The functions described here provide access to basic information stored for a generic abelian group A. If some access functions require that the structure of A be known, then it is automatically computed should it not already be known.
Note the distinction between Generators and UserGenerators. From now on, unless otherwise specified, whenever mention is made of the generators of A, we refer to the generators as given by the Generators function.
The universe over which the generic abelian group A is defined.
The order of the generic abelian group A, returned as an ordinary integer.
The i-th generator for the generic abekian group A.
A sequence containing the generators for the generic abelian group A as elements of A. The set of generators of A is a reduced set of generators as constructed during the group structure computation. Therefore, if the group structure of A has been computed from a user-supplied set of generators, it is more than likely that Generators(A) and UserGenerators(A) do not coincide.
A sequence containing the user-supplied generators for the generic abelian group A as elements of A.
The number of generators for the generic abelian group A.
The torsion invariants of the finite abelian group A.
> Universe(G); Residue class ring of integers modulo 34384 > Generators(G); [ 21489, 17191, 12281, 27021 ]and
> Universe(GA_qf); Binary quadratic forms of discriminant -4000004 > Generators(GA_qf); [ <101,0,9901>, <103,102,9734> ] > UserGenerators(GA_qf); [ <3,2,333334>, <59,14,16950>, <47,42,21286>, <31,22,32262>, <19,16,52635>, <5,4,200001>, <11,6,90910>, <23,8,43479>, <29,16,34485>, <103,102,9734> ]