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}, .00292567, .00165757) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00864597, .0658972) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00929975, .0216104}, {.00888617, .00698937}, {.0241401, .0113602}, ------------------------------------------------------------------------ {.0091839, .0167794}, {.00945955, .0236271}, {.0108955, .0232113}, ------------------------------------------------------------------------ {.00954175, .013813}, {.0107112, .0127029}, {.0218175, .00902765}, ------------------------------------------------------------------------ {.0101419, .0140606}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .012407735 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .01531818 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.