005: 10985: 10964:(6): 377–387. 10939: 10910: 10891: 10890: 10888: 10885: 10882: 10881: 10868: 10855: 10842: 10829: 10816: 10802: 10801: 10799: 10796: 10794: 10793: 10791:Codd's theorem 10788: 10783: 10778: 10773: 10768: 10763: 10758: 10753: 10748: 10743: 10738: 10733: 10728: 10723: 10718: 10713: 10708: 10703: 10698: 10693: 10687: 10681: 10679: 10676: 10663: 10660: 10657: 10654: 10651: 10648: 10645: 10642: 10639: 10636: 10633: 10630: 10627: 10624: 10621: 10618: 10615: 10612: 10609: 10543: 10540: 10539: 10538: 10527: 10524: 10521: 10518: 10515: 10512: 10509: 10506: 10503: 10500: 10497: 10494: 10491: 10488: 10485: 10482: 10479: 10476: 10473: 10458: 10455: 10454: 10453: 10442: 10439: 10436: 10431: 10427: 10423: 10419: 10415: 10412: 10409: 10406: 10401: 10397: 10393: 10389: 10385: 10382: 10379: 10376: 10373: 10370: 10365: 10361: 10357: 10353: 10342: 10331: 10328: 10325: 10320: 10316: 10312: 10308: 10304: 10301: 10298: 10295: 10290: 10286: 10282: 10278: 10274: 10271: 10268: 10265: 10262: 10259: 10254: 10250: 10246: 10242: 10231: 10220: 10217: 10214: 10209: 10205: 10201: 10197: 10193: 10190: 10187: 10184: 10179: 10175: 10171: 10167: 10163: 10160: 10157: 10154: 10151: 10148: 10143: 10139: 10135: 10131: 10115: 10112: 10111: 10110: 10097: 10094: 10091: 10088: 10083: 10079: 10075: 10071: 10067: 10062: 10058: 10054: 10050: 10046: 10043: 10040: 10037: 10034: 10029: 10025: 10021: 10017: 10013: 10008: 10004: 10000: 9996: 9985: 9972: 9969: 9966: 9961: 9957: 9953: 9949: 9945: 9942: 9939: 9936: 9933: 9928: 9924: 9920: 9916: 9912: 9907: 9903: 9899: 9895: 9878: 9875: 9873: 9870: 9865: 9858: 9857: 9846: 9842: 9839: 9836: 9833: 9830: 9826: 9823: 9819: 9816: 9813: 9810: 9807: 9804: 9801: 9798: 9795: 9790: 9786: 9782: 9779: 9776: 9773: 9770: 9767: 9764: 9761: 9758: 9755: 9752: 9749: 9746: 9743: 9738: 9734: 9722: 9721: 9710: 9707: 9704: 9701: 9698: 9695: 9692: 9689: 9686: 9683: 9680: 9676: 9673: 9669: 9666: 9663: 9660: 9657: 9654: 9651: 9648: 9645: 9642: 9639: 9636: 9633: 9630: 9627: 9624: 9621: 9618: 9615: 9612: 9609: 9604: 9600: 9585: 9584: 9573: 9570: 9567: 9564: 9561: 9558: 9555: 9552: 9549: 9546: 9543: 9539: 9536: 9532: 9529: 9526: 9523: 9520: 9517: 9514: 9511: 9508: 9503: 9499: 9495: 9492: 9489: 9486: 9483: 9480: 9477: 9474: 9471: 9468: 9465: 9462: 9459: 9456: 9451: 9447: 9435: 9434: 9423: 9420: 9417: 9414: 9411: 9407: 9404: 9400: 9397: 9394: 9391: 9388: 9385: 9382: 9379: 9376: 9373: 9370: 9367: 9364: 9361: 9358: 9355: 9352: 9349: 9346: 9343: 9340: 9335: 9331: 9316: 9315: 9303: 9300: 9297: 9294: 9287: 9283: 9279: 9276: 9273: 9268: 9264: 9259: 9255: 9252: 9249: 9246: 9239: 9235: 9231: 9228: 9225: 9220: 9216: 9211: 9207: 9204: 9201: 9198: 9195: 9192: 9185: 9181: 9177: 9174: 9171: 9166: 9162: 9157: 9140:Projection is 9137: 9134: 9133: 9132: 9121: 9116: 9112: 9108: 9105: 9102: 9097: 9093: 9089: 9086: 9083: 9078: 9074: 9070: 9067: 9064: 9059: 9055: 9051: 9043: 9040: 9037: 9030: 9026: 9022: 9019: 9016: 9011: 9007: 9002: 8998: 8995: 8992: 8989: 8986: 8979: 8975: 8971: 8968: 8965: 8960: 8956: 8951: 8947: 8940: 8936: 8932: 8929: 8926: 8921: 8917: 8912: 8896: 8893: 8891: 8888: 8887: 8886: 8875: 8870: 8866: 8862: 8859: 8856: 8851: 8847: 8843: 8840: 8837: 8829: 8826: 8823: 8820: 8813: 8809: 8805: 8802: 8799: 8794: 8790: 8785: 8781: 8776: 8772: 8768: 8765: 8762: 8759: 8756: 8751: 8747: 8743: 8736: 8732: 8728: 8725: 8722: 8717: 8713: 8708: 8691: 8688: 8687: 8686: 8675: 8672: 8669: 8664: 8660: 8656: 8653: 8650: 8647: 8644: 8641: 8638: 8635: 8630: 8626: 8622: 8619: 8616: 8613: 8608: 8604: 8600: 8597: 8594: 8591: 8586: 8582: 8578: 8575: 8572: 8569: 8566: 8563: 8558: 8554: 8543: 8532: 8529: 8526: 8521: 8517: 8513: 8510: 8507: 8504: 8499: 8495: 8491: 8488: 8485: 8482: 8479: 8476: 8471: 8467: 8456: 8445: 8442: 8439: 8436: 8433: 8428: 8424: 8420: 8417: 8414: 8411: 8406: 8402: 8398: 8395: 8392: 8389: 8384: 8380: 8376: 8373: 8370: 8367: 8364: 8361: 8356: 8352: 8327: 8324: 8323: 8322: 8311: 8308: 8305: 8302: 8297: 8293: 8289: 8286: 8283: 8280: 8275: 8271: 8267: 8262: 8258: 8254: 8251: 8248: 8245: 8242: 8239: 8234: 8231: 8228: 8225: 8222: 8218: 8214: 8211: 8208: 8205: 8202: 8199: 8194: 8190: 8122: 8119: 8116: 8113: 8110: 8107: 8104: 8065: 8062: 8059: 8056: 8053: 8048: 8044: 8020: 8017: 7993: 7990: 7989: 7988: 7977: 7974: 7971: 7966: 7962: 7958: 7955: 7952: 7949: 7944: 7940: 7936: 7933: 7930: 7927: 7922: 7919: 7916: 7912: 7901: 7890: 7887: 7884: 7881: 7876: 7872: 7868: 7863: 7859: 7855: 7852: 7849: 7846: 7843: 7838: 7834: 7830: 7825: 7821: 7817: 7814: 7811: 7808: 7803: 7800: 7797: 7793: 7768: 7765: 7764: 7763: 7750: 7747: 7744: 7739: 7735: 7729: 7725: 7721: 7718: 7715: 7712: 7707: 7703: 7697: 7693: 7682: 7669: 7666: 7663: 7658: 7654: 7648: 7644: 7640: 7637: 7634: 7631: 7626: 7622: 7598: 7595: 7585: 7582: 7567: 7566: 7563: 7556: 7495:triangle query 7494: 7487: 7486: 7477: 7476: 7468: 7467: 7466: 7465: 7464: 7461: 7460: 7411: 7409: 7402: 7396: 7393: 7366: 7365: 7353: 7347: 7343: 7339: 7336: 7333: 7330: 7327: 7324: 7321: 7316: 7312: 7308: 7305: 7302: 7299: 7296: 7293: 7290: 7285: 7281: 7277: 7274: 7271: 7268: 7265: 7262: 7258: 7254: 7251: 7248: 7245: 7242: 7239: 7223:that contains 7180: 7177: 7164: 7156: 7141: 7126: 7118: 7077: 7060: 7054: 7053: 7042: 7039: 7036: 7028: 7024: 7018: 7014: 7008: 7003: 6999: 6995: 6992: 6989: 6986: 6982: 6976: 6972: 6966: 6961: 6957: 6953: 6950: 6946: 6940: 6936: 6930: 6925: 6921: 6916: 6907: 6903: 6899: 6896: 6893: 6888: 6884: 6880: 6875: 6871: 6853: 6846: 6839: 6828: 6825: 6784: 6781: 6780: 6779: 6711: 6710: 6704: 6703: 6700: 6697: 6694: 6690: 6689: 6686: 6683: 6680: 6676: 6675: 6672: 6669: 6666: 6662: 6661: 6658: 6655: 6652: 6648: 6647: 6644: 6641: 6638: 6634: 6633: 6630: 6627: 6624: 6620: 6619: 6616: 6613: 6610: 6594: 6591: 6590: 6587: 6583: 6582: 6579: 6575: 6574: 6571: 6559: 6556: 6555: 6552: 6549: 6545: 6544: 6541: 6538: 6534: 6533: 6530: 6527: 6523: 6522: 6519: 6516: 6512: 6511: 6508: 6505: 6501: 6500: 6497: 6494: 6479: 6458:and tuples in 6408: 6405: 6404: 6403: 6392: 6389: 6386: 6383: 6380: 6377: 6374: 6367: 6363: 6359: 6356: 6353: 6348: 6344: 6340: 6335: 6331: 6326: 6322: 6319: 6316: 6313: 6310: 6307: 6304: 6301: 6298: 6295: 6292: 6289: 6286: 6283: 6280: 