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}, .0017345, .000943429) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00494363, .0356324) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00538138, .0125745}, {.00516339, .00437146}, {.0230297, .00687456}, ------------------------------------------------------------------------ {.00532672, .0102689}, {.00550688, .0134468}, {.0060593, .0123981}, ------------------------------------------------------------------------ {.00531354, .00859745}, {.00615749, .0079658}, {.0209465, .00585037}, ------------------------------------------------------------------------ {.00603365, .00823475}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0088918548 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00905827440000001 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.