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}, .00232235, .00123352)
o3 : Sequence
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i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)
o4 = ({50, 2.30853e454, 98}, .00648193, .0768791)
o4 : Sequence
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i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})
o5 = {{.00743195, .0237191}, {.00739743, .00651745}, {.00957756, .0100793},
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{.0179554, .0162873}, {.00645966, .0227989}, {.00871469, .0215794},
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{.00746409, .0120605}, {.00809047, .0109241}, {.00536722, .00908606},
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{.00729697, .012017}}
o5 : List
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i6 : 1/10*sum(L,t->t_0) o6 = .00857554479999998 o6 : RR (of precision 53) |
i7 : 1/10*sum(L,t->t_1) o7 = .014506919 o7 : RR (of precision 53) |