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The relational data model is based on a collection of tables The user of the database system may query these tables, insert new tuples, delete tuples, and update (modify) tuples There are several languages for expressing these operations The relational algebra de nes a set of algebraic operations that operate on tables, and output tables as their results These operations can be combined to get expressions that express desired queries The algebra de nes the basic operations used within relational query languages The operations in relational algebra can be divided into Basic operations Additional operations that can be expressed in terms of the basic operations Extended operations, some of which add further expressive power to relational algebra Databases can be modi ed by insertion, deletion, or update of tuples We used the relational algebra with the assignment operator to express these modi cations Different users of a shared database may bene t from individualized views of the database Views are virtual relations de ned by a query expression We evaluate queries involving views by replacing the view with the expression that de nes the view Views are useful mechanisms for simplifying database queries, but modi cation of the database through views may cause problems Therefore, database systems severely restrict updates through views For reasons of query-processing ef ciency, a view may be materialized that is, the query is evaluated and the result stored physically When database relations are updated, the materialized view must be correspondingly updated The tuple relational calculus and the domain relational calculus are nonprocedural languages that represent the basic power required in a relational query language The basic relational algebra is a procedural language that is equivalent in power to both forms of the relational calculus when they are restricted to safe expressions The relational algebra and the relational calculi are terse, formal languages that are inappropriate for casual users of a database system Commercial database systems, therefore, use languages with more syntactic sugar In Chap-.

The McGraw Hill Companies, 2001

ters 4 and 5, we shall consider the three most in uential languages: SQL, which is based on relational algebra, and QBE and Datalog, which are based on domain relational calculus

h 1 075 05 025

Table Relation Tuple variable Atomic domain Null value Database schema Database instance Relation schema Relation instance Keys Foreign key Referencing relation Referenced relation Schema diagram Query language Procedural language Nonprocedural language Relational algebra Relational algebra operations Select Project Union Set difference Cartesian product Rename Additional operations Set-intersection Natural-join 1 Division / Assignment operation Extended relational-algebra operations Generalized projection Outer join Left outer join 1 Right outer join 1 Full outer join 1 Aggregation G Multisets Grouping Null values Modi cation of the database Deletion Insertion Updating Views View de nition Materialized views View update View expansion Recursive views Tuple relational calculus Domain relational calculus

Contents of menu template drawer FIGURE 11-2

31 Design a relational database for a university registrar s of ce The of ce maintains data about each class, including the instructor, the number of students enrolled, and the time and place of the class meetings For each student class pair, a grade is recorded

The McGraw Hill Companies, 2001

3

What is the power delivered by the voltage source The current owing through the circuit can be found using Ohm s law I = The power is P = VI = (8 V)(1 A) = 8 W Many times in a circuit diagram you will see a ground or reference node All voltages in a circuit are taken to be positive with respect to this node, which is usually placed at the bottom of the circuit diagram The symbol used for a ground node is shown in Fig 2-11 Now consider a set of resistors in parallel, as shown in Fig 2-12 Using KVL, it is easy to convince yourself that the same voltage V is found across each resistor What is the value of that voltage The sum of the currents leaving the rst node in Fig 2-12 must be equal to the current source Is = I1 + I2 + I3 = 1 1 1 V+ V+ V = R1 R2 R3 1 1 1 + + R1 R2 R3 V 3V =1A 3