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}, .0027576, .00134452) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00816207, .0622447) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00849034, .0204274}, {.00798563, .00689257}, {.029999, .0107267}, ------------------------------------------------------------------------ {.0086392, .016521}, {.00889333, .0229309}, {.0105345, .0225708}, ------------------------------------------------------------------------ {.00942449, .0135937}, {.0109875, .0123316}, {.0289603, .00870962}, ------------------------------------------------------------------------ {.00964666, .0135816}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0133560898 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0148285961 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.