#18645: Add some methods to CartanMatrix
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Reporter: jonathan.judge | Owner: jonathan.judge
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: days65 | Merged in:
Authors: | Reviewers: Ben Salisbury, Travis
Report Upstream: N/A | Scrimshaw
Branch: | Work issues:
u/jonathan.judge/add_some_methods_to_cartanmatrix| Commit:
Dependencies: | 12895862c647d103d134c98ef18a5d8a934aeb5f
| Stopgaps:
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Changes (by tscrim):
* reviewer: Ben Salisbury => Ben Salisbury, Travis Scrimshaw
Comment:
Replying to [comment:17 jonathan.judge]:
> @tscrim: I think I've made all the changes you suggested.
Thanks. Although I would not cache `principal_submatrices` as it returns a
list of mutable matrices. I would change the output of
`indecomposable_blocks` to a tuple so that the output list cannot be
changed. Once this is changed, you can set a positive review on my behalf.
> A couple things that we should probably do (on another ticket?):
>
> - add {{{ is_hyperbolic }}}, {{{ is_lorentzian }}} and {{{ is_indefinite
}}} methods to !DynkinDiagram.
I'm happy doing this on another ticket as well. You might be interested in
#15974 (which I have half forgotten about, half didn't have time for).
> - unify results here with those for reducible Cartan types. To see what
I mean, note the difference between CM2 and CM3 below, where the matrices
are the same, but where CM2 knows its !CartanType while CM3 does not.
> {{{
> sage: CM1 = CartanMatrix("A2xA2")
> sage: CM1.is_finite()
> True
> sage: CM2 = CartanMatrix("A2~xA2")
> sage: CM2
> [ 2 -1 -1 0 0]
> [-1 2 -1 0 0]
> [-1 -1 2 0 0]
> [ 0 0 0 2 -1]
> [ 0 0 0 -1 2]
> sage: CM2.is_finite()
> False
> sage: CM2.is_affine()
> False
> sage: CM3 =
CartanMatrix([[2,-1,-1,0,0],[-1,2,-1,0,0],[-1,-1,2,0,0],[0,0,0,2,-1],[0,0,0,-1,2]])
> sage: CM3.is_affine()
> True
> }}}
Yes, we do not have good type recognition for Cartan types. I think the
better thing to do is to compare the Dynkin diagrams (as digraphs) and do
type recognition and relabeling that way. However this is definitely a
separate ticket.
Also, please add your real name as the author.
--
Ticket URL: <http://trac.sagemath.org/ticket/18645#comment:18>
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