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}, .00292588, .00159082) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00895452, .0663271) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00977645, .0215225}, {.0092541, .00728872}, {.0104616, .0116078}, ------------------------------------------------------------------------ {.00992565, .0173633}, {.0104209, .0241829}, {.0114782, .0236634}, ------------------------------------------------------------------------ {.0124186, .0140474}, {.0107424, .0129967}, {.0086074, .00934283}, ------------------------------------------------------------------------ {.0113637, .0145196}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0104449 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .01565351 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.