#16953: Faster enumeration of points for toric varieties
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Reporter: vbraun | Owner:
Type: enhancement | Status: needs_review
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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Comment (by vdelecroix):
Replying to [comment:18 vbraun]:
> Replying to [comment:17 vdelecroix]:
> > What about all your useless `cached_method`?
>
> They give names to quantities. Its true that you can replace the
multiplicative order with q-1 everywhere, but it is not true that q-1 in a
formula always refers to the order. Giving names to quantities makes code
more readable as it explains the "why".
What annoys me is that you add 20 lines of code + documentation + a non
documented function for something which can be replaced by
{{{self.ring.cardinality() - 1}}} and
{{{self.ring.multiplicative_generator()}}} for which the names are not at
all mysterious.
> And I'm using the general pattern of caching frequently-accessed
methods, an extra `cached_method` has no performance impact but a
forgotten `cached_method` can be very bad.
`cached_method` can also have '''negative''' impact on performances (for
not that frequently-accessed methods). Creating dictionaries is costly,
object creation is costly, function call is costly.
> Also, why should you have to read the finite fields implementation just
to decide whether to cache something in this module?
Hopefully I did it for you. It is clear that `multiplicative_generator` is
something critical in many application and it looks natural to cache this
method at the level of finite fields. And as a finite field is mostly
defined by its cardinality, you can expect the method `cardinality` to be
fast.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/16953#comment:20>
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