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}, .00319752, .00162185) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00895655, .065643) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0100569, .022893}, {.00957963, .00779029}, {.0103082, .0123547}, ------------------------------------------------------------------------ {.00998424, .0183385}, {.0105804, .024692}, {.0113001, .0231523}, ------------------------------------------------------------------------ {.0105757, .0151752}, {.0113494, .0140444}, {.0285677, .0100123}, ------------------------------------------------------------------------ {.0111345, .0148071}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0123436759 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0163259905 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.