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}, .00289396, .00161844) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00869223, .0742108) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0090147, .0246852}, {.00896526, .00801383}, {.0236319, .0129883}, ------------------------------------------------------------------------ {.00882459, .0195814}, {.0089095, .0276577}, {.0102963, .0263853}, ------------------------------------------------------------------------ {.00881169, .0157449}, {.010181, .0147206}, {.0201071, .0102059}, ------------------------------------------------------------------------ {.00983925, .0160693}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0118581242 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0176052431 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.