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}, .00312582, .00166495) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00887558, .0658615) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0096941, .0211598}, {.00931575, .00702638}, {.028649, .0114326}, ------------------------------------------------------------------------ {.00956377, .0169277}, {.0100302, .0237869}, {.0112615, .023469}, ------------------------------------------------------------------------ {.0105141, .013872}, {.0114333, .012882}, {.0241107, .00895862}, ------------------------------------------------------------------------ {.0105362, .0142332}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .013510855 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0153748375 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.