#16953: Faster enumeration of points for toric varieties
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Reporter: vbraun | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers:
Authors: Volker Braun | Work issues:
Report Upstream: N/A | Commit:
Branch: | 49a72410a19784c05c9fe320e28382df7e5b7338
u/vbraun/faster_enumeration | Stopgaps:
Dependencies: |
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Changes (by vdelecroix):
* status: needs_review => needs_work
Comment:
Hello,
Some quick comments (I will not be able to check most of the mathematical
contents of the code).
Some cached method are really not needed. The multiplicative generator of
finite field is already cached. So you could remove the
`FiniteFieldPointEnumerator.multiplicative_generator`. And the
multiplicative order of the multiplicative generator is `q-1` (where `q`
is the cardinality of the field), isn't it?
Instead of using `CartesianProduct`, use `itertools.product` (actually
this is indirectely used). `CartesianProduct` is about to disappear.
If you want to copy a list, the fastest is by far `zero[:]` and not
`copy(zero)`.
{{{
sage: timeit("copy(zero)")
625 loops, best of 3: 2.59 µs per loop
sage: timeit("zero[:]")
625 loops, best of 3: 248 ns per loop
}}}
The fastest way for zero test is `X.is_zero()` and not `X == 0`. The
latter might involves coercion.
{{{
sage: K = GF(53**3, 'a')
sage: b = K('a')+3*K('a')**2+12
sage: timeit("b == 0")
625 loops, best of 3: 2.17 µs per loop
sage: timeit("b.is_zero()")
625 loops, best of 3: 317 ns per loop
}}}
Vincent
PS: the hook for modifying the category code was very funny! Hopefully I
erase the `Sets.ParentMethods.cardinality` before this ticket gets in ;-)
--
Ticket URL: <http://trac.sagemath.org/ticket/16953#comment:12>
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