# Relation - The Stanford University InfoLab

25 Pages · 2001 · 119 KB · English

\Core&quot; Relational Algebra A small set of set-based op erators that allo wus to manipulate relations in limited but useful w a ys. The op erators are:

\Core" Relational Algebra A small set of set-based op erators that allowusto manipulate relations in limited but useful ways. The op erators are: 1.Union, intersection, and di erence:the usual set op erators. F But the relation schemas must b e the same. 2.Selection:Picking certain rows from a relation. 3.Projection:Picking certain columns. 4.Products and joins:Comp osing relations in useful ways. 5.Renamingof relations and their attributes.1 SelectionR1 =C (R2 ) whereCis a condition involving the attributes of relationR2 . Example RelationSells: bar b eer price Jo e's Bud 2.50 Jo e's Miller 2.75 Sue's Bud 2.50 Sue's Co ors 3.00 JoeMenu =bar=Joe 0s (Sells) bar b eer price Jo e's Bud 2.50 Jo e's Miller 2.75 2 Pro jectionR1 =L (R2 ) whereLis a list of attributes from the schema of R2 . Example beer;pr ice (Sells)b eer price Bud 2.50 Miller 2.75 Co ors 3.00 Notice elimination of duplicate tuples.3 Pro ductR=R1 R2 pairs each tuplet1 ofR1 with each tuplet2 ofR2 and puts inRa tuplet1 t2 . Theta-JoinR=R1 ./ C R2 is equivalenttoR=C (R1 R2 ). 4 Example Sells=bar b eer price Jo e's Bud 2.50 Jo e's Miller 2.75 Sue's Bud 2.50 Sue's Co ors 3.00 Bars=name addr Jo e's Maple St. Sue's River Rd. BarInfo = Sells ./ S ells:bar=B ar s:name Bars bar b eer price name addr Jo e's Bud 2.50 Jo e's Maple St. Jo e's Miller 2.75 Jo e's Maple St. Sue's Bud 2.50 Sue's River Rd. Sue's Co ors 3.00 Sue's River Rd. 5 Natural JoinR=R1 ./R2 calls for the theta-join ofR1 andR2 with the condition that all attributes of the same name b e equated.Then, one column for each pair of equated attributes is pro jected out. Example Supp ose the attributenamein relationBarswas changed tobar, to match the bar name inSells. BarInfo = Sells./Bars bar b eer price addr Jo e's Bud 2.50 Maple St. Jo e's Miller 2.75 Maple St. Sue's Bud 2.50 River Rd. Sue's Co ors 3.00 River Rd. 6 Renaming S(A1 ;::: ;An ) (R) pro duces a relation identical toR but namedSand with attributes, in order, named A1 ;:: ;An . Example Bars=name addr Jo e's Maple St. Sue's River Rd. R(bar;addr) (Bars)= bar addr Jo e's Maple St. Sue's River Rd. The name of the ab ove relation isR. 7 Combining Op erations Algebra = 1.Basis arguments + 2.Ways of constructing expressions. For relational algebra: 1.Arguments = variables standing for relations + nite, constant relations. 2.Expressions constructed by applying one of the op erators + parentheses. Query = expression of relational algebra.8 Op erator Precedence

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