#20973: Cartan type Aoo
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Reporter: andrew.mathas | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: combinatorics | Resolution:
Keywords: Cartan type, A | Merged in:
infinity |
Authors: Andrew Mathas | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/andrew.mathas/cartan_type_aoo | 9778f9738c6bf83c66f51ff22ba722e75e96d6ba
Dependencies: | Stopgaps:
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Comment (by andrew.mathas):
Replying to [comment:13 tscrim]:
> I would like to future proof this by deciding how we want to
differentiate between A,,+oo,, and A,,oo,,. Unfortunately `oo` is
`+Infinity`, so something as subtle as the difference between unsigned
infinity and plus infinity might not go over so well. I don't want to hold
this up (because this is a good improvement and test use-case), but I do
think it is something we should discuss for a moment.
As you suggested implementing both the `oo` and `+oo` cases I thought
about this and got stuck on precisely the problem that `oo == +Infinity`.
If anyone has a good idea as to how this should work in terms of syntax I
am happy to implement it. It is unfortunate that we can't use:
{{{#!sage
sage: CartanType(['A', oo])
sage: CartanType(['A',+oo])
}}}
but, as you say, this won't work.
Another direction for relatively easy generalisation is `B_oo` etc.
I have a related question concerning `cartan_matrix`, and possibly
`dynkin_diagram`. I was surprised that matrices indexed by `Z` and `N` are
not implemented in sage and, similarly, that graphs with infinite vertex
sets are not supported. It would be very easy to implement a fake Cartan
matrix, say `C`, that given two integers make `C[i,j]`, or `C[i][j]`,
return the corresponding entry of the Cartan matrix. Is some one able to
tell me what functionality such a matrix would need in order to be useful
to the root system code? Similarly, implementing a fake Dynkin diagram
class would be straightforward as long as I knew what methods I have to
implement.
--
Ticket URL: <https://trac.sagemath.org/ticket/20973#comment:15>
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