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}, .00121947, .000649184) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00340133, .0302936) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00354203, .0106402}, {.00383128, .00365222}, {.0230721, .00646176}, ------------------------------------------------------------------------ {.00404019, .00972304}, {.0037331, .013157}, {.00463209, .0106123}, ------------------------------------------------------------------------ {.00368809, .00716356}, {.00430927, .00694876}, {.0232526, .00569321}, ------------------------------------------------------------------------ {.00461698, .00802099}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0078717703 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0082073005 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.