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}, .00186375, .0010645) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0054904, .0756885) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00623027, .0214121}, {.005722, .00617108}, {.0137325, .0103615}, ------------------------------------------------------------------------ {.00570398, .0165785}, {.00610537, .025223}, {.00704977, .0241865}, ------------------------------------------------------------------------ {.00574894, .0125773}, {.0064019, .0117769}, {.0132071, .00769642}, ------------------------------------------------------------------------ {.00614595, .0139603}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00760477289999999 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0149943697 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.