#11316: Weighted degree term orders added
--------------------------------+-------------------------------------------
   Reporter:  klee              |          Owner:  AlexGhitza  
       Type:  enhancement       |         Status:  needs_review
   Priority:  major             |      Milestone:  sage-4.7.1  
  Component:  basic arithmetic  |       Keywords:              
Work_issues:                    |       Upstream:  N/A         
   Reviewer:                    |         Author:  Kwankyu Lee 
     Merged:                    |   Dependencies:              
--------------------------------+-------------------------------------------

Comment(by SimonKing):

 With the fourth patch, it is still allowed to do
 {{{
 sage: N.<a,b,c> = PolynomialRing(QQ, 3,
 order=TermOrder('wdeglex',[0,-2,3]))
 }}}

 There should an error be raised, because negative degrees do not work at
 all, due to the limitations imposed by Singular:
 {{{
 sage: a
 0*a
 }}}

 Another example:
 {{{
 sage: N.<a,b,c> = PolynomialRing(QQ, 3,
 order=TermOrder('wdeglex',[1.1,2,3]))
 sage: a.degree()
 1
 }}}
 Hence, one may think that the degree is converted to an integer. But in
 fact the "broken" value of the degree is still hanging around:
 {{{
 sage: singular(N)
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)
 ...
 TypeError: Singular error:
    ? no ring active
    ? error occurred in or before STDIN line 27: `ring sage7=0,(a, b,
 c),Wp(1.10000000000000,2,3);`
    ? expected ring-expression. type 'help ring;'
 }}}

 I am not sure what to do in the second case: Raise an error, or silently
 convert `1.1` to `1`?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11316#comment:31>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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