#13404: Improved printing for symmetric function bases and misc refactoring
---------------------------------------+------------------------------------
       Reporter:  nthiery              |         Owner:  sage-combinat 
           Type:  enhancement          |        Status:  needs_info    
       Priority:  major                |     Milestone:  sage-5.4      
      Component:  combinatorics        |    Resolution:                
       Keywords:  symmetric functions  |   Work issues:                
Report Upstream:  N/A                  |     Reviewers:  Anne Schilling
        Authors:  Nicolas M. ThiƩry    |     Merged in:                
   Dependencies:  #13399               |      Stopgaps:                
---------------------------------------+------------------------------------

Comment (by nthiery):

 Replying to [comment:19 aschilling]:
 > There is one more thing that Mike pointed out to me. Currently we have
 > {{{
 > sage: Sym = SymmetricFunctions(FractionField(QQ['t']))
 > sage: ks = Sym.kschur(4)
 > sage: ks
 > 4-Schur functions with t=t
 > sage: s = Sym.schur()
 > sage: s
 > Symmetric Functions over Fraction Field of Univariate Polynomial Ring in
 t over Rational Field in the Schur basis
 > }}}
 > Should ks be changed to
 > {{{
 > 4-Bounded Subspace of Symmetric Functions over Fraction Field of
 Univariate Polynomial Ring in t over Rational Field in the 4-Schur basis
 > }}}

 Good question. It's a bit long, but has some desirable features
 besides consistency with realizations/bases:

 - The ground field is specified
 - It refers to Sym, in such a way that if Sym is renamed to something
 short, this gets shorter as well

 Btw 1: it would be good to have t specified in the name of the
 kBoundedSubspace.

 {{{
 sage: Sym.kBoundedSubspace(3)
 3-bounded Subspace of Symmetric Functions over Fraction Field of
 Univariate Polynomial Ring in t over Rational Field
 sage: Sym.kBoundedSubspace(3,1)
 3-bounded Subspace of Symmetric Functions over Fraction Field of
 Univariate Polynomial Ring in t over Rational Field with t = 1
 }}}

 Btw 2: in the docstrings of new_kschur, wouldn't we want to change

 {{{
 sage: KBoundedSubspace(Sym,3,1)
 }}}

 to
 {{{
 sage: Sym.kBoundedSubspace(3,1)
 }}}

 (except probably once in the __init__, for testing purposes)?

 I am not sure I'll have the time to implement that before Tuesday, so
 feel free to beat me to it.

 Cheers,
                            Nicolas

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13404#comment:21>
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