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RandomComplexes :: testTimeForLLLonSyzygies

testTimeForLLLonSyzygies -- test timing for LLL on syzygies

Synopsis

Description

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}, .00172264, .000950367)

o3 : Sequence
i4 : (m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100)

o4 = ({50, 2.30853e454, 98}, .00490151, .0408884)

o4 : Sequence
i5 : L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2})

o5 = {{.00532667, .0139207}, {.00517715, .00470322}, {.0304021, .0076968},
     ------------------------------------------------------------------------
     {.00545783, .0112373}, {.00556734, .0149975}, {.00656991, .0142093},
     ------------------------------------------------------------------------
     {.00506928, .00922144}, {.012545, .00861117}, {.00465078, .00607183},
     ------------------------------------------------------------------------
     {.00626673, .00908654}}

o5 : List
i6 : 1/10*sum(L,t->t_0)

o6 = .00870327059999999

o6 : RR (of precision 53)
i7 : 1/10*sum(L,t->t_1)

o7 = .00997557169999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :