Let V be a vector space, and U a subspace of V. The set v + U = { v + u; u in U} is called a coset of U in V.
In GAP, cosets are of course domains that can be formed using the Functions for Row Space Cosets for an overview of applicable operators and functions, and Row Space Coset Records for details of the implementation.
A coset C = v + U is described by any representative v and the space U.
Equal cosets may have different representatives. A canonical representative
of the coset C can be computed using CanonicalRepresentative( C ), it
does only depend on C, especially not on the basis of U.
Row spaces cosets can be regarded as elements of quotient spaces (see Quotient Spaces).
GAP 3.4.4