#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):
This sounds good to me. With respect to the code, I think the following
changes to the most recent push should take care of things:
- change {{{ is_finite() }}} to check if the matrix is positive definite;
- change {{{ is_affine() }}} to check if the determinant is zero and if
each indecomposable block is either finite or affine. With respect to
checking affine-ness, I didn't find a matrix method for positive semi-
definiteness. Is there a smarter way to do this than checking if the
determinants of proper principal submatrices are positive?
Based on the discussion of levels and strictness above, I believe that the
methods {{{ is_hyperbolic() }}} and {{{ is_lorentzian() }}} will yield
correct results as they stand.
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Ticket URL: <http://trac.sagemath.org/ticket/18645#comment:13>
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