6277: 6274: 6271: 6268: 6265: 6224: 6217: 6210: 6151: 6150: 6144: 6143: 6140: 6137: 6134: 6130: 6129: 6126: 6123: 6120: 6116: 6115: 6112: 6109: 6106: 6102: 6101: 6098: 6095: 6092: 6076: 6073: 6072: 6069: 6065: 6064: 6061: 6057: 6056: 6053: 6041: 6038: 6037: 6034: 6031: 6027: 6026: 6023: 6020: 6016: 6015: 6012: 6009: 6005: 6004: 6001: 5998: 5994: 5993: 5990: 5987: 5983: 5982: 5979: 5976: 5961: 5924:is written as 5907: 5904: 5903: 5902: 5891: 5888: 5885: 5882: 5879: 5876: 5873: 5870: 5867: 5864: 5861: 5858: 5855: 5852: 5849: 5846: 5843: 5836: 5832: 5828: 5825: 5822: 5817: 5813: 5809: 5804: 5800: 5795: 5791: 5788: 5785: 5782: 5779: 5776: 5773: 5770: 5767: 5764: 5723: 5716: 5709: 5642: 5641: 5635: 5634: 5631: 5628: 5625: 5621: 5620: 5617: 5614: 5611: 5607: 5606: 5603: 5600: 5597: 5593: 5592: 5589: 5586: 5583: 5579: 5578: 5575: 5572: 5569: 5565: 5564: 5561: 5558: 5555: 5539: 5536: 5535: 5532: 5528: 5527: 5524: 5520: 5519: 5516: 5504: 5501: 5500: 5497: 5494: 5490: 5489: 5486: 5483: 5479: 5478: 5475: 5472: 5468: 5467: 5464: 5461: 5457: 5456: 5453: 5450: 5446: 5445: 5442: 5439: 5424: 5372: 5369: 5334: 5331: 5326: 5323: 5319: 5318: 5312: 5311: 5307: 5306: 5302: 5301: 5277: 5263: 5260: 5259: 5255: 5254: 5242: 5239: 5238: 5234: 5233: 5229: 5228: 5224: 5223: 5210: 5202: 5201: 5200: 5199: 5198: 5186: 5165: 5158: 5154: 5133: 5132: 5126: 5125: 5121: 5120: 5105: 5104: 5103: 5102: 5101: 5093: 5087: 5069: 5062: 5058: 5027: 5026: 5020: 5019: 5016: 5012: 5011: 5008: 5001:what's missing 4976: 4973: 4972: 4969: 4965: 4964: 4961: 4957: 4956: 4953: 4949: 4948: 4945: 4941: 4940: 4937: 4933: 4932: 4929: 4925: 4924: 4921: 4917: 4916: 4913: 4897: 4894: 4893: 4890: 4886: 4885: 4882: 4878: 4877: 4874: 4870: 4869: 4866: 4862: 4861: 4858: 4854: 4853: 4850: 4846: 4845: 4842: 4827: 4826: 4825: 4824: 4823: 4815: 4805: 4780: 4779: 4746: 4745: 4739: 4738: 4735: 4731: 4730: 4727: 4723: 4722: 4719: 4715: 4714: 4711: 4707: 4706: 4703: 4699: 4698: 4695: 4691: 4690: 4687: 4672: 4671: 4670: 4669: 4668: 4656: 4650: 4639: 4638: 4624: 4617: 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3604: 3601: 3585: 3584: 3578: 3577: 3574: 3571: 3567: 3566: 3563: 3560: 3556: 3555: 3552: 3549: 3533: 3530: 3529: 3526: 3522: 3521: 3518: 3514: 3513: 3510: 3498: 3495: 3494: 3491: 3488: 3484: 3483: 3480: 3477: 3473: 3472: 3469: 3466: 3462: 3461: 3458: 3455: 3451: 3450: 3447: 3444: 3429: 3408: 3388: 3368: 3344: 3324: 3304: 3301: 3298: 3286: 3283: 3252: 3251: 3238: 3227: 3146: 3140: 3134: 3129: 3123: 3117: 3091: 3085: 3079: 3074: 3068: 3062: 3036: 3035: 3029: 3028: 3025: 3022: 3019: 3015: 3014: 3011: 3008: 3005: 3001: 3000: 2997: 2994: 2991: 2987: 2986: 2983: 2980: 2977: 2973: 2972: 2969: 2966: 2963: 2944: 2941: 2938: 2935: 2932: 2929: 2926: 2923: 2920: 2917: 2914: 2911: 2908: 2905: 2902: 2899: 2896: 2893: 2888: 2885: 2882: 2879: 2876: 2873: 2870: 2867: 2852: 2849: 2848: 2845: 2841: 2840: 2837: 2833: 2832: 2829: 2825: 2824: 2821: 2809: 2806: 2805: 2802: 2798: 2797: 2794: 2790: 2789: 2786: 2782: 2781: 2778: 2763: 2736: 2720: 2714: 2711: 2710: 2701: 2699: 2688: 2685: 2682: 2675: 2671: 2667: 2664: 2661: 2656: 2652: 2648: 2643: 2639: 2635: 2632: 2629: 2624: 2620: 2616: 2611: 2607: 2603: 2600: 2597: 2592: 2588: 2583: 2579: 2576: 2558: 2557: 2548: 2546: 2535: 2532: 2529: 2526: 2523: 2520: 2517: 2514: 2507: 2503: 2499: 2494: 2490: 2485: 2481: 2478: 2471: 2467: 2463: 2458: 2454: 2449: 2445: 2438: 2434: 2430: 2425: 2421: 2416: 2412: 2409: 2406: 2403: 2400: 2397: 2390: 2386: 2382: 2377: 2373: 2369: 2366: 2363: 2358: 2354: 2350: 2345: 2341: 2336: 2332: 2329: 2311: 2310: 2301: 2299: 2288: 2285: 2282: 2279: 2276: 2273: 2266: 2262: 2257: 2251: 2247: 2242: 2238: 2235: 2228: 2224: 2219: 2213: 2209: 2204: 2200: 2193: 2189: 2184: 2178: 2174: 2169: 2165: 2162: 2159: 2156: 2149: 2145: 2140: 2134: 2130: 2126: 2123: 2120: 2115: 2111: 2106: 2100: 2096: 2091: 2087: 2084: 2053: 2046: 2033: 2026: 2013: 2006: 1989: 1982: 1929: 1928: 1919: 1917: 1905: 1901: 1898: 1895: 1892: 1889: 1884: 1881: 1878: 1870: 1864: 1861: 1858: 1852: 1846: 1843: 1840: 1834: 1828: 1825: 1822: 1818: 1814: 1811: 1808: 1805: 1700: 1699: 1693: 1692: 1689: 1686: 1683: 1679: 1678: 1675: 1672: 1669: 1665: 1664: 1661: 1658: 1655: 1651: 1650: 1647: 1644: 1641: 1637: 1636: 1633: 1630: 1627: 1611: 1608: 1607: 1604: 1600: 1599: 1596: 1592: 1591: 1588: 1584: 1583: 1580: 1568: 1565: 1564: 1561: 1558: 1554: 1553: 1550: 1547: 1543: 1542: 1539: 1536: 1532: 1531: 1528: 1525: 1521: 1520: 1517: 1514: 1510: 1509: 1506: 1503: 1488: 1429: 1426: 1423: 1422: 1400: 1398: 1391: 1385: 1382: 1369: 1364: 1360: 1356: 1353: 1350: 1345: 1341: 1337: 1317: 1312: 1308: 1304: 1301: 1298: 1293: 1289: 1285: 1272:is renamed to 1257: 1254: 1251: 1246: 1241: 1237: 1233: 1230: 1227: 1222: 1218: 1214: 1211: 1207: 1183: 1175: 1166: 1126: 1123: 1120: 1115: 1111: 1107: 1103: 1075:Main article: 1072: 1069: 1048: 1040: 1029: 1019: 977: 953: 929: 891: 888: 885: 880: 876: 862:(σ) is a 852:Main article: 849: 846: 811: 806: 802: 798: 795: 792: 787: 783: 779: 745: 741: 737: 734: 731: 726: 722: 701: 698: 695: 688: 684: 680: 677: 674: 669: 665: 660: 632:Main article: 629: 626: 595: 592: 589: 586: 581: 577: 573: 570: 567: 562: 558: 554: 549: 545: 541: 538: 535: 532: 529: 524: 520: 516: 513: 510: 505: 501: 497: 492: 488: 484: 480: 476: 471: 467: 463: 460: 457: 452: 448: 444: 439: 435: 431: 426: 422: 418: 415: 412: 407: 403: 399: 394: 390: 386: 383: 380: 377: 374: 371: 348:-tuple and an 289:set difference 280: 277: 272:set difference 223: 220: 217: 214: 211: 207: 203: 198: 195: 191: 187: 184: 181: 178: 173: 170: 166: 162: 157: 154: 150: 146: 143: 140: 137: 114: 111: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 11923: 11912: 11909: 11907: 11904: 11902: 11899: 11898: 11896: 11881: 11873: 11871: 11863: 11861: 11853: 11852: 11849: 11843: 11840: 11838: 11835: 11833: 11830: 11828: 11825: 11823: 11820: 11818: 11815: 11813: 11810: 11808: 11805: 11803: 11800: 11798: 11795: 11793: 11790: 11789: 11787: 11783: 11777: 11774: 11772: 11769: 11767: 11764: 11762: 11759: 11758: 11756: 11752: 11746: 11743: 11741: 11738: 11736: 11733: 11731: 11728: 11726: 11723: 11721: 11718: 11716: 11713: 11711: 11708: 11706: 11703: 11702: 11700: 