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}, .00179376, .000963685) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00510538, .0400288) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00530301, .0143246}, {.00529179, .00490497}, {.0107152, .0075423}, ------------------------------------------------------------------------ {.00520512, .0128764}, {.00587392, .0161978}, {.00822905, .0161981}, ------------------------------------------------------------------------ {.00586767, .0094377}, {.00664565, .0109836}, {.0111385, .00731794}, ------------------------------------------------------------------------ {.00706819, .0110086}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0071338108 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0110791993 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.