#18390: cleanup variable factories
-------------------------------------+------------------------
       Reporter:  vdelecroix         |        Owner:
           Type:  enhancement        |       Status:  new
       Priority:  major              |    Milestone:  sage-6.7
      Component:  algebra            |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Vincent Delecroix  |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
   Dependencies:                     |     Stopgaps:
-------------------------------------+------------------------
Description changed by vdelecroix:

Old description:

> The `PolynomialRing` factory is written in a very complicated way and is
> slightly different to `FreeAlgebra`. In this ticket, we normalize the
> inputs of all factories involving variables.
>
> Some changes are noticeable
>
> 1. the following will now raise `TypeError`
> {{{
> sage: R.<a,b> = PolynomialRing(QQ, ('a', 'b'))
> sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')
> }}}
>
> 2. The `var_array` argument in `PolynomialRing` is deprecated
>
> As a sided effect, we got some speedup in polynomial ring creation!

New description:

 The `PolynomialRing` factory is written in a very complicated way and is
 slightly different to `FreeAlgebra`. In this ticket, we normalize the
 inputs of all factories involving variables.

 Some changes are noticeable

 1. the following will now raise `TypeError`
 {{{
 sage: R.<a,b> = PolynomialRing(QQ, ('a', 'b'))
 sage: A.<x,y,z> = FreeAlgebra(QQ, 'x,y,z')
 }}}

 2. The many versions are `normalize_names` are fused in
 `sage.misc.variables.normalize_names`

 3. Deprecations:
    - the `var_array` argument in `PolynomialRing`
    - the methods `normalize_names`, `_certify_name` of `CategoryObject`

 As a sided effect, we got some speedup in polynomial ring creation!

--

--
Ticket URL: <http://trac.sagemath.org/ticket/18390#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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