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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
External tables (in Informix [3] or Oracle, [4] [5] for example) can also be thought of as views. In many systems for computational statistics, such as R and Python's pandas, a data frame or data table is a data type supporting the table abstraction. Conceptually, it is a list of records or observations all containing
The symbol table must have some means of differentiating references to the different "p"s. A common data structure used to implement symbol tables is the hash table. The time for searching in hash tables is independent of the number of elements stored in the table, so it is efficient for a large number of elements.
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, [1] [2] where all data are represented in terms of tuples, grouped into relations.
An example of a database that has not enforced referential integrity. In this example, there is a foreign key (artist_id) value in the album table that references a non-existent artist — in other words there is a foreign key value with no corresponding primary key value in the referenced table.
A database index is a data structure that improves the speed of data retrieval operations on a database table at the cost of additional writes and storage space to maintain the index data structure. Indexes are used to quickly locate data without having to search every row in a database table every time said table is accessed.
For most organisations, most or all reference data is defined and managed within that organisation. Some reference data, however, may be externally defined and managed, for example by standards organizations. [5] An example of externally-defined reference data is the set of country codes as defined in ISO 3166-1. [6] [7]
In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, at amortized constant average cost per operation. [3] [4] [5] Hashing is an example of a space-time tradeoff.