#16585: improved PolynomialSequence
-------------------------------------+-------------------------------------
       Reporter:  malb               |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.4
      Component:  commutative        |   Resolution:
  algebra                            |    Merged in:
       Keywords:  sd59               |    Reviewers:  Jakob Kroeker
        Authors:  Martin Albrecht    |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  6e9ef02bae16c9ec564b901d2a573bcb8f65ee6d
  u/malb/t16585_mpolynomial_sequence |     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by jakobkroeker):

 Ok, here the missing review comments:

 ##############################################################################
 1.
 "make sure we use the polynomial ring as ring not the monoid", in
 file {{{./src/sage/rings/polynomial/multi_polynomial_sequence.py}}}


 I think there is a failing example, if the input below is legal:
 {{{
 R.<x,y,z> = PolynomialRing(QQ)
 I = Ideal(5000*x*R,y*x+5) #error
 # Ring is Monoid of ideals of Multivariate Polynomial Ring in x, y, z over
 Rational Field =>error:
 # R must be a commutative ring
 }}}

 a second failing example (different error):
 {{{
 R.<x,y,z> = PolynomialRing(QQ)
 I = Ideal(5000*x*K+y*x,y*x+5)
 # TypeError: not a constant polynomial
 }}}

 #######################################################
 2.
 in  commit
 
[http://git.sagemath.org/sage.git/commit/?h=9ee750ef52d6d6ba43254a07ffbf9cea1160315f&id=9ee750ef52d6d6ba43254a07ffbf9cea1160315f
 9ee750ef52d6d6ba43254a07ffbf9cea1160315f]
 snippet:
 {{{
 + try:
 + c = K.characteristic()
 + except NotImplementedError:
 + c = 0
 }}}

 Why is c set to zero?  At least this should be documented.
 Is it not possible to have a different characteristic in case of an
 NotImplementedError? Do you have an example which hits this issue?

 ####################################################################
 3.
 refactored (lib)Singular GB code,
 in commit
 
[http://git.sagemath.org/sage.git/commit/?h=6e9ef02bae16c9ec564b901d2a573bcb8f65ee6d&id=e60f83a9e1584a899e8c79171ce177474b9fed06
 e60f83a9e1584a899e8c79171ce177474b9fed06]
 in src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx ,
 line 114, ff.{{{sage_ideal_to_singular_ideal}}}
 Is there a corresponding test for a conversion from "{{{or a list of
 generators}}}"?
 If not, could you add one?

 Same commit,
 in file 'src/sage/rings/polynomial/polynomial_singular_interface.py
 renaming {{{singular_default}}} to {{{singular}}}; why?
 At other places there are singular_default usages.
 Is there a difference?

 ####################################################################
 4.
 Same commit,
 It seems that reduce examples show no examples for explicitly reducing
 leading coefficient,
 Could you add an example or a test which hits
 "{{{ret.append(f.lc()**(-1)*f)}}}"?

 ####################################################################
 5.
 Sequence has no 'reduced' function
 Is that ok?
 Example:
 {{{
 R.<x> = PolynomialRing(QQ)
 F = Sequence([x,x+1])
 F.reduced() # fails
 }}}



 ####################################################################
 6.
 commit
 
[http://git.sagemath.org/sage.git/commit/?h=a88b44703751c13e451252ca2da671679077711e&id=a88b44703751c13e451252ca2da671679077711e
 a88b44703751c13e451252ca2da671679077711e]
 (fix Magma interface broken when moving decorators around):

 Could you explain what may get wrong and add an example?

--
Ticket URL: <http://trac.sagemath.org/ticket/16585#comment:7>
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