#12630: Add representations of quivers and quiver algebras to sage
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Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.11
Component: algebra | Resolution:
Keywords: algebra, quiver, module, days49 | Work issues: Split into
different modules. Use parents and elements.
Report Upstream: N/A | Reviewers:
Authors: Jim Stark, Simon King | Merged in:
Dependencies: #12412, #12413 | Stopgaps:
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Changes (by SimonKing):
* cc: nthiery (added)
Comment:
Some comments from a discussion with Nicolas:
- Currently, we say `FreeSmallCategory`. Isn't it simply a semi-group?
- If it is a semi-group (in particular, if it is declared in the category
of semi-groups, and not in the category of magmas, it might be possible
that we can inherit most of the functionality that is now in
`QuiverAlgebra`. Namely, there already is `Semigroups.Algebras`.
- Slight problem: Currently, the invalid path is not mentioned in the list
of elements of the free small category / semi-group of a quiver, but it is
''recognised'' as an element. This is odd, but on the other hand, when we
add it to the list of elements, then the dimension of the algebra will be
one more.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:52>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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