关系代数叉积和自然连接
Relational Algebra Cross Product and Natural Join
我对何时使用这两个运算符有点困惑。我觉得我理解它们，但我很难弄清楚什么时候在关系代数语句中需要它们。有人可以给我一些 insight/advice 吗？
某些版本的关系代数具有关系标题，这些关系标题是（无序、唯一命名的）属性集。 Then (relational (Cartesian)) PRODUCT, aka CROSS JOIN, aka CROSS PRODUCT, 仅在输入关系不共享属性名称时才定义，但在其他方面类似于 NATURAL JOIN。所以它的作用是确认你期望没有共享属性名。
（某些版本的关系代数具有非集合的关系标题；属性可以排序 and/or 多个属性可以具有相同的名称。通常 PRODUCT 为每个输入属性输出一个属性。如果有NATURAL JOIN 然后它的结果就像首先做 PRODUCT，然后限制 same-named 属性对的相等性，然后投影出每对的一个属性。所以 PRODUCT 适用于任何两个输入，而 NATURAL JOIN 可能在以下情况下未定义一个输入具有重复的属性名称，但当没有共享属性名称时它们将给出相同的结果。）
至于why you would compose any particular relational algebra query:
Every table/relation has a statement parameterized by
columns/attributes. (Its "characteristic predicate".) The rows/tuples
that make the statement true go in the table/relation. First find the
statements for the given tables/relations:
// customer [Cust-Name] has £[Balance] in account [Acc-No] at branch [Branch]
Deposit (Branch, Acc-No, Cust-Name, Balance)
// customer [Cust-Name] loan [Loan-No] balance is £[Balance] at branch [Branch]
Loan(Branch, Loan-No, Cust-Name, Balance)
Now put these given statements together to get a statement that only
the rows we want satisfy. Use AND, OR, AND NOT, AND condition. Keep or
drop names. Use a new name if you need one.
customer [Cust-Name] loan [Loan-No] balance is £[Loan-Balance] at branch [Branch]
AND customer [Cust-Name] has £[Balance] in account [Acc-No] at branch [Branch]
Now to get the algebra replace:
- every statement by its table/relation
- every AND of table/relation statements by ⋈ (natural join)
- every OR of table/relation statements (which must have the same columns/attributes) by ∪ (union)
- every AND NOT of statements (which must have the same columns/attributes) by \ (difference)
- every AND condition by σ condition
- every Keeping names to keep by π names to keep (projection) (and Dropping by π names to keep)
- every column/attribute renaming in a given statement by ρ (rename).
∩ (intersection) and x (product) are special cases of ⋈ (∩ for both
sides the same columns/attributes and x for no shared
columns/attributes).
(ρ Loan-Balance/Balance Loan) ⋈ Deposit
我对何时使用这两个运算符有点困惑。我觉得我理解它们，但我很难弄清楚什么时候在关系代数语句中需要它们。有人可以给我一些 insight/advice 吗？
某些版本的关系代数具有关系标题，这些关系标题是（无序、唯一命名的）属性集。 Then (relational (Cartesian)) PRODUCT, aka CROSS JOIN, aka CROSS PRODUCT, 仅在输入关系不共享属性名称时才定义，但在其他方面类似于 NATURAL JOIN。所以它的作用是确认你期望没有共享属性名。
（某些版本的关系代数具有非集合的关系标题；属性可以排序 and/or 多个属性可以具有相同的名称。通常 PRODUCT 为每个输入属性输出一个属性。如果有NATURAL JOIN 然后它的结果就像首先做 PRODUCT，然后限制 same-named 属性对的相等性，然后投影出每对的一个属性。所以 PRODUCT 适用于任何两个输入，而 NATURAL JOIN 可能在以下情况下未定义一个输入具有重复的属性名称，但当没有共享属性名称时它们将给出相同的结果。）
至于why you would compose any particular relational algebra query:
Every table/relation has a statement parameterized by columns/attributes. (Its "characteristic predicate".) The rows/tuples that make the statement true go in the table/relation. First find the statements for the given tables/relations:
// customer [Cust-Name] has £[Balance] in account [Acc-No] at branch [Branch] Deposit (Branch, Acc-No, Cust-Name, Balance) // customer [Cust-Name] loan [Loan-No] balance is £[Balance] at branch [Branch] Loan(Branch, Loan-No, Cust-Name, Balance)
Now put these given statements together to get a statement that only the rows we want satisfy. Use AND, OR, AND NOT, AND condition. Keep or drop names. Use a new name if you need one.
customer [Cust-Name] loan [Loan-No] balance is £[Loan-Balance] at branch [Branch] AND customer [Cust-Name] has £[Balance] in account [Acc-No] at branch [Branch]
Now to get the algebra replace:
- every statement by its table/relation
- every AND of table/relation statements by ⋈ (natural join)
- every OR of table/relation statements (which must have the same columns/attributes) by ∪ (union)
- every AND NOT of statements (which must have the same columns/attributes) by \ (difference)
- every AND condition by σ condition
- every Keeping names to keep by π names to keep (projection) (and Dropping by π names to keep)
- every column/attribute renaming in a given statement by ρ (rename).
∩ (intersection) and x (product) are special cases of ⋈ (∩ for both sides the same columns/attributes and x for no shared columns/attributes).
(ρ Loan-Balance/Balance Loan) ⋈ Deposit