11696: 11690: 11687: 11685: 11682: 11680: 11677: 11675: 11672: 11670: 11667: 11665: 11662: 11660: 11657: 11655: 11652: 11648: 11645: 11643: 11640: 11638: 11635: 11634: 11633: 11630: 11629: 11627: 11623: 11617: 11614: 11612: 11611:Surrogate key 11609: 11607: 11604: 11602: 11599: 11597: 11596:Candidate key 11594: 11592: 11589: 11587: 11584: 11582: 11579: 11577: 11574: 11572: 11569: 11567: 11564: 11562: 11559: 11558: 11556: 11552: 11546: 11543: 11541: 11538: 11534: 11531: 11530: 11529: 11526: 11522: 11519: 11518: 11517: 11514: 11512: 11509: 11507: 11504: 11502: 11499: 11497: 11494: 11492: 11489: 11485: 11482: 11481: 11480: 11477: 11475: 11472: 11468: 11465: 11463: 11460: 11459: 11458: 11455: 11451: 11448: 11447: 11446: 11443: 11442: 11440: 11436: 11432: 11425: 11420: 11418: 11413: 11411: 11406: 11405: 11402: 11396: 11393: 11391: 11388: 11385: 11382: 11380: 11377: 11375: 11372: 11370: 11367: 11364: 11361: 11359: 11356: 11353: 11350: 11347: 11344: 11341: 11338: 11337: 11330: 11327: 11319: 11309: 11305: 11304:inappropriate 11301: 11297: 11291: 11289: 11282: 11273: 11272: 11266: 11261: 11254: 11249: 11245: 11241: 11240: 11235: 11231: 11227: 11226: 11222: 11207: 11201: 11198: 11184: 11177: 11174: 11163: 11159: 11152: 11149: 11144: 11140: 11135: 11130: 11126: 11122: 11115: 11112: 11107: 11101: 11097: 11093: 11089: 11085: 11079: 11077: 11075: 11071: 11066: 11060: 11056: 11055: 11047: 11044: 11039: 11033: 11029: 11028: 11023: 11016: 11013: 11008: 11002: 10998: 10997: 10989: 10986: 10981: 10977: 10972: 10967: 10963: 10959: 10958: 10953: 10950:(June 1970). 10949: 10943: 10940: 10935: 10929: 10921: 10917: 10913: 10907: 10903: 10896: 10893: 10886: 10878: 10872: 10869: 10865: 10859: 10856: 10852: 10846: 10843: 10839: 10833: 10830: 10826: 10820: 10817: 10813: 10807: 10804: 10797: 10792: 10789: 10787: 10784: 10782: 10779: 10777: 10774: 10772: 10769: 10767: 10764: 10762: 10759: 10757: 10754: 10752: 10749: 10747: 10744: 10742: 10739: 10737: 10734: 10732: 10729: 10727: 10724: 10722: 10719: 10717: 10714: 10712: 10709: 10707: 10704: 10702: 10699: 10697: 10694: 10691: 10688: 10686: 10683: 10682: 10677: 10675: 10658: 10652: 10646: 10640: 10634: 10628: 10625: 10616: 10613: 10610: 10599: 10595: 10591: 10587: 10582: 10580: 10576: 10572: 10568: 10564: 10560: 10555: 10553: 10549: 10541: 10522: 10519: 10516: 10510: 10507: 10504: 10498: 10495: 10492: 10486: 10480: 10477: 10474: 10464: 10463: 10462: 10456: 10437: 10429: 10425: 10421: 10417: 10413: 10407: 10399: 10395: 10391: 10387: 10383: 10377: 10374: 10371: 10363: 10359: 10355: 10351: 10343: 10326: 10318: 10314: 10310: 10306: 10302: 10296: 10288: 10284: 10280: 10276: 10272: 10266: 10263: 10260: 10252: 10248: 10244: 10240: 10232: 10215: 10207: 10203: 10199: 10195: 10185: 10177: 10173: 10169: 10165: 10161: 10155: 10149: 10141: 10137: 10133: 10129: 10121: 10120: 10119: 10113: 10089: 10081: 10077: 10073: 10069: 10060: 10056: 10052: 10048: 10044: 10035: 10027: 10023: 10019: 10015: 10006: 10002: 9998: 9994: 9986: 9967: 9959: 9955: 9951: 9947: 9943: 9934: 9926: 9922: 9918: 9914: 9905: 9901: 9897: 9893: 9885: 9884: 9883: 9876: 9871: 9869: 9863: 9844: 9837: 9824: 9821: 9817: 9814: 9811: 9808: 9805: 9802: 9788: 9784: 9768: 9765: 9762: 9759: 9756: 9753: 9750: 9736: 9732: 9724: 9723: 9702: 9699: 9696: 9687: 9674: 9671: 9667: 9664: 9661: 9658: 9655: 9652: 9634: 9631: 9628: 9625: 9622: 9619: 9616: 9602: 9598: 9590: 9589: 9588: 9565: 9562: 9559: 9550: 9537: 9534: 9530: 9527: 9524: 9521: 9518: 9515: 9501: 9497: 9493: 9481: 9478: 9475: 9472: 9469: 9466: 9463: 9449: 9445: 9437: 9436: 9418: 9405: 9402: 9398: 9395: 9392: 9389: 9386: 9383: 9374: 9365: 9362: 9359: 9356: 9353: 9350: 9347: 9333: 9329: 9321: 9320: 9319: 9301: 9295: 9285: 9281: 9277: 9274: 9271: 9266: 9262: 9257: 9253: 9247: 9237: 9233: 9229: 9226: 9223: 9218: 9214: 9209: 9205: 9199: 9196: 9193: 9183: 9179: 9175: 9172: 9169: 9164: 9160: 9155: 9147: 9146: 9145: 9143: 9135: 9114: 9110: 9106: 9103: 9100: 9095: 9091: 9084: 9076: 9072: 9068: 9065: 9062: 9057: 9053: 9038: 9028: 9024: 9020: 9017: 9014: 9009: 9005: 9000: 8996: 8987: 8977: 8973: 8969: 8966: 8963: 8958: 8954: 8949: 8938: 8934: 8930: 8927: 8924: 8919: 8915: 8910: 8902: 8901: 8900: 8894: 8889: 8868: 8864: 8860: 8857: 8854: 8849: 8845: 8838: 8835: 8821: 8811: 8807: 8803: 8800: 8797: 8792: 8788: 8783: 8774: 8770: 8766: 8757: 8749: 8745: 8734: 8730: 8726: 8723: 8720: 8715: 8711: 8706: 8698: 8697: 8696: 8689: 8670: 8662: 8658: 8654: 8651: 8648: 8645: 8642: 8636: 8628: 8624: 8620: 8614: 8606: 8602: 8598: 8592: 8584: 8580: 8576: 8570: 8567: 8564: 8556: 8552: 8544: 8527: 8519: 8515: 8511: 8505: 8497: 8493: 8489: 8483: 8480: 8477: 8469: 8465: 8457: 8443: 8434: 8426: 8422: 8418: 8412: 8404: 8400: 8390: 8382: 8378: 8374: 8368: 8362: 8354: 8350: 8342: 8341: 8340: 8338: 8333: 8330:Selection is 8325: 8303: 8295: 8291: 8287: 8281: 8273: 8269: 8260: 8256: 8252: 8246: 8243: 8240: 8232: 8229: 8226: 8223: 8220: 8216: 8212: 8206: 8203: 8200: 8192: 8188: 8180: 8179: 8178: 8176: 8172: 8168: 8165:. Note, that 8164: 8160: 8156: 8152: 8148: 8144: 8140: 8136: 8120: 8117: 8114: 8111: 8108: 8105: 8102: 8094: 8090: 8086: 8082: 8077: 8060: 8057: 8054: 8046: 8042: 8032: 8018: 8015: 8007: 8003: 7999: 7991: 7972: 7964: 7960: 7956: 7950: 7942: 7938: 7934: 7928: 7920: 7917: 7914: 7910: 7902: 7882: 7874: 7870: 7861: 7857: 7853: 7844: 7836: 7832: 7823: 7819: 7815: 7809: 7801: 7798: 7795: 7791: 7783: 7782: 7781: 7778: 7774: 7766: 7745: 7737: 7733: 7727: 7723: 7719: 7713: 7705: 7701: 7695: 7691: 7683: 7664: 7656: 7652: 7646: 7642: 7638: 7632: 7624: 7620: 7612: 7611: 7610: 7608: 7604: 7601:Selection is 7596: 7594: 7592: 7583: 7581: 7578: 7576: 7572: 7564: 7561: 7557: 7554: 7553: 7552: 7550: 7546: 7542: 7540: 7536: 7532: 7497: 7491: 7488:Two possible 7481: 7472: 7457: 7454: 7446: 7436: 7432: 7428: 7422: 7421: 7417: 7412:This section 7410: 7406: 7401: 7400: 7394: 7392: 7390: 7385: 7383: 7379: 7375: 7371: 7351: 7345: 7341: 7337: 7331: 7328: 7325: 7314: 7310: 7306: 7300: 7297: 7294: 7288: 7283: 7279: 7275: 7269: 7266: 7263: 7256: 7252: 7246: 7240: 7230: 7229: 7228: 7226: 7222: 7218: 7214: 7210: 7206: 7202: 7198: 7194: 7190: 7186: 7178: 7176: 7163: 7153: 7140: 7125: 7103: 7101: 