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}, .00440115, .00172431) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0126998, .0649362) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0135611, .0227265}, {.0138443, .00839892}, {.0204486, .0125415}, ------------------------------------------------------------------------ {.0135, .0181907}, {.0142539, .025433}, {.0153085, .0220478}, {.014031, ------------------------------------------------------------------------ .0162103}, {.0147338, .0151005}, {.0192857, .0128853}, {.022785, ------------------------------------------------------------------------ .019338}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0161751874 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .017287254 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.