#9788: The coordinates appearing in the output of variety(L) should be easier to
access
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       Reporter:  mmezzarobba        |        Owner:  malb
           Type:  enhancement        |       Status:  needs_review
       Priority:  minor              |    Milestone:  sage-6.4
      Component:  commutative        |   Resolution:
  algebra                            |    Merged in:
       Keywords:                     |    Reviewers:
        Authors:  Martin von Gagern  |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  53e75728cd5ab67e39a3def6ddb3cc35af6a7e8a
  u/gagern/ticket/9788               |     Stopgaps:
   Dependencies:                     |
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Comment (by mmezzarobba):

 Replying to [comment:9 gagern]:
 > OK, here is an implementation for this.

 As you implemented it as a generic programming utility rather than as part
 of the parent/element/coercion/... infrastructure, perhaps it should go in
 `sage.misc` rather than `sage.structure`?

 > The object returned from the `variety()` call no longer is a sequence,
 since converting to sequence will cause some argument misalignment and
 therefore make all solutions come up as empty dicts. One alternative would
 be making the key conversion function a named argument, perhaps even
 guessing it from the type of the keys provided so far. Another alternative
 would be introducing a category for conversion dicts, one for every
 possible conversion function. But I doubt either of these is neccessary,
 since I doubt anyone really relies on receiving a Sequence out of this.

 I agree, but I'd prefer to get a second opinion.

 > Should `BooleanPolynomialIdeal.variety()` in `pbori.pyx` behave the
 same? Should other code make use of this as well, e.g. the symbolic
 `solve` function with `solutions_dict=True`?

 I'd say yes.

 > Should these things be handled in separate tickets?

 If that's easy to do, doing at least some of what you suggest here would
 give `KeyConvertingDict` a bit of field-testing before it is merged...

--
Ticket URL: <http://trac.sagemath.org/ticket/9788#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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