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}, .00153769, .000773931) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00437929, .0344087) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00482808, .0117343}, {.00462456, .00397779}, {.0178866, .00634608}, ------------------------------------------------------------------------ {.0049959, .00958963}, {.0052456, .0127051}, {.00599295, .0120714}, ------------------------------------------------------------------------ {.00514963, .0077852}, {.00559255, .00717644}, {.0168001, .00519738}, ------------------------------------------------------------------------ {.00562607, .00773409}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0076742042 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0084317459 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.