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}, .00155733, .00087735) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00399516, .0898098) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00387055, .0419042}, {.00806296, .0037181}, {.0555035, .00713048}, ------------------------------------------------------------------------ {.0323082, .0120636}, {.00525852, .0410282}, {.00512107, .0112056}, ------------------------------------------------------------------------ {.0317093, .00731692}, {.00433694, .00671539}, {.0489452, .00567149}, ------------------------------------------------------------------------ {.00481596, .035503}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0199932212 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0172256941 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.