On Friday, July 8, 2016 at 10:17:20 AM UTC-7, chandra chowdhury wrote: > > Hi, > I have lattice L generated by row vectors > (1,1,2), (1,2,1) & (4,5,1) over Z_7. It is clear > that (4,5,1)-3*(1,1,2)-(1,2,1)= (0,0,1) over Z_7. > > So (0,0,1) is on the Lattice L. Is it possible > to find the shortest vector of L in Sage? Norm is > normal Euclidean norm. >
You'll find that over Z/7Z, the "normal Euclidean norm" is not a norm at all. Is there any concept of LLL algorithm over Z_7. > No, because there is no concept of "short vector" that behaves sufficiently well. You can try to find short representatives of vectors by lifting your module over Z/7Z to one over Z In your case, you'd be looking at the module generated by (1,1,2), (1,2,1),(4,5,1),(7,0,0),(0,7,0),(0,0,7) over Z. If you run LLL on that, you will get short vectors over Z that reduce to vectors that lie in the module over Z/7Z that you specified. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
