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}, .00199224, .000957375) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00587246, .0352593) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.00643189, .0125548}, {.00572322, .00433886}, {.0336492, .00690547}, ------------------------------------------------------------------------ {.0062374, .0102292}, {.00628645, .0133724}, {.00704673, .0122952}, ------------------------------------------------------------------------ {.00603198, .00856696}, {.00809655, .00788038}, {.0310509, .00564544}, ------------------------------------------------------------------------ {.00719511, .0083499}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .0117749464 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .00901386219999999 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.