#15536: Implement symplectic and orthogonal bases of Sym
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: combinatorics | Resolution:
Keywords: days54, sym | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/sf/sp_orth | 9536f54a96401a5bdabdaa56dc65640f8bb1bfda
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by darij):
I fear Nicolas is wrong here:
{{{
sage: o = Sym.o()
sage: TestSuite(o).run()
Failure in _test_antipode:
Traceback (most recent call last):
File "/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/misc/sage_unittest.py", line 282, in run
test_method(tester = tester)
File "/home/darij/gitsage/sage-5.13.beta1/local/lib/python2.7/site-
packages/sage/categories/hopf_algebras_with_basis.py", line 263, in
_test_antipode
tester.assert_(SI(x) == self.counit(x) * self.one())
File
"/home/darij/gitsage/sage-5.13.beta1/local/lib/python/unittest/case.py",
line 424, in assertTrue
raise self.failureException(msg)
AssertionError: False is not true
------------------------------------------------------------
The following tests failed: _test_antipode
}}}
The problem is that the counit is still defined as the constant
coefficient, but that's only true for graded bases. Concrete example:
{{{
sage: o[2].counit()
0
sage: s(o[2]).counit()
-1
}}}
The same issue would be happening with antipode and degree_negation if not
for the fact that the o and sp bases happen to be graded w.r.t. the
induced ZZ/2ZZ-grading.
--
Ticket URL: <http://trac.sagemath.org/ticket/15536#comment:2>
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