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}, .00190951, .00097045) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00538203, .0354582) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00589019, .0125447}, {.0055373, .00436098}, {.0294494, .00695182}, ------------------------------------------------------------------------ {.00612162, .0103123}, {.00628857, .0134775}, {.00715218, .0124655}, ------------------------------------------------------------------------ {.00653984, .00867206}, {.00754762, .00805695}, {.0279603, .0057446}, ------------------------------------------------------------------------ {.00674335, .00826105}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0109230367 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0090847459 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.