7096: 7091: 7089: 7085: 7080: 7076: 7072: 7068: 7063: 7059: 7037: 7022: 7016: 7012: 7001: 6997: 6993: 6990: 6987: 6980: 6974: 6970: 6959: 6955: 6951: 6944: 6938: 6934: 6923: 6919: 6914: 6905: 6901: 6897: 6894: 6891: 6886: 6882: 6878: 6873: 6869: 6861: 6860: 6859: 6856: 6852: 6845: 6838: 6834: 6826: 6824: 6822: 6782: 6777: 6773: 6769: 6765: 6761: 6757: 6754: 6753: 6752: 6749: 6747: 6743: 6739: 6735: 6731: 6727: 6723: 6719: 6709: 6701: 6698: 6695: 6692: 6691: 6687: 6684: 6681: 6678: 6677: 6673: 6670: 6667: 6664: 6663: 6659: 6656: 6653: 6650: 6649: 6645: 6642: 6639: 6636: 6635: 6631: 6628: 6625: 6622: 6621: 6617: 6614: 6611: 6608: 6607: 6604: 6600: 6595: 6588: 6585: 6584: 6580: 6577: 6576: 6572: 6569: 6568: 6565: 6560: 6553: 6550: 6547: 6546: 6542: 6539: 6536: 6535: 6531: 6528: 6525: 6524: 6520: 6517: 6514: 6513: 6509: 6506: 6503: 6502: 6498: 6495: 6492: 6491: 6488: 6483: 6482: 6478: 6476: 6472: 6467: 6465: 6461: 6457: 6453: 6449: 6445: 6441: 6437: 6433: 6429: 6425: 6420: 6418: 6414: 6406: 6381: 6378: 6375: 6365: 6361: 6357: 6354: 6351: 6346: 6342: 6338: 6333: 6329: 6324: 6320: 6317: 6311: 6302: 6299: 6296: 6293: 6290: 6278: 6272: 6269: 6266: 6256: 6255: 6254: 6252: 6248: 6244: 6240: 6236: 6232: 6227: 6223: 6216: 6209: 6204: 6202: 6198: 6194: 6190: 6186: 6182: 6178: 6173: 6171: 6167: 6163: 6159: 6149: 6141: 6138: 6135: 6132: 6131: 6127: 6124: 6121: 6118: 6117: 6113: 6110: 6107: 6104: 6103: 6099: 6096: 6093: 6090: 6089: 6086: 6082: 6077: 6070: 6067: 6066: 6062: 6059: 6058: 6054: 6051: 6050: 6047: 6042: 6035: 6032: 6029: 6028: 6024: 6021: 6018: 6017: 6013: 6010: 6007: 6006: 6002: 5999: 5996: 5995: 5991: 5988: 5985: 5984: 5980: 5977: 5974: 5973: 5970: 5965: 5964: 5960: 5958: 5954: 5949: 5947: 5943: 5939: 5935: 5931: 5927: 5923: 5919: 5916: 5911: 5905: 5880: 5877: 5874: 5871: 5868: 5859: 5850: 5847: 5844: 5834: 5830: 5826: 5823: 5820: 5815: 5811: 5807: 5802: 5798: 5793: 5789: 5786: 5777: 5771: 5768: 5765: 5755: 5754: 5753: 5751: 5747: 5743: 5739: 5735: 5731: 5726: 5722: 5715: 5708: 5703: 5701: 5697: 5693: 5689: 5685: 5681: 5677: 5673: 5669: 5664: 5662: 5658: 5654: 5650: 5640: 5632: 5629: 5626: 5623: 5622: 5618: 5615: 5612: 5609: 5608: 5604: 5601: 5598: 5595: 5594: 5590: 5587: 5584: 5581: 5580: 5576: 5573: 5570: 5567: 5566: 5562: 5559: 5556: 5553: 5552: 5549: 5545: 5540: 5533: 5530: 5529: 5525: 5522: 5521: 5517: 5514: 5513: 5510: 5505: 5498: 5495: 5492: 5491: 5487: 5484: 5481: 5480: 5476: 5473: 5470: 5469: 5465: 5462: 5459: 5458: 5454: 5451: 5448: 5447: 5443: 5440: 5437: 5436: 5433: 5428: 5427: 5423: 5421: 5417: 5412: 5410: 5406: 5402: 5398: 5394: 5390: 5386: 5382: 5378: 5370: 5368: 5365: 5363: 5358: 5354: 5350: 5345: 5340: 5332: 5330: 5324: 5317: 5309: 5308: 5304: 5303: 5299: 5298: 5287: 5283: 5269: 5264: 5257: 5256: 5252: 5251: 5248: 5243: 5236: 5235: 5231: 5230: 5226: 5225: 5221: 5220: 5216: 5206: 5205: 5196: 5192: 5184: 5180: 5179: 5178: 5174: 5168: 5164: 5157: 5152: 5149: 5148: 5147: 5145: 5141: 5131: 5123: 5122: 5118: 5117: 5114: 5109: 5108: 5099: 5091: 5088: 5085: 5081: 5080: 5078: 5072: 5068: 5061: 5056: 5053: 5052: 5051: 5049: 5045: 5041: 5036: 5035: 5025: 5017: 5014: 5013: 5009: 5006: 5005: 5002: 4994: 4990: 4982: 4977: 4970: 4967: 4966: 4962: 4959: 4958: 4954: 4951: 4950: 4946: 4943: 4942: 4938: 4935: 4934: 4930: 4927: 4926: 4922: 4919: 4918: 4914: 4911: 4910: 4907: 4903: 4898: 4891: 4888: 4887: 4883: 4880: 4879: 4875: 4872: 4871: 4867: 4864: 4863: 4859: 4856: 4855: 4851: 4848: 4847: 4843: 4840: 4839: 4836: 4831: 4830: 4821: 4813: 4809: 4806: 4803: 4799: 4795: 4794: 4793: 4792: 4791: 4789: 4785: 4778: 4774: 4770: 4767: 4766: 4765: 4763: 4759: 4758: 4754: 4744: 4736: 4733: 4732: 4728: 4725: 4724: 4720: 4717: 4716: 4712: 4709: 4708: 4704: 4701: 4700: 4696: 4693: 4692: 4688: 4685: 4684: 4681: 4676: 4675: 4666: 4662: 4654: 4651: 4647: 4646: 4645: 4644: 4643: 4637: 4633: 4627: 4623: 4616: 4611: 4608: 4607: 4606: 4604: 4600: 4596: 4591: 4587: 4580: 4576: 4571: 4567: 4560: 4555: 4553: 4549: 4545: 4541: 4537: 4532: 4528: 4521: 4512: 4505: 4503: 4499: 4495: 4491: 4487: 4483: 4479: 4475: 4471: 4467: 4463: 4459: 4458: 4455: 4452: 4442: 4434: 4433: 4429: 4428: 4424: 4423: 4420: 4416: 4411: 4404: 4403: 4399: 4398: 4394: 4393: 4390: 4385: 4378: 4375: 4374: 4370: 4367: 4366: 4362: 4359: 4358: 4354: 4351: 4350: 4346: 4343: 4342: 4338: 4335: 4334: 4330: 4327: 4326: 4322: 4319: 4318: 4315: 4310: 4309: 4302: 4300: 4298: 4294: 4290: 4286: 4282: 4278: 4274: 4270: 4262: 4260: 4257: 4250: 4243: 4241: 4238: 4234: 4230: 4226: 4222: 4218: 4217: 4214: 4212: 4207: 4203: 4199: 4195: 4184: 4180: 4176: 4172: 4168: 4164: 4160: 4156: 4152: 4148: 4144: 4143: 4142: 4134: 4130: 4126: 4122: 4118: 4114: 4110: 4106: 4102: 4098: 4094: 4093: 4092: 4084: 4076: 4073: 4070: 4069: 4065: 4062: 4059: 4058: 4054: 4051: 4048: 4047: 4044: 4040: 4035: 4028: 4025: 4024: 4020: 4017: 4016: 4012: 4009: 4008: 4005: 4000: 3993: 3990: 3987: 3986: 3982: 3979: 3976: 3975: 3971: 3968: 3965: 3964: 3960: 3957: 3954: 3953: 3949: 3946: 3943: 3942: 3939: 3934: 3933: 3929: 3927: 3923: 3918: 3916: 3912: 3908: 3904: 3900: 3896: 3892: 3888: 3880: 3878: 3875: 3872: 3859: 3853: 3850: 3847: 3837: 3833: 3829: 3826: 3823: 3818: 3814: 3805: 3802: 3799: 3796: 3788: 3774: 3752: 3748: 3744: 3741: 3738: 3733: 3729: 3719: 3702: 3696: 3693: 3684: 3662: 3659: 3656: 3650: 3647: 3641: 3638: 3635: 3629: 3626: 3623: 3620: 3617: 3614: 3608: 3605: 3602: 3599: 3591: 3583: 3575: 3572: 3569: 3568: 3564: 3561: 3558: 3557: 3553: 3550: 3547: 3546: 3543: 3539: 3534: 3527: 3524: 3523: 3519: 3516: 3515: 3511: 3508: 3507: 3504: 3499: 3492: 3489: 3486: 3485: 3481: 3478: 3475: 3474: 3470: 3467: 3464: 3463: 3459: 3456: 3453: 3452: 3448: 3445: 3442: 3441: 3438: 3433: 3432: 3428: 3426: 3422: 3406: 3386: 3366: 3358: 3342: 3322: 3302: 3299: 3296: 3284: 3282: 3279: 3275: 3270: 3268: 3263: 3261: 3257: 3249: 3245: 3241: 3234: 3230: 3225: 3222: 3221: 3220: 3217: 3215: 3211: 3207: 3203: 3200:that satisfy 3199: 3195: 3191: 3187: 3183: 3175: 3171: 3167: 3163: 3144: 3138: 3132: 3127: 3121: 3115: 3089: 3083: 3077: 3072: 3066: 3060: 3049: 3045: 3034: 3026: 3023: 3020: 3017: 3016: 3012: 3009: 3006: 3003: 3002: 2998: 2995: 2992: 2989: 2988: 2984: 2981: 2978: 2975: 