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}, .00322784, .00158897) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00899374, .0656607) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0101025, .022785}, {.00990481, .00784198}, {.0105349, .012164}, ------------------------------------------------------------------------ {.00995409, .0182874}, {.0102543, .0246452}, {.0111678, .0230409}, ------------------------------------------------------------------------ {.0104572, .0150724}, {.011116, .0140494}, {.0281414, .0100683}, ------------------------------------------------------------------------ {.01148, .0147938}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .012311305 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0162748374 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.