- sage.groups.abelian_gps.abelian_group: Multiplicative Abelian Groups
AUTHOR:
-- David Joyner (2006-03) (based on free abelian monoids by David Kohel)
-- David Joyner (2006-05) several significant bug fixes
-- David Joyner (2006-08) trivial changes to docs, added random,
fixed bug in how invariants are recorded
-- David Joyner (2006-10) added dual_group method
-- David Joyner (2008-02) fixed serious bug in word_problem
-- David Joyner (2008-03) fixed bug in trivial group case
TODO:
* additive abelian groups should also be supported
Background on elementary divisors, invariant factors and the Smith
normal form (according to section 4.1 of [C1]): An abelian group is a
group A for which there exists an exact sequence $\Z^k \rightarrow
\Z^\ell \rightarrow A \rightarrow 1$, for some positive integers
$k,\ell$ with $k\leq \ell$.
- sage.groups.abelian_gps.abelian_group_element: Abelian group elements
AUTHORS:
- David Joyner (2006-02); based on free_abelian_monoid_element.py, written by David Kohel.
- sage.groups.abelian_gps.abelian_group_morphism: Homomorphisms of abelian groups...
- sage.groups.abelian_gps.all: all.py -- export of abelian groups to SAGE
- sage.groups.abelian_gps.dual_abelian_group: Basic functionality for dual groups of finite multiplicative Abelian groups
AUTHOR:
-- David Joyner (2006-08) (based on abelian_groups)
-- David Joyner (2006-10) modifications suggested by William Stein
TODO:
* additive abelian groups should also be supported.
- sage.groups.abelian_gps.dual_abelian_group_element: Elements (characters) of the dual group of a finite Abelian group.
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