2974: 2970: 2967: 2964: 2961: 2960: 2942: 2939: 2936: 2933: 2930: 2927: 2924: 2921: 2918: 2915: 2912: 2909: 2906: 2903: 2900: 2897: 2894: 2891: 2886: 2883: 2880: 2877: 2874: 2871: 2868: 2865: 2853: 2846: 2843: 2842: 2838: 2835: 2834: 2830: 2827: 2826: 2822: 2819: 2818: 2815: 2810: 2803: 2800: 2799: 2795: 2792: 2791: 2787: 2784: 2783: 2779: 2776: 2775: 2772: 2767: 2766: 2762: 2760: 2756: 2752: 2748: 2744: 2739: 2734: 2730: 2726: 2718: 2715: 2709: 2702: 2700: 2683: 2673: 2669: 2665: 2662: 2659: 2654: 2650: 2646: 2641: 2637: 2633: 2630: 2627: 2622: 2618: 2614: 2609: 2605: 2601: 2598: 2595: 2590: 2586: 2577: 2574: 2567: 2566: 2563: 2556: 2549: 2547: 2527: 2521: 2518: 2515: 2505: 2501: 2497: 2492: 2488: 2483: 2479: 2469: 2465: 2461: 2456: 2452: 2447: 2436: 2432: 2428: 2423: 2419: 2414: 2410: 2404: 2401: 2398: 2388: 2384: 2380: 2375: 2371: 2367: 2364: 2361: 2356: 2352: 2348: 2343: 2339: 2334: 2330: 2327: 2320: 2319: 2316: 2309: 2302: 2300: 2280: 2274: 2264: 2260: 2255: 2249: 2245: 2240: 2236: 2226: 2222: 2217: 2211: 2207: 2202: 2191: 2187: 2182: 2176: 2172: 2167: 2163: 2157: 2147: 2143: 2138: 2132: 2128: 2124: 2121: 2118: 2113: 2109: 2104: 2098: 2094: 2089: 2085: 2082: 2075: 2074: 2071: 2069: 2065: 2061: 2056: 2052: 2045: 2041: 2036: 2032: 2025: 2021: 2016: 2012: 2005: 2001: 1997: 1992: 1988: 1981: 1976: 1974: 1970: 1966: 1962: 1958: 1954: 1951: 1947: 1944: 1940: 1936: 1927: 1920: 1918: 1903: 1896: 1893: 1890: 1868: 1862: 1859: 1856: 1850: 1844: 1841: 1838: 1826: 1823: 1820: 1816: 1812: 1809: 1806: 1803: 1796: 1795: 1792: 1789: 1787: 1783: 1779: 1775: 1771: 1767: 1763: 1759: 1755: 1751: 1747: 1743: 1739: 1733: 1731: 1730:fiber product 1727: 1723: 1719: 1715: 1711: 1706: 1698: 1690: 1687: 1684: 1681: 1680: 1676: 1673: 1670: 1667: 1666: 1662: 1659: 1656: 1653: 1652: 1648: 1645: 1642: 1639: 1638: 1634: 1631: 1628: 1625: 1624: 1621: 1618: ⨝ 1617: 1612: 1605: 1602: 1601: 1597: 1594: 1593: 1589: 1586: 1585: 1581: 1578: 1577: 1574: 1569: 1562: 1559: 1556: 1555: 1551: 1548: 1545: 1544: 1540: 1537: 1534: 1533: 1529: 1526: 1523: 1522: 1518: 1515: 1512: 1511: 1507: 1504: 1501: 1500: 1497: 1492: 1491: 1487: 1485: 1481: 1477: 1473: 1469: 1465: 1461: 1457: 1453: 1449: 1442: 1435: 1427: 1419: 1414: 1410: 1409: 1404: 1399: 1390: 1389: 1383: 1381: 1362: 1358: 1354: 1351: 1348: 1343: 1339: 1310: 1306: 1302: 1299: 1296: 1291: 1287: 1275: 1271: 1252: 1239: 1235: 1231: 1228: 1225: 1220: 1216: 1209: 1205: 1195: 1164: 1154: 1152: 1148: 1144: 1140: 1121: 1113: 1109: 1105: 1101: 1092: 1088: 1084: 1078: 1070: 1068: 1027: 1017: 1007: 1004: 999: 995: 991: 967: 951: 943: 927: 919: 915: 911: 906: 886: 878: 874: 865: 861: 855: 847: 845: 843: 832: 828: 823: 804: 800: 796: 793: 790: 785: 781: 769: 765: 761: 743: 739: 735: 732: 729: 724: 720: 696: 686: 682: 678: 675: 672: 667: 663: 649: 641: 635: 627: 625: 623: 619: 615: 611: 606: 590: 587: 579: 575: 571: 568: 565: 560: 556: 552: 547: 543: 536: 533: 530: 522: 518: 514: 511: 508: 503: 499: 495: 490: 486: 469: 465: 461: 458: 455: 450: 446: 442: 437: 433: 429: 424: 420: 416: 413: 410: 405: 401: 397: 392: 388: 378: 375: 372: 369: 361: 359: 355: 351: 347: 341: 338: + 337: 331: 327: 323: 318: 315: 313: 309: 305: 300: 298: 294: 290: 286: 279:Set operators 278: 276: 274: 273: 268: 267: 262: 258: 257:cross product 254: 253: 248: 247: 242: 241: 235: 218: 215: 212: 209: 196: 193: 189: 185: 182: 179: 176: 171: 168: 164: 160: 155: 152: 148: 138: 135: 126: 124: 120: 112: 110: 107: 105: 101: 97: 93: 89: 85: 82: 77: 75: 71: 67: 63: 58: 56: 55:Edgar F. Codd 52: 48: 44: 40: 33: 19: 11821: 11322: 11316:January 2017 11313: 11298:by removing 11285: 11243: 11237: 11209:. Retrieved 11200: 11189:. Retrieved 11176: 11165:. Retrieved 11161: 11156:C. J. Date. 11151: 11124: 11114: 11095: 11053: 11046: 11026: 11015: 10995: 10988: 10961: 10955: 10942: 10901: 10895: 10871: 10858: 10845: 10832: 10819: 10806: 10583: 10578: 10574: 10570: 10566: 10556: 10545: 10460: 10117: 9880: 9861: 9859: 9586: 9317: 9142:distributive 9139: 8898: 8693: 8332:distributive 8329: 8174: 8170: 8166: 8162: 8158: 8154: 8150: 8146: 8142: 8138: 8134: 8092: 8088: 8084: 8080: 8078: 8033: 8005: 8001: 7995: 7770: 7600: 7587: 7579: 7575:optimization 7568: 7543: 7529: 7493: 7449: 7440: 7425:Please help 7413: 7386: 7381: 7377: 7373: 7369: 7367: 7224: 7220: 7216: 7212: 7208: 7204: 7200: 7196: 7192: 7182: 7161: 7154: 7138: 7123: 7104: 7099: 7094: 7092: 7087: 7083: 7078: 7074: 7070: 7066: 7061: 7057: 7055: 6854: 6850: 6843: 6836: 6830: 6820: 6786: 6775: 6771: 6767: 6763: 6759: 6755: 6750: 6745: 6741: 6740:also take a 6737: 6733: 6732:. Tuples in 6729: 6725: 6721: 6717: 6715: 6707: 6602: 6598: 6563: 6486: 6474: 6470: 6468: 6463: 6459: 6455: 6451: 6447: 6443: 6435: 6431: 6427: 6423: 6421: 6416: 6412: 6410: 6250: 6246: 6242: 6238: 6234: 6230: 6225: 6221: 6214: 6207: 6205: 6200: 6196: 6192: 6188: 6184: 6180: 6176: 6174: 6169: 6165: 6161: 6157: 6155: 6147: 6084: 6080: 6045: 5968: 5956: 5952: 5950: 5945: 5941: 5937: 5933: 5929: 5925: 5921: 5917: 5912: 5909: 5749: 5745: 5741: 5737: 5733: 5729: 5724: 5720: 5713: 5706: 5704: 5699: 5695: 5691: 5687: 5683: 5679: 5675: 5671: 5667: 5665: 5660: 5656: 5652: 5648: 5646: 5638: 5547: 5543: 5508: 5431: 5419: 5415: 5413: 5408: 5404: 5400: 5396: 5388: 5384: 5380: 5376: 5374: 5366: 5352: 5348: 5346: 5342: 5328: 5315: 5285: 5281: 5267: 5246: 5214: 5194: 5190: 5182: 5176: 5172: 5166: 5162: 5155: 5150: 5143: 5139: 5137: 5129: 5112: 5097: 5089: 5083: 5082:EG: Project 5076: 5070: 5066: 5059: 5054: 5047: 5043: 5039: 5037: 5033: 5031: 5023: 5000: 4992: 4988: 4980: 4905: 4901: 4834: 4819: 4816:Student,Task 4811: 4807: 4801: 4797: 4787: 4783: 4781: 4776: 4772: 4768: 4760: 4756: 4752: 4750: 4742: 4679: 4664: 4660: 4652: 4640: 4635: 4631: 4625: 4621: 4614: 4609: 4602: 4598: 4594: 4589: 4585: 4578: 4574: 4569: 4565: 4558: 4556: 4551: 4547: 4543: 4539: 4535: 4530: 4526: 4519: 4517: 4506: 4497: 4493: 4489: 4485: 4481: 4477: 4473: 4469: 4465: 4461: 4450: 4448: 4440: 4418: 4414: 4388: 4313: 4296: 4292: 4288: 4284: 4280: 4276: 4272: 4268: 4266: 4258: 4255: 4244: 4236: 4232: 4228: 4224: 4220: 4208: 4201: 4197: 4193: 4190: 4182: 4178: 4174: 4170: 4166: 4162: 4158: 4154: 4150: 4146: 4140: 4132: 4128: 