#21123: monomials() and lt() for SymmetricFunctions over SymbolicRing broken
----------------------------+-------------------------
       Reporter:  schilly   |         Type:  defect
         Status:  new       |     Priority:  major
      Milestone:  sage-7.3  |    Component:  symbolics
       Keywords:            |    Merged in:
        Authors:            |    Reviewers:
Report Upstream:  N/A       |  Work issues:
         Branch:            |       Commit:
   Dependencies:            |     Stopgaps:
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 smc user reported these inconsistencies related to listing monomials of a
 symmetric function:

 {{{
 e = SymmetricFunctions(SR).e()
 f = e([2]).expand(3)
 f
 f.monomials()
 f.lt()

 x0*x1 + x0*x2 + x1*x2
 [1]
 x0*x1 + x0*x2 + x1*x2
 }}}

 i.e. just `[1]` and the whole polynomial, while over `QQ`:

 {{{
 e = SymmetricFunctions(QQ).e()
 f = e([2]).expand(3)
 f
 f.monomials()
 f.lt()

 x0*x1 + x0*x2 + x1*x2
 [x0*x1, x0*x2, x1*x2]
 x0*x1
 }}}

 lists all three monomials and only one term for `lt()`.

--
Ticket URL: <https://trac.sagemath.org/ticket/21123>
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