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}, .00326621, .00161066) o3 : Sequence |
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) o4 = ({50, 2.30853e454, 98}, .00917056, .0662752) o4 : Sequence |
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) o5 = {{.0104485, .0231312}, {.0100035, .00803823}, {.0316644, .0126502}, ------------------------------------------------------------------------ {.0101431, .0187983}, {.0101943, .0251417}, {.0116813, .0235936}, ------------------------------------------------------------------------ {.0101372, .0155594}, {.0115972, .0143447}, {.0284433, .0102393}, ------------------------------------------------------------------------ {.0117055, .0151247}} o5 : List |
i6 : 1/10*sum(L,t->t_0) o6 = .014601824 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0166621371 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.