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}, .00316285, .00160295)
o3 : Sequence
|
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
o4 = ({50, 2.30853e454, 98}, .00891255, .0662941)
o4 : Sequence
|
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
o5 = {{.01056, .0232895}, {.00976994, .00792503}, {.0320568, .0123416},
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{.00972302, .0185553}, {.0100933, .0249464}, {.0113188, .0233009},
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{.00989724, .0153723}, {.0115703, .0143681}, {.0287223, .0101582},
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{.0111581, .0149933}}
o5 : List
|
i6 : 1/10*sum(L,t->t_0) o6 = .0144869923 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0165250735 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.