#19473: FiniteDimensionalAlgebra.is_unitary is not sufficient
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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 darij):
One more thing. The definition
{{{
v = vector(k, (n - 1) * ([1] + n * [0]) + [1])
}}}
of `v` is one step back from the currently present definition
{{{
v = vector(Matrix.identity(k, n).list())
}}}
because it is far better for the entries of `v` to be defined as the
zero/one elements of `R` rather than the ints `0` and `1`. There are,
after all, rings whose zero/one elements are distinct from `0` and `1`.
(So far we probably don't have fields like that, but it could be
imaginable. More importantly, coercions like `R(0)` take time,
particularly when they are cast on each entry of the vector separately.
--
Ticket URL: <http://trac.sagemath.org/ticket/19473#comment:20>
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