We randomly choose an r × 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}, .00158013, .000906959)
o3 : Sequence
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i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
o4 = ({50, 2.30853e454, 98}, .00468922, .044792)
o4 : Sequence
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i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
o5 = {{.00515508, .0143994}, {.00485648, .00458426}, {.0153493, .0074972}, {.00559239, .0118002}, {.00553504, .0154432},
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{.00961423, .01559}, {.00533012, .00929622}, {.0167665, .00851387}, {.00441615, .00589004}, {.00649972, .00937721}}
o5 : List
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i6 : 1/10*sum(L,t->t_0) o6 = .00791150700000002 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0102391689 o7 : RR (of precision 53) |