#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                 |  524f00ea3d1d3734a9915cd6052d0bf677fdb6e3
   Dependencies:  #18211             |     Stopgaps:
-------------------------------------+-------------------------------------

Comment (by vdelecroix):

 Replying to [comment:25 ncohen]:
 > Here are some comments. Please understand that doing everything at once
 makes things *MUCH* harder to understand for the reviewer.

 I am very sorry.

 > - The projection is not the orthogona projection I expected:

 Which one did you expected? I improved the documentation.

 > - 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?

 > - What about this error?
 >
 >   {{{
 >   sage: polytopes.icosahedron(base_ring=QQ)
 >   ...
 >   TypeError: unable to convert 1/4*sqrt(5) + 1/4 to a rational
 >   }}}

 Is it not clear enough? The coordinates of the icosahedron need to be
 defined in `QQ[sqrt(5)]`, hence the error. The following is ok (but very
 slow, ~3secs on my computer)
 {{{
 sage: I = polytopes.icosahedron(base_ring=AA)
 }}}
 Apart adding your example to the documentation, I do not see much what I
 can do (see the last commit). A deprecation?

 Vincent

--
Ticket URL: <http://trac.sagemath.org/ticket/18213#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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