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}, .00165852, .000902405) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00466784, .0374905) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00514665, .0130828}, {.00478695, .00435279}, {.0146395, .00701573}, ------------------------------------------------------------------------ {.00495334, .0101514}, {.00522017, .0138536}, {.00595572, .012957}, ------------------------------------------------------------------------ {.00548431, .00867409}, {.0062749, .00773958}, {.0134891, .0056123}, ------------------------------------------------------------------------ {.00567895, .00837994}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0071629566 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00918191330000002 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.