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}, .00151051, .00083048) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00442003, .0345297) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00487266, .0119476}, {.00459098, .00403372}, {.00493623, .0063271}, ------------------------------------------------------------------------ {.00486973, .00967588}, {.00500769, .0129405}, {.0055429, .0122369}, ------------------------------------------------------------------------ {.00532118, .00779023}, {.00559028, .00727135}, {.00419256, .00517873}, ------------------------------------------------------------------------ {.00537668, .00778993}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .005030091 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00851919339999999 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.