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}, .00320701, .00171779) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00911518, .0670186) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.010525, .0233026}, {.00995652, .00799578}, {.0104214, .0125847}, ------------------------------------------------------------------------ {.0100142, .0186179}, {.0104062, .025053}, {.0112117, .0235035}, ------------------------------------------------------------------------ {.0107768, .0156788}, {.0112575, .014478}, {.00925961, .0103349}, ------------------------------------------------------------------------ {.011307, .0151289}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0105135871 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0166678122 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.