1 A program that accepts the definition of an operation that is to be accomplished, and automatically constructs a program for the purpose. The earliest example of this kind of program was the sort generator, which took a specification of the file format and the sorted order required, and produced a sorting program. This was followed by report generators, which constructed programs to print reports from files containing information in a specified format. The best-known program of this kind is RPG II. See also application generator.
2 An element g of a group G with the property that the various powersg0, g1, g2,…ultimately include all the elements of G. Such a group is said to be a cyclic group; it is also an abelian group. Generators can also be defined for monoids in a similar way.
g0, g1, g2,…
The set of generators S of a group G is a subset of G having the property that every element of G can be expressed as a combination of elements of S. See also group graph.
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