#8997: riemann_roch_basis is implemented incorrectly in sage
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   Reporter:  was                 |       Owner:  AlexGhitza
       Type:  defect              |      Status:  needs_work
   Priority:  major               |   Milestone:  sage-4.5.1
  Component:  algebraic geometry  |    Keywords:            
     Author:                      |    Upstream:  N/A       
   Reviewer:                      |      Merged:            
Work_issues:                      |  
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Comment(by minz):

 My impression is that the problem lies with Singular. I adapted the
 example in the description above and typed directly into Singular the
 following:

 {{{
 kill s, C, Ctemp, temp, G, R, LG;

 LIB "brnoeth.lib";
 int plevel=printlevel;
 printlevel=-1;
 system("random", 1);

 ring s=5,(x,y),lp;
 list C=Adj_div(x7+y7+1);
 C=NSplaces(1,C);
 def R=C[1][2];

 # I want to look at the points to be able to define
 # the same divisor each time, see below
 def Ctemp=extcurve(1,C);
 def temp=Ctemp[1][5];
 setring temp;
 print(POINTS);

 setring R;

 # adapt the line below according to the ordering of the points
 # i always chose the divisor 3(0,-1,1)-1(1,2,1)+10(2,1,1)
 intvec G = ;

 list LG=BrillNoether(G,C);
 LG;

 printlevel=plevel;
 }}}

 Not only did the bases vary each time I ran this code (even though I fixed
 the random seed in the sixth line), the resulting bases also had different
 cardinality (either 0 or 2).

 (I also tried to post this on the Singular trac server, but failed to do
 so. Maybe someone else is able to update the Singular ticket?)

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8997#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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