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}, .00163787, .000876771) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00463734, .036506) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00526773, .0126722}, {.00483652, .00420702}, {.0183944, .00664548}, ------------------------------------------------------------------------ {.00499044, .0105009}, {.00550381, .0140043}, {.00645649, .0127664}, ------------------------------------------------------------------------ {.00575012, .00828755}, {.00663137, .00795341}, {.0165756, .0055096}, ------------------------------------------------------------------------ {.00556079, .00821209}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0079967245 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00907590010000001 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.