Generating union queries using tensor representations

Apparatus for performing a query in a relational database system by operating upon a relation comprising a plurality of tuples formed over a plurality of attributes, comprising:

• a data storage device storing said relation in a relational tensor having a plurality of orders, wherein an order of said relational tensor corresponds to an attribute of the relation represented by the relational tensor, and coordinates along an order of said relational tensor correspond to values of the corresponding attribute, and numeric values at coordinate locations within said relational tensor represent a count of tuples in said relation having the attribute values that correspond to the coordinates of the numeric value along the orders of the relational tensor, and
• a processor executing the query by combining numeric values at matching coordinates along an operand order of said relational tensor to produce the result of combining said values for each distinct value of a grouping order of said relational tensor.

A program product comprising:

• a relational database comprising one or more relations, each relation comprising one or more tuples on one or more attributes, the relational database comprising a relational tensor having a plurality of orders, wherein an order of said relational tensor corresponds to an attribute of the relation represented by the relational tensor, and coordinates along an order of said relational tensor correspond to values of the corresponding attribute, and numeric values at coordinate locations within said relational tensor represent a count of tuples in said relation having the attribute values that correspond to the coordinates of the numeric value along the orders of the relational tensor, and
• relational database system adapted to retrieve data from said relational database and combine numeric values at matching coordinates along an operand order of said relational tensor to produce the result of combining said values for each distinct value of a grouping order of said relational tensor, and
• signal bearing media bearing the relational tensor and the relational database system.