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}, .00198444, .00096443) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00579872, .0422961) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00670006, .0148534}, {.00644387, .00505461}, {.0191224, .00808559}, ------------------------------------------------------------------------ {.00663447, .0118434}, {.00669264, .0160887}, {.00721637, .0143325}, ------------------------------------------------------------------------ {.00701974, .00972917}, {.00734914, .00891882}, {.0166217, .0066221}, ------------------------------------------------------------------------ {.00706035, .00963631}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00908607869999999 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0105164551 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.