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}, .00319405, .00163391) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0092077, .0658944) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00995433, .022659}, {.00940252, .00769471}, {.010122, .0119845}, ------------------------------------------------------------------------ {.00996092, .0174784}, {.0103602, .0231033}, {.010904, .0212316}, ------------------------------------------------------------------------ {.0106764, .0137611}, {.010971, .012437}, {.0297573, .00870072}, ------------------------------------------------------------------------ {.010122, .0127366}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0122230725 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0151786907 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.