#19586: Add is_cayley_graph
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Reporter: jaanos | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: graph theory | Resolution:
Keywords: Cayley graphs | Merged in:
groups | Reviewers:
Authors: Janoš Vidali | Work issues:
Report Upstream: N/A | Commit:
Branch: | 4aaf3014fee5bb08d861636908d6733047d4a869
u/jaanos/add_is_cayley_graph | Stopgaps:
Dependencies: |
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Comment (by jaanos):
Hello!
> not all silly designs in Sage should be copied...
> Looks like someone didn't know, or forgot, about `None`
I don't know, it seems pretty reasonable to me to have an `is_property`
method with the option to return a certificate for either having or not
having this property. Now, I don't know of any way to provide an easy-to-
check certificate of non-Cayleyness, but if one is eventually found, it
can be returned alongside the boolean telling whether a graph is a Cayley
graph - so the user doesn't need to check what kind of certificate the
function returned.
As for the certificate of Cayleyness, I am thinking that a better option
would be to return a map from vertices to group elements (which the
current function already computes when computing the generators) - now it
can be easily checked that the elements form a group, and that the
generating set is well defined (instead of having to compute an
isomorphism between the graph and the Cayley graph built from the group
and generating set). Actually computing the group (and returning it
alongside the generating set and the map, if requested) would then be
delegated to `cayley_graph_group`, as you proposed.
> only the generators? Why? it's one quick function call away from the
group, why would you
> do this in library code? In particular, as you are computing the group,
not its generators, in the first place.
Well, I think if we're giving the user the choice of what they want
returned, it would be unreasonable to forbid a certain choice just because
we see no use for it.
Janoš
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Ticket URL: <http://trac.sagemath.org/ticket/19586#comment:35>
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