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}, .00325689, .0015953) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00944075, .0655334) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0102276, .0228377}, {.0100606, .00781131}, {.0110113, .0122867}, ------------------------------------------------------------------------ {.0104239, .0182734}, {.0111091, .0246254}, {.0119341, .0231954}, ------------------------------------------------------------------------ {.0113654, .0151353}, {.0123503, .0139809}, {.00932745, .0100482}, ------------------------------------------------------------------------ {.0118137, .0149013}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0109623419 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0163095555 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.