#17567: Cross product matrix (hat operator)
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Reporter: gagern | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.5
Component: linear algebra | Resolution:
Keywords: | Merged in:
Authors: Martin von Gagern | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/gagern/ticket/17567 | 57cf33d49d93bb828261ab1a39a1ba3ff82cb256
Dependencies: | Stopgaps:
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Comment (by tscrim):
A few comments. Please remove the `self` as input, it's not considered as
such. I would also consider using the
{{{:wikipedia:`Hat_operator#Cross_product`}}} in the documentation.
A bit more substantial, I would instead check the rank by
`self.parent().rank()` and define `s` inside of each of the 2 cases. This
is a slight speed penalty in the general ring case, but for `ZZ`, which
always copies the list, this could result in a big speedup:
{{{
sage: m = (ZZ^4).random_element()
sage: %timeit len(m.list(copy=False))
1000000 loops, best of 3: 1.39 µs per loop
sage: %timeit m.parent().rank()
1000000 loops, best of 3: 955 ns per loop
sage: m = (QQ['t']^4).random_element()
sage: %timeit len(m.list(copy=False))
1000000 loops, best of 3: 791 ns per loop
sage: m = (ZZ^20).random_element()
sage: %timeit len(m.list(copy=False))
100000 loops, best of 3: 3.03 µs per loop
}}}
Plus this is more robust if the behavior is changed to mimic `ZZ` (i.e.,
it always copies the elements). I might also consider adding the
definition of `R` and `zero` inside of the 2 cases as well, but that is a
definite micro-optimization.
Somewhat of a side note, constructing the basis might be an expensive
operation. So if you don't really need it, then let's stay away from using
it.
Nice little patch; looks good otherwise.
--
Ticket URL: <http://trac.sagemath.org/ticket/17567#comment:5>
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