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}, .00322131, .00163054)
o3 : Sequence
|
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
o4 = ({50, 2.30853e454, 98}, .00915277, .0661496)
o4 : Sequence
|
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
o5 = {{.0104876, .0232892}, {.0100696, .00800777}, {.0104771, .012475},
------------------------------------------------------------------------
{.0100773, .0187131}, {.0103897, .0250763}, {.0112959, .0235886},
------------------------------------------------------------------------
{.0106772, .015397}, {.0114071, .0142782}, {.00921138, .0102217},
------------------------------------------------------------------------
{.0115125, .0151467}}
o5 : List
|
i6 : 1/10*sum(L,t->t_0) o6 = .0105605395 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0166193655 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.