#15150: Implement NCSym
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15143 | Stopgaps:
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Comment (by tscrim):
I would have thought that the total ordering on set partitions in #15143
would have `CombinatorialFreeModule` give a unique sorting on the
elements:
{{{
sage: SetPartition([[1,3],[2]]) < SetPartition([[1],[2],[3]])
False
sage: SetPartition([[1,3],[2]]) > SetPartition([[1],[2],[3]])
True
sage: SetPartition([[1],[2],[3]]) < SetPartition([[1,3],[2]])
True
sage: SetPartition([[1],[2],[3]]) > SetPartition([[1,3],[2]])
False
}}}
My guess as to why we're getting different output is a failure in the
comparisons (I didn't see any tickets that seemed like would change the
output of `linear_comb()`). Try running:
{{{
sage: e = SymmetricFunctionsNonCommutingVariables(QQ).e()
sage: e.print_options()
{'bracket': False,
'latex_bracket': False,
'latex_prefix': None,
'latex_scalar_mult': None,
'monomial_cmp': <function cmp>,
'prefix': 'e',
'scalar_mult': '*',
'tensor_symbol': None}
sage: cmp(SetPartition([[1],[2],[3]]), SetPartition([[1,3],[2]]))
-1
sage: elt = 2*e[[1],[2],[3]] - e[[1,3],[2]]
sage: L = elt._monomial_coefficients.items()
sage: L.sort(cmp=cmp, key=lambda (x,y): x)
sage: L
[({{1, 3}, {2}}, -1), ({{1}, {2}, {3}}, 2)]
}}}
Do you get anything different, in particular the last one?
--
Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:13>
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