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}, .00192002, .00103095) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00551222, .0462642) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0060447, .0156659}, {.0056958, .00522027}, {.0246983, .00837187}, ------------------------------------------------------------------------ {.0057903, .0125622}, {.00602284, .0170897}, {.00691338, .0160212}, ------------------------------------------------------------------------ {.00644568, .0103085}, {.00749126, .00953934}, {.0218793, .00678786}, ------------------------------------------------------------------------ {.00650485, .0102603}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00974863799999998 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0111827166 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.