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}, .00189652, .00101042) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0054921, .0423928) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00600803, .0147611}, {.00575465, .00504853}, {.0195413, .00793708}, ------------------------------------------------------------------------ {.00612717, .0119217}, {.00649716, .0159535}, {.00706368, .0151918}, ------------------------------------------------------------------------ {.00708877, .00982866}, {.00697381, .00902076}, {.0191889, .00646084}, ------------------------------------------------------------------------ {.00674505, .00968184}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0090988486 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0105805875 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.