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}, .00169428, .000783331) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00473917, .0345933) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00537531, .0117575}, {.00491865, .00407765}, {.00557391, .00639948}, ------------------------------------------------------------------------ {.00562837, .00952579}, {.00600104, .0132786}, {.00653392, .0121106}, ------------------------------------------------------------------------ {.00606587, .00778452}, {.00610902, .00719314}, {.00478424, .00511012}, ------------------------------------------------------------------------ {.00583946, .0077894}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .00568297790000001 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00850268659999999 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.