#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|
7e17029e1388141ba3cce2f160adc296afb18fcb
Dependencies: | Stopgaps:
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Comment (by jonathan.judge):
Is there a generally accepted convention for deciding how to classify
Cartan matrices whose blocks are of mixed type? For example, should a
Cartan matrix with a finite block and an affine block be considered
affine?
For now, the methods {{{ is_finite() }}}, {{{ is_affine() }}}, {{{
is_hyperbolic() }}} return false if the matrix is decomposable.
Indecomposability is assumed in the classification in Kac's book (and
Carter's), but I've seen other conventions (e.g. calling a Cartan matrix
with multiple finite blocks a finite matrix).
With this in mind, I added the {{{ indecomposable_blocks() }}} method to
make it easy for a user to check blocks individually for finiteness,
affineness, and hyperbolicity.
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Ticket URL: <http://trac.sagemath.org/ticket/18645#comment:8>
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