#19473: FiniteDimensionalAlgebra.is_unitary is not sufficient
-------------------------------------+-------------------------------------
Reporter: darij | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: algebra | Resolution:
Keywords: finite- | Merged in:
dimensional algebra, linear | Reviewers: Travis Scrimshaw
algebra | Work issues: clear up
Authors: Darij Grinberg, | associativity requirement; if
Travis Scrimshaw | necessary, change superclass and
Report Upstream: N/A | is_unitary method
Branch: | Commit:
public/algebra/finite_dim_algebra_fixes-19473|
0cfe0366fc527d2f692c835be3d40f60aa61c471
Dependencies: | Stopgaps:
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Comment (by pbruin):
Here is Johan Bosman's implementation of `is_unitary()` from #12141 before
my wrong rewrite (and after some editing and simplification):
{{{
#!python
@cached_method
def is_unitary(self):
"""
Return True if ``self`` is unitary.
EXAMPLES::
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0],[0,1]]),
Matrix([[0,1],[-1,0]])])
sage: B.is_unitary()
True
sage: C = FiniteDimensionalAlgebra(QQ, [Matrix([[0,0],[0,0]]),
Matrix([[0,0],[0,0]])])
sage: C.is_unitary()
False
"""
n = self._degree
k = self.base_ring()
if n == 0:
self._one = vector(k, [])
return True
B1 = reduce(lambda x, y: x.augment(y),
self._table, Matrix(k, n, 0))
B2 = reduce(lambda x, y: x.augment(y),
self.left_table(), Matrix(k, n, 0))
# This is the vector obtained by concatenating the rows of the
# n times n identity matrix:
v = vector(k, (n - 1) * ([1] + n * [0]) + [1])
try:
sol1 = B1.solve_left(v)
sol2 = B2.solve_left(v)
except ValueError:
return False
if sol1 == sol2:
self._one = sol1
return = True
else:
return False
}}}
If this is correct, we can just re-use it.
--
Ticket URL: <http://trac.sagemath.org/ticket/19473#comment:14>
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