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}, .00234755, .00109962) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00670504, .0429339) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00718767, .0150765}, {.00758156, .00548967}, {.0245612, .00811158}, ------------------------------------------------------------------------ {.00645868, .0118921}, {.00671136, .0162734}, {.00750079, .0153794}, ------------------------------------------------------------------------ {.00816328, .0101098}, {.00854802, .00918518}, {.0280472, .00671588}, ------------------------------------------------------------------------ {.00803364, .00989971}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0112793398 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .010813323 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.