On Friday, July 8, 2016 at 7:23:01 PM UTC+1, Nils Bruin wrote: > > 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. >
it is not 100% true; Z_7 is a field, thus you get a vector space, and a coding theory-like problem of finding a some sort of measure to see how far apart two vectors are. For instance it can be Hamming distance (# of coordinates in which two vectors differ), and then it's the classical coding theory setup. Dima > > 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 sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
