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}, .00329833, .00172825) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00950127, .0671133) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0105114, .0216402}, {.00984645, .00717147}, {.0288526, .0116959}, ------------------------------------------------------------------------ {.0101529, .0172899}, {.0106653, .0243056}, {.0120157, .0238515}, ------------------------------------------------------------------------ {.0112398, .0142693}, {.0127523, .0131769}, {.0255504, .009263}, ------------------------------------------------------------------------ {.0114088, .0144688}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0142995775 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0157132425 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.