4124: 4120: 4116: 4112: 4108: 4104: 4100: 4096: 4090: 4082: 4042: 4038: 4003: 3937: 3925: 3921: 3919: 3914: 3910: 3906: 3898: 3894: 3890: 3886: 3884: 3876: 3873: 3789: 3720: 3685: 3592: 3589: 3581: 3541: 3537: 3502: 3436: 3424: 3420: 3288: 3277: 3273: 3271: 3266: 3264: 3259: 3255: 3253: 3247: 3243: 3236: 3232: 3228: 3223: 3218: 3213: 3209: 3205: 3201: 3197: 3193: 3189: 3185: 3181: 3172:is a binary 3169: 3165: 3161: 3047: 3043: 3040: 3032: 2813: 2770: 2758: 2754: 2750: 2746: 2742: 2737: 2732: 2728: 2724: 2722: 2716: 2703: 2561: 2550: 2314: 2303: 2067: 2063: 2059: 2054: 2050: 2043: 2039: 2034: 2030: 2023: 2019: 2014: 2010: 2003: 1999: 1995: 1990: 1986: 1979: 1977: 1972: 1968: 1964: 1960: 1956: 1952: 1945: 1934: 1932: 1921: 1790: 1785: 1781: 1777: 1773: 1769: 1765: 1761: 1757: 1753: 1749: 1745: 1734: 1721: 1717: 1713: 1707: 1704: 1696: 1619: 1615: 1572: 1495: 1483: 1479: 1475: 1471: 1463: 1459: 1455: 1451: 1445: 1428:Natural join 1418:(March 2023) 1417: 1406: 1273: 1269: 1196: 1155: 1146: 1142: 1138: 1086: 1082: 1080: 1008: 1002: 997: 904: 859: 857: 824: 767: 639: 637: 621: 617: 613: 609: 607: 362: 357: 353: 349: 345: 339: 335: 329: 325: 319: 316: 307: 301: 282: 270: 264: 260: 256: 250: 244: 238: 236: 127: 116: 113:Introduction 108: 86: 78: 59: 42: 36: 11880:WikiProject 11771:Replication 11659:Transaction 11601:Foreign key 11581:CAP theorem 11528:Multi-model 11127:: 110–119. 10563:Hugh Darwen 7777:disjunction 7773:conjunction 7607:commutative 7558:leaves are 7539:query plans 7490:query plans 7175:) instead. 7158:Branch_Name 7120:Branch_Name 7056:where each 6827:Aggregation 6806:total_price 6770:) ∪ ( 5333:Outer joins 3994:Production 3576:Production 3493:Production 3176:in the set 1742:foreign key 1738:idempotence 1178:addressBook 1093:written as 1043:addressBook 866:written as 650:written as 11895:Categories 11745:Query plan 11698:Components 11616:Unique key 11533:comparison 11467:comparison 11457:Relational 11450:comparison 11246:: 80–102. 11211:2024-07-04 11191:2024-07-04 11167:2020-12-27 10948:Codd, E.F. 10920:1080554130 10887:References 10575:Tutorial D 10571:Tutorial D 10567:Tutorial D 10559:Chris Date 8890:Projection 7603:idempotent 6794:unit_price 6699:Production 6586:Production 6554:Executive 6413:outer join 6233:and let {( 6201:Production 6185:Production 6139:Production 6068:Production 6036:Executive 5732:and let {( 5531:Production 5499:Executive 5337:See also: 5284:) − 5193:) − 5185: := π 5175:) − 5153: := π 5092: := π 5057: := π 5018:Database2 4971:Database2 4963:Database1 4955:Compiler1 4947:Database1 4939:Compiler1 4931:Database2 4923:Database1 4892:Database2 4884:Database1 4876:Database2 4868:Database1 4860:Database2 4852:Database1 4737:Database2 4729:Database1 4721:Database2 4713:Database1 4705:Database2 4697:Database1 4655: := π 4612: := π 4405:Database2 4400:Database1 4379:Database2 4371:Database1 4363:Compiler1 4355:Database1 4347:Compiler1 4339:Database2 4331:Database1 4211:complement 4026:Production 3525:Production 3276:, and the 3274:inner join 2971:BoatPrice 2823:BoatPrice 2761:) itself. 1603:Production 1000:for which 640:projection 628:Projection 297:set theory 269:, and the 261:cross join 246:projection 104:difference 11754:Functions 11689:Partition 11516:In-memory 11474:Key–value 11300:excessive 10980:207549016 10928:cite book 10656:∖ 10647:∪ 10638:∖ 10623:∖ 10614:∪ 10594:relations 10520:∪ 10511:× 10496:× 10487:∪ 10478:× 10418:ρ 10414:∩ 10388:ρ 10375:∩ 10352:ρ 10307:ρ 10303:∪ 10277:ρ 10264:∪ 10241:ρ 10196:ρ 10192:∖ 10166:ρ 10153:∖ 10130:ρ 10070:ρ 10049:ρ 10016:ρ 9995:ρ 9948:ρ 9915:ρ 9894:ρ 9841:∅ 9829:⟩ 9800:⟨ 9785:π 9781:∖ 9772:⟩ 9748:⟨ 9733:π 9706:⟩ 9694:⟨ 9679:⟩ 9650:⟨ 9644:∖ 9638:⟩ 9614:⟨ 9599:π 9569:⟩ 9557:⟨ 9542:⟩ 9513:⟨ 9498:π 9494:∩ 9485:⟩ 9461:⟨ 9446:π 9422:∅ 9410:⟩ 9381:⟨ 9375:∩ 9369:⟩ 9345:⟨ 9330:π 9275:… 9258:π 9254:∪ 9227:… 9210:π 9197:∪ 9173:… 9156:π 9104:… 9085:⊆ 9066:… 9018:… 9001:π 8967:… 8950:π 8928:… 8911:π 8858:… 8839:⊆ 8801:… 8784:π 8771:σ 8746:σ 8724:… 8707:π 8659:σ 8655:∩ 8643:∩ 8625:σ 8603:σ 8599:∩ 8581:σ 8568:∩ 8553:σ 8516:σ 8512:∪ 8494:σ 8481:∪ 8466:σ 8441:∖ 8423:σ 8401:σ 8397:∖ 8379:σ 8366:∖ 8351:σ 8292:σ 8288:× 8270:σ 8257:σ 8244:× 8230:∧ 8224:∧ 8217:σ 8204:× 8189:σ 8118:∧ 8112:∧ 8058:× 8043:σ 7998:relations 7961:σ 7957:∪ 7939:σ 7918:∨ 7911:σ 7871:σ 7858:σ 7833:σ 7820:σ 7799:∧ 7792:σ 7734:σ 7724:σ 7702:σ 7692:σ 7653:σ 7643:σ 7621:σ 7591:relations 7584:Selection 7560:relations 7443:June 2013 7414:does not 7376:) taking 7338:∈ 7320:⇒ 7307:∈ 7289:∧ 7276:∈ 7250:∀ 7244:∀ 7238:∀ 7185:relations 6991:… 6895:… 6685:Executive 6499:DeptName 6440:relations 6379:⋈ 6355:… 6325:π 6321:− 6312:× 6303:ω 6297:… 6291:ω 6279:∪ 6270:⋈ 5981:DeptName 5915:relations 5881:ω 5875:… 5869:ω 5860:× 5848:⋈ 5824:… 5794:π 5790:− 5778:∪ 5769:⋈ 5700:Executive 5680:Executive 5630:Executive 5444:DeptName 5393:relations 4906:Completed 4814:− π 4810: := 4771: := 4451:DBProject 4419:DBProject 4415:Completed 4389:DBProject 4314:Completed 4055:DeptName 3950:DeptName 3913:tuple in 3903:relations 3851:⋈ 3827:… 3810:Π 3800:⋉ 3742:… 3697:⁡ 3660:∪ 3651:⁡ 3639:∈ 3633:∃ 3630:∧ 3624:∈ 3603:⋉ 3554:DeptName 3449:DeptName 3357:relations 3300:⋉ 3139:θ 3122:⋈ 3084:θ 3067:⋈ 2968:BoatModel 2916:≥ 2875:⋈ 2820:BoatModel 2780:CarPrice 2747:BoatPrice 2663:… 2631:… 2599:… 2582:Π 2528:… 2519:× 2484:σ 2480:… 2448:σ 2415:σ 2402:× 2365:… 2335:σ 2281:… 2241:ρ 2237:… 2203:ρ 2168:ρ 2122:… 2090:ρ 1939:predicate 1894:∪ 1869:∧ 1860:∈ 1851:∧ 1842:∈ 1824:∪ 1807:⋈ 1508:DeptName 1468:relations 1441:The Armed 1352:… 1300:… 1229:… 1206:ρ 1165:ρ 1102:ρ 1067:is true. 1028:∨ 1018:σ 976:¬ 952:∨ 928:∧ 879:φ 875:σ 848:Selection 794:… 733:… 676:… 659:Π 588:∈ 569:… 531:∈ 512:… 459:… 414:… 373:× 304:relations 285:set union 266:set union 240:selection 213:∈ 119:E.F. Codd 81:operators 74:relations 51:semantics 11860:Category 11776:Sharding 11632:Relation 11606:Superkey 11561:Database 11554:Concepts 11094:(2009). 11024:(2001). 