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}, .00427382, .00176473) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0126292, .0660027) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0135647, .0230022}, {.0134354, .00854485}, {.0246642, .0135945}, ------------------------------------------------------------------------ {.0134622, .0197903}, {.0136098, .0250205}, {.014697, .0224512}, ------------------------------------------------------------------------ {.0137989, .0159311}, {.0144154, .0148069}, {.0227349, .0125223}, ------------------------------------------------------------------------ {.015862, .0165895}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0160244418 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .017225338 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.