Indexed Free Groups¶
Free groups and free abelian groups implemented using an indexed set of generators.
AUTHORS:
- Travis Scrimshaw (2013-10-16): Initial version
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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'}
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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'}
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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