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}, .00256522, .00229359) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00955829, .0987403) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00981151, .0203111}, {.010073, .00931701}, {.0110663, .0151781}, ------------------------------------------------------------------------ {.0116963, .0226841}, {.00462198, .0144851}, {.00514814, .0151523}, ------------------------------------------------------------------------ {.00528319, .147271}, {.00629381, .0097889}, {.00459622, .00605011}, ------------------------------------------------------------------------ {.0102895, .0198303}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00788799370000001 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0280068118 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.