10726:Relation 10696:Database 10678:See also 10598:multiset 10557:In 1998 9825:′ 9675:′ 9538:′ 9406:′ 8337:relation 7551:, where 7492:for the 7023:′ 6981:′ 6945:′ 6800:quantity 6702:Charles 6674:Harriet 6646:Harriet 6618:Manager 6615:DeptName 6599:Employee 6589:Charles 6581:Harriet 6573:Manager 6570:DeptName 6532:Finance 6510:Finance 6487:Employee 6471:Employee 6197:DeptName 6181:DeptName 6177:Employee 6142:Charles 6128:Harriet 6114:Harriet 6100:Manager 6097:DeptName 6081:Employee 6071:Charles 6063:Harriet 6055:Manager 6052:DeptName 6014:Finance 5992:Finance 5969:Employee 5953:Employee 5692:DeptName 5688:Employee 5672:DeptName 5619:Harriet 5591:Harriet 5563:Manager 5560:DeptName 5544:Employee 5534:Charles 5526:Harriet 5518:Manager 5515:DeptName 5477:Finance 5455:Finance 5432:Employee 5416:Employee 5300:Student 5253:Student 5222:Student 5119:Student 4991:− 4775:− 4762:relation 4472: : 4454:follows: 4425:Student 4263:Division 4200:∪ 4181:∪ 4157: : 4131:∪ 4107: : 4077:Finance 4066:Finance 4039:Employee 4029:Harriet 4013:Manager 4010:DeptName 3983:Finance 3961:Finance 3938:Employee 3922:Employee 3881:Antijoin 3538:Employee 3528:Harriet 3512:Manager 3509:DeptName 3482:Finance 3460:Finance 3437:Employee 3421:Employee 3285:Semijoin 3260:equijoin 2965:CarPrice 2962:CarModel 2777:CarModel 2743:CarPrice 2735:-join (⋈ 1943:relation 1786:equijoin 1778:Employee 1762:Employee 1758:DeptName 1750:DeptName 1746:Employee 1722:DeptName 1714:Employee 1691:Harriet 1663:Harriet 1635:Manager 1632:DeptName 1616:Employee 1606:Charles 1598:Harriet 1582:Manager 1579:DeptName 1541:Finance 1519:Finance 1496:Employee 1480:Employee 1458:) where 1151:relation 1061:isFriend 990:negation 840:DISTINCT 831:multiset 11870:Outline 11669:Trigger 11625:Objects 11294:Please 11286:use of 11143:3242505 10877:Unicode 10864:Unicode 10851:Unicode 10838:Unicode 10825:Unicode 10812:Unicode 10786:Datalog 7545:Queries 7435:removed 7420:sources 7173:Account 7167:Balance 7150:Account 7144:Balance 7135:Account 7129:Balance 7115:Balance 7107:Account 7065:', 1 ≤ 6744:value, 6728:value, 6724:take a 6665:Harriet 6657:Finance 6629:Finance 6537:Harriet 6415:(⟗) or 6237:, ..., 6220:, ..., 6179:with a 6168:value, 6164:take a 6119:Harriet 6019:Harriet 5736:, ..., 5719:, ..., 5696:Finance 5690:have a 5676:Finance 5670:with a 5659:value, 5655:take a 5610:Harriet 5602:Finance 5574:Finance 5482:Harriet 5351:value, 5278:Student 5258:Eugene 5232:Eugene 5211:Student 5187:Student 5124:Eugene 5094:Student 5007:Student 4912:Student 4904:a.k.a. 4841:Student 4686:Student 4657:Student 4518:where { 4320:Student 4303:Example 3988:Harriet 3787:, then 3570:Harriet 3487:Harriet 3027:40,000 3013:10,000 2999:10,000 2985:10,000 2847:60,000 2839:40,000 2831:10,000 2804:50,000 2796:30,000 2788:20,000 2062:nor in 1774:Manager 1682:Harriet 1677:George 1674:Finance 1649:George 1646:Finance 1590:George 1587:Finance 1546:Harriet 1413:Discuss 1089:) is a 1006:holds. 842:keyword 646:) is a 263:), the 11684:Cursor 11642:column 11511:NewSQL 11141: 11102: 11061: 11034: 11003: 10978: 10918: 10908: 10590:tables 9872:Rename 9860:where 8149:, and 7082:, 1 ≤ 7032: 6911: 6849:, ... 6817:EXTEND 6791:SELECT 6708: 6651:George 6543:Sales 6526:George 6521:Sales 6430:where 6243:unique 6148: 6025:Sales 6008:George 6003:Sales 5742:unique 5639: 5596:George 5488:Sales 5471:George 5466:Sales 5383:where 5316: 5310:Sarah 5237:Sarah 5130: 5024: 5015:Eugene 4952:Eugene 4944:Eugene 4873:Eugene 4865:Eugene 4743: 4718:Eugene 4710:Eugene 4441: 4435:Sarah 4360:Eugene 4352:Eugene 4191:where 4083: 4071:George 4021:Sally 3977:George 3972:Sales 3893:where 3686:where 3582: 3565:Sales 3520:Sally 3476:George 3471:Sales 3315:where 3160:where 3142: 3136: 3125: 3119: 3087: 3081: 3070: 3064: 3033: 3021:50,000 3007:50,000 2993:30,000 2979:20,000 1935:Fun(t) 1933:where 1872: 1866: 1854: 1848: 1836: 1830: 1724:. In 1697: 1668:George 1552:Sales 1535:George 1530:Sales 1083:rename 1071:Rename 994:tuples 968:) and 902:where 835:Π 764:tuples 712:where 644:Π 291:, and 249:, the 243:, the 92:tuples 11674:Index 11637:table 11540:Cloud 11506:NoSQL 11501:Graph 11438:Types 11186:(PDF) 11139:S2CID 10976:S2CID 10798:Notes 8000:have 6671:Sales 6643:Sales 6637:Sally 6623:Harry 6612:EmpId 6578:Sales 6515:Sally 6504:Harry 6496:EmpId 6125:Sales 6111:Sales 6105:Sally 6094:EmpId 6060:Sales 5997:Sally 5986:Harry 5978:EmpId 5616:Sales 5588:Sales 5582:Sally 5568:Harry 5557:EmpId 5523:Sales 5460:Sally 5449:Harry 5441:EmpId 5305:Fred 5227:Fred 5161:,..., 5065:,..., 5010:Task 4968:Sarah 4960:Sarah 4915:Task 4889:Sarah 4881:Sarah 4844:Task 4755:from 4734:Sarah 4726:Sarah 4689:Task 4620:,..., 4584:,..., 4564:,..., 4525:,..., 4430:Fred 4395:Task 4376:Sarah 4368:Sarah 4323:Task 4060:Harry 4052:EmpId 4018:Sales 3966:Sally 3955:Harry 3947:EmpId 3559:Sally 3551:EmpId 3517:Sales 3465:Sally 3454:Harry 3446:EmpId 3024:Boat2 3010:Boat1 2996:Boat1 2982:Boat1 2844:Boat3 2836:Boat2 2828:Boat1 2759:Price 2755:Price 2751:Price 2049:,..., 2029:,..., 2009:,..., 1985:,..., 1937:is a 1688:Sales 1660:Sales 1654:Sally 1640:Harry 1629:EmpId 1595:Sales 1524:Sally 1513:Harry 1505:EmpId 1403:split 914:atoms 908:is a 620:| × | 616:| = | 295:from 100:union 11725:ODBC 11715:JDBC 11654:View 11591:Null 11586:CRUD 11566:ACID 11521:list 11484:list 11462:list 11100:ISBN 11059:ISBN 11032:ISBN 11001:ISBN 10934:link 10916:OCLC 10906:ISBN 10577:and 10561:and 10548:ISBL 9587:and 8161:and 8133:and 8091:and 8004:and 7549:tree 7517:and 7505:and 7418:any 7416:cite 7165:Max( 7142:Max( 7127:Max( 7113:and 6809:FROM 6742:null 6726:null 6682:1123 6668:2202 6654:3401 6640:2241 6626:3415 6609:Name 6603:Dept 6564:Dept 6551:1123 6540:2202 6529:3401 6518:2241 6507:3415 6493:Name 6475:Dept 6473:and 6446:and 6438:are 6434:and 6411:The 6206:Let 6195:had 6193:Dept 6166:null 6122:2202 6108:2241 6091:Name 6085:Dept 6046:Dept 6033:1123 6022:2202 6011:3401 6000:2241 5989:3415 5975:Name 5957:Dept 5955:and 5936:and 5920:and 5705:Let 5668:Dept 5657:null 5627:1123 5613:2202 5599:3401 5585:2241 5571:3415 5554:Name 5548:Dept 5509:Dept 5496:1123 5485:2202 5474:3401 5463:2241 5452:3415 5438:Name 5420:Dept 5418:and 5399:and 5391:are 5387:and 5357:NULL 5349:null 5292:aka 5272:aka 5181:EG: 4997:aka 4985:aka 4936:Fred 4928:Fred 4920:Fred 4857:Fred 4849:Fred 4800:and 4702:Fred 4694:Fred 4663:) × 4634:) × 4577:and 4538:and 4500:) } 4496:) ∈ 4468:= { 4344:Fred 4336:Fred 4328:Fred 4153:= { 4103:= { 4074:3401 4063:3415 4049:Name 4043:Dept 4004:Dept 3991:2202 3980:3401 3969:2241 3958:3415 3944:Name 3926:Dept 3924:and 3901:are 3897:and 3573:2202 3562:2241 3548:Name 3542:Dept 3503:Dept 3490:2202 3479:3401 3468:2241 3457:3415 3443:Name 3425:Dept 3423:and 3355:are 3335:and 3212:and 3196:and 3188:and 3164:and 3018:CarC 3004:CarC 2990:CarB 2976:CarA 2814:Boat 2801:CarC 2793:CarB 2785:CarA 2729:Boat 2727:and 2022:and 1998:and 1971:and 1963:and 1782:Name 1770:Dept 1766:Dept 1764:and 1754:Dept 1718:Dept 1716:and 1685:2202 1671:3401 1657:2241 1643:3415 1626:Name 1620:Dept 1573:Dept 1560:1257 1557:Mary 1549:2202 1538:3401 1527:2241 1516:3415 1502:Name 1484:Dept 1482:and 1474:and 1466:are 1462:and 216:1... 