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}, .00424391, .00146888) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .0106503, .135498) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0110107, .0414667}, {.0096733, .0164731}, {.0486524, .0106528}, ------------------------------------------------------------------------ {.00596876, .0316928}, {.00631135, .043179}, {.0109992, .0484153}, ------------------------------------------------------------------------ {.0109926, .0210592}, {.0176943, .0235434}, {.0349374, .01255}, ------------------------------------------------------------------------ {.0103752, .0211562}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0166615155 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0270188429 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.