Something with indexing could be done. The reduction   
   would be then be like running a Prolog interpreter,   
      
   and the indexing would be like he clause indexing   
   a Prolog interperter. This could give some speed!   
      
   Am Donnerstag, 13. Juli 2017 12:37:55 UTC+2 schrieb j4n bur53:   
   > This idea breaks, in that the reduction step again   
   > uses the whole basis. But still it might have some   
   >   
   > potential, the reduction step need not use all basis   
   > elements, when it is computed:   
   >   
   >      f = a1*g1 + .. + an*gn + r   
   >   
   > When some of the ai are zero, then gi from the basis   
   > was not used. How do we detect for some gi that they   
   >   
   > will always not be used anymore from some step on   
   > forwards in the algorithm?   
      
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