11720:XQJ 11647:row 11302:or 11248:doi 11129:doi 10966:doi 10875:In 10862:In 10849:In 10836:In 10823:In 10810:In 10781:SQL 10586:SQL 8173:or 7429:by 7211:of 7152:). 6762:= ( 6679:Tim 6601:⟗ 6548:Tim 6199:of 6183:of 6083:⟖ 6030:Tim 5698:or 5694:of 5678:or 5674:of 5624:Tim 5546:⟕ 5493:Tim 4782:In 4649:on. 4488:( ( 4480:∧ ∀ 4449:If 4194:Fun 4175:Fun 4169:of 4141:or 4125:Fun 3694:Fun 3648:Fun 3180:}, 3105:or 2771:Car 2725:Car 1950:iff 1776:to 1752:to 1411:. ( 996:in 944:), 942:and 827:SQL 766:in 760:set 624:|. 322:set 259:or 121:'s 70:SQL 37:In 11897:: 11262:). 11244:28 11242:. 11236:. 11160:. 11137:. 11123:. 11090:; 11086:; 11073:^ 10974:. 10962:13 10960:. 10954:. 10930:}} 10926:{{ 10914:. 10581:. 9868:. 9866:b' 8169:, 8141:, 8087:, 7384:. 7090:. 7086:≤ 7069:≤ 6842:, 6823:. 6803:AS 6774:⟖ 6766:⟕ 6758:⟗ 6748:. 6688:ω 6660:ω 6632:ω 6426:⟗ 6213:, 6203:. 6187:, 6172:. 5948:. 5928:⟖ 5712:, 5702:. 5682:, 5663:. 5633:ω 5605:ω 5577:ω 5411:. 5379:⟕ 5276:(π 5217:) 5146:: 5079:) 5050:: 4764:: 4605:: 4492:∪ 4484:∈ 4476:∈ 4464:÷ 4417:÷ 4299:. 4271:÷ 4235:⋉ 4227:= 4223:▷ 4161:∈ 4149:▷ 4135:)) 4119:∈ 4111:∈ 4099:▷ 4041:▷ 3911:no 3889:▷ 3540:⋉ 3278:on 3262:. 3246:× 3235:= 2745:≥ 2002:, 1788:. 1732:. 1454:⨝ 1415:) 1380:. 1081:A 966:or 858:A 844:. 822:. 638:A 612:× 379::= 356:× 287:, 275:. 57:. 41:, 11423:e 11416:t 11409:v 11329:) 11323:( 11318:) 11314:( 11310:. 11292:. 11256:. 11250:: 11214:. 11194:. 11170:. 11145:. 11131:: 11108:. 11067:. 11040:. 11009:. 10982:. 10968:: 10936:) 10922:. 10662:) 10659:T 10653:S 10650:( 10644:) 10641:T 10635:R 10632:( 10629:= 10626:T 10620:) 10617:S 10611:R 10608:( 10526:) 10523:C 10517:B 10514:( 10508:A 10505:= 10502:) 10499:C 10493:A 10490:( 10484:) 10481:B 10475:A 10472:( 10441:) 10438:P 10435:( 10430:b 10426:/ 10422:a 10411:) 10408:R 10405:( 10400:b 10396:/ 10392:a 10384:= 10381:) 10378:P 10372:R 10369:( 10364:b 10360:/ 10356:a 10330:) 10327:P 10324:( 10319:b 10315:/ 10311:a 10300:) 10297:R 10294:( 10289:b 10285:/ 10281:a 10273:= 10270:) 10267:P 10261:R 10258:( 10253:b 10249:/ 10245:a 10219:) 10216:P 10213:( 10208:b 10204:/ 10200:a 10189:) 10186:R 10183:( 10178:b 10174:/ 10170:a 10162:= 10159:) 10156:P 10150:R 10147:( 10142:b 10138:/ 10134:a 10096:) 10093:) 10090:R 10087:( 10082:b 10078:/ 10074:a 10066:( 10061:d 10057:/ 10053:c 10045:= 10042:) 10039:) 10036:R 10033:( 10028:d 10024:/ 10020:c 10012:( 10007:b 10003:/ 9999:a 9971:) 9968:R 9965:( 9960:c 9956:/ 9952:a 9944:= 9941:) 9938:) 9935:R 9932:( 9927:c 9923:/ 9919:b 9911:( 9906:b 9902:/ 9898:a 9862:b 9845:, 9838:= 9835:) 9832:} 9822:b 9818:= 9815:B 9812:, 9809:a 9806:= 9803:A 9797:{ 9794:( 9789:A 9778:) 9775:} 9769:b 9766:= 9763:B 9760:, 9757:a 9754:= 9751:A 9745:{ 9742:( 9737:A 9709:} 9703:a 9700:= 9697:A 9691:{ 9688:= 9685:) 9682:} 9672:b 9668:= 9665:B 9662:, 9659:a 9656:= 9653:A 9647:{ 9641:} 9635:b 9632:= 9629:B 9626:, 9623:a 9620:= 9617:A 9611:{ 9608:( 9603:A 9572:} 9566:a 9563:= 9560:A 9554:{ 9551:= 9548:) 9545:} 9535:b 9531:= 9528:B 9525:, 9522:a 9519:= 9516:A 9510:{ 9507:( 9502:A 9491:) 9488:} 9482:b 9479:= 9476:B 9473:, 9470:a 9467:= 9464:A 9458:{ 9455:( 9450:A 9419:= 9416:) 9413:} 9403:b 9399:= 9396:B 9393:, 9390:a 9387:= 9384:A 9378:{ 9372:} 9366:b 9363:= 9360:B 9357:, 9354:a 9351:= 9348:A 9342:{ 9339:( 9334:A 9302:. 9299:) 9296:P 9293:( 9286:n 9282:a 9278:, 9272:, 9267:1 9263:a 9251:) 9248:R 9245:( 9238:n 9234:a 9230:, 9224:, 9219:1 9215:a 9206:= 9203:) 9200:P 9194:R 9191:( 9184:n 9180:a 9176:, 9170:, 9165:1 9161:a 9120:} 9115:m 9111:b 9107:, 9101:, 9096:1 9092:b 9088:{ 9082:} 9077:n 9073:a 9069:, 9063:, 9058:1 9054:a 9050:{ 9042:) 9039:R 9036:( 9029:n 9025:a 9021:, 9015:, 9010:1 9006:a 8997:= 8994:) 8991:) 8988:R 8985:( 8978:m 8974:b 8970:, 8964:, 8959:1 8955:b 8946:( 8939:n 8935:a 8931:, 8925:, 8920:1 8916:a 8874:} 8869:n 8865:a 8861:, 8855:, 8850:1 8846:a 8842:{ 8836:A 8828:) 8825:) 8822:R 8819:( 8812:n 8808:a 8804:, 8798:, 8793:1 8789:a 8780:( 8775:A 8767:= 8764:) 8761:) 8758:R 8755:( 8750:A 8742:( 8735:n 8731:a 8727:, 8721:, 8716:1 8712:a 8674:) 8671:P 8668:( 8663:A 8652:R 8649:= 8646:P 8640:) 8637:R 8634:( 8629:A 8621:= 8618:) 8615:P 8612:( 8607:A 8596:) 8593:R 8590:( 8585:A 8577:= 8574:) 8571:P 8565:R 8562:( 8557:A 8531:) 8528:P 8525:( 8520:A 8509:) 8506:R 8503:( 8498:A 8490:= 8487:) 8484:P 8478:R 8475:( 8470:A 8444:P 8438:) 8435:R 8432:( 8427:A 8419:= 8416:) 8413:P 8410:( 8405:A 8394:) 8391:R 8388:( 8383:A 8375:= 8372:) 8369:P 8363:R 8360:( 8355:A 8310:) 8307:) 8304:P 8301:( 8296:C 8285:) 8282:R 8279:( 8274:B 8266:( 8261:D 8253:= 8250:) 8247:P 8241:R 8238:( 8233:D 8227:C 8221:B 8213:= 8210:) 8207:P 8201:R 8198:( 8193:A 8175:D 8171:C 8167:B 8163:P 8159:R 8155:A 8151:D 8147:P 8143:C 8139:R 8135:B 8121:D 8115:C 8109:B 8106:= 8103:A 8093:D 8089:C 8085:B 8081:A 8064:) 8061:P 8055:R 8052:( 8047:A 8019:M 8016:N 8006:M 8002:N 7976:) 7973:R 7970:( 7965:B 7954:) 7951:R 7948:( 7943:A 7935:= 7932:) 7929:R 7926:( 7921:B 7915:A 7889:) 7886:) 7883:R 7880:( 7875:A 7867:( 7862:B 7854:= 7851:) 7848:) 7845:R 7842:( 7837:B 7829:( 7824:A 7816:= 7813:) 7810:R 7807:( 7802:B 7796:A 7749:) 7746:R 7743:( 7738:A 7728:B 7720:= 7717:) 7714:R 7711:( 7706:B 7696:A 7668:) 7665:R 7662:( 7657:A 7647:A 7639:= 7636:) 7633:R 7630:( 7625:A 7562:, 7523:T 7519:S 7515:R 7511:R 7507:T 7503:S 7456:) 7450:( 7445:) 7441:( 7437:. 7423:. 7382:R 7378:R 7374:R 7372:( 7370:E 7352:) 7346:+ 7342:R 7335:) 7332:z 7329:, 7326:x 7323:( 7315:+ 7311:R 7304:) 7301:z 7298:, 7295:y 7292:( 7284:+ 7280:R 7273:) 7270:y 7267:, 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