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}, .00179602, .00107094) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00528837, .048069) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00574942, .0163465}, {.00549943, .00544778}, {.00590118, .00871458}, ------------------------------------------------------------------------ {.00560416, .0131183}, {.0058125, .0177715}, {.00646752, .0166482}, ------------------------------------------------------------------------ {.0063815, .0107013}, {.00599688, .0163718}, {.00477836, .00705977}, ------------------------------------------------------------------------ {.00630147, .0106244}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0058492428 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0122804083 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.