Indexed Free Groups

Free groups and free abelian groups implemented using an indexed set of generators.

AUTHORS:

  • Travis Scrimshaw (2013-10-16): Initial version
sage.groups.indexed_free_group.IndexedFreeAbelianGroup

An indexed free abelian group.

EXAMPLES:

sage: G = Groups().Commutative().free(index_set=ZZ)
sage: G
Free abelian group indexed by Integer Ring
sage: G = Groups().Commutative().free(index_set='abcde')
sage: G
Free abelian group indexed by {'a', 'b', 'c', 'd', 'e'}
sage.groups.indexed_free_group.IndexedFreeGroup

An indexed free group.

EXAMPLES:

sage: G = Groups().free(index_set=ZZ)
sage: G
Free group indexed by Integer Ring
sage: G = Groups().free(index_set='abcde')
sage: G
Free group indexed by {'a', 'b', 'c', 'd', 'e'}
sage.groups.indexed_free_group.IndexedGroup

Base class for free (abelian) groups whose generators are indexed by a set.

sage: G = Groups().Commutative().free(index_set=ZZ)
sage: G.is_finite()
False
sage: G = Groups().Commutative().free(index_set='abc')
sage: G.is_finite()
False
sage: G = Groups().Commutative().free(index_set=[])
sage: G.is_finite()
True