#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
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jonathan.judge/add_some_methods_to_cartanmatrix|
12895862c647d103d134c98ef18a5d8a934aeb5f
Dependencies: | Stopgaps:
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Comment (by jonathan.judge):
@tscrim: I think I've made all the changes you suggested.
A couple things that we should probably do (on another ticket?):
- add {{{ is_hyperbolic }}}, {{{ is_lorentzian }}} and {{{ is_indefinite
}}} methods to !DynkinDiagram.
- 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
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/18645#comment:17>
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