We randomly choose an $r \times\ n$ matrix A over ZZ with entries up to the given Height, and take the time to compute B=ker A and an LLL basis of B.
i1 : setRandomSeed "nice example 2"; |
i2 : r=10,n=20 o2 = (10, 20) o2 : Sequence |
i3 : (m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) o3 = ({5, 2.91596e52, 9}, .00184768, .000997352) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00524223, .0426742) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00574166, .0147941}, {.00548502, .00503755}, {.0171259, .00800232}, ------------------------------------------------------------------------ {.00573408, .0118459}, {.0060073, .0160509}, {.00656851, .0152747}, ------------------------------------------------------------------------ {.00641341, .00981032}, {.00658287, .00900342}, {.0131126, .00664634}, ------------------------------------------------------------------------ {.00633902, .00963147}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00791103329999998 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .010609697 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.