#18744: Improve Cartan Type Recognition
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Reporter: jonathan.judge | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: combinatorics | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This ticket is to improve Cartan type recognition when constructing Cartan
matrices.
Specifically, when constructing a !CartanMatrix from a Matrix or from a
list of lists, !CartanMatrix applies the function
{{{find_cartan_type_from_matrix}}}. This function tests against Cartan
matrices coming from built-in finite and affine !CartanTypes. Currently,
it does not detect Cartan types for relabellings of (Dynkin diagrams of)
indecomposable Cartan matrices, nor does it detect reducible Cartan types
for decomposable Cartan matrices. Improving the automatic detection of
Cartan types is helpful when creating Cartan matrices on the fly, which in
turn is useful for #18000.
After some preliminary analysis, it looks like the bulk of the work here
can be accomplished by using the {{{indecomposable_blocks}}} method added
to !CartanMatrix in #18645, as well as the {{{is_isomorphic}}} method of
the !GenericGraph class (of which !DynkinDiagram is a child class).
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Ticket URL: <http://trac.sagemath.org/ticket/18744>
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