#18213: A lot of polytopes constructor are broken
-------------------------------------+-------------------------------------
       Reporter:  vdelecroix         |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.7
      Component:  geometry           |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Vincent Delecroix  |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/vdelecroix/18213                 |  fac3cffdb326dad1d3c61045d1c33044c99b8b32
   Dependencies:  #18211             |     Stopgaps:
-------------------------------------+-------------------------------------

Comment (by vdelecroix):

 Replying to [comment:28 ncohen]:
 > Hello,
 >
 > > Which one did you expected? I improved the documentation.
 >
 > Well, I expected an orthogonal projection on this hyperplane. And I
 probably expected the base of the hyperplane to be the projection of d-1
 vectors of the base from the original space I guess.

 The description is explicit in the doc (commit ​fac3cff)

 > > > - At this point I still do not know if it is very wise to use this
 definition of
 > > >   the projection, but it would be cool if every function which uses
 this
 > > >   projection (like !Simplex) could redirect toward the matrix
 function. This way
 > > >   people would have a chance to learn what exactly they get as a
 result.
 > >
 > > I see. But I am really not confortable in moving this to
 `matrix.<tab>` as well. One possibility is to move it back to
 `polytopes.<tab>`. What do you think?
 >
 > All I was suggesting in the message above was to add a link in the doc.
 The message you added in `project_points` is perfect
 > {{{
 > The projection used is the matrix given by :func:`zero_sum_projection`.
 > }}}
 >
 > To me it should appear whenever there is a 'project' argument in the
 function.

 Will do!

 > > Is it not clear enough? The coordinates of the icosahedron need to be
 defined in `QQ[sqrt(5)]`, hence the error.
 >
 > Precisely: Could you add somewhere in the doc that the field must
 contain `QQ(sqrt(5))`?

 There is one example at the end of the doc (from fac3cff)

--
Ticket URL: <http://trac.sagemath.org/ticket/18213#comment:31>
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