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}, .00331436, .00163693)
o3 : Sequence
|
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
o4 = ({50, 2.30853e454, 98}, .00938811, .0661667)
o4 : Sequence
|
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
o5 = {{.0104359, .0231251}, {.00976666, .00798152}, {.0109362, .0125525},
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{.0102686, .0185149}, {.0106887, .0248776}, {.0118373, .0233202},
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{.0110919, .0154276}, {.0125746, .014311}, {.00918485, .010181},
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{.0119037, .0151527}}
o5 : List
|
i6 : 1/10*sum(L,t->t_0) o6 = .0108688343 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .0165444118 o7 : RR (of precision 53) |
The object testTimeForLLLonSyzygies is a method function with options.