#18175: Implement categories for topological and metric spaces and related
categories
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers: Eric Gourgoulhon
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 041a5d10259ca0ec083a313bd4ad1fe6cfb8d9c0
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by tscrim):
Replying to [comment:56 egourgoulhon]:
> 1/ The new categories do not appear in the reference manual, in the
section "Individual Categories". Shouldn't they ?
Yes they should and now they do.
> 2/ The p-adic fields implemented in Sage seems not to have been taken
into account:
>
> {{{
> sage: Qp(5) in Fields().Topological()
> False
> sage: Qp(5) in Fields().Metric()
> False
> }}}
>
> One should actually have
>
> {{{
> sage: Qp(5) in Fields().Metric().Complete()
> True
> }}}
>
> There could be other metric fields in Sage, or more generally
topological rings, that should be included. But maybe this is too much
work for this ticket and should be delayed to some subsequent ticket ?
I've added them in and I reworked the default `dist` to use the `abs`
method of the elements. I also made it so that there is a call loop
`P.metric -> E.dist -> P.dist -> E.abs -> P.metric` so one just needs to
implement one of these methods (`P` is the parent and `E` is the element).
This is a slight abuse as not all metric spaces have a `0` (more generally
a distinguished base point), nor implement subtraction. I think this is
something we can live with for now and on a followup ticket better refine
the categories for these generic metrics as most parents who additive
groups (well, this might be a stronger condition than needed, but I'm not
worrying about that now). I also really don't want to go back through Sage
and make all those trivial category changes again...
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:58>
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