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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}, .00299413, .00170192)

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

o4 = ({50, 2.30853e454, 98}, .0104572, .160034)

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

o5 = {{.01167, .0424543}, {.0107323, .0113998}, {.0117609, .019521},
     ------------------------------------------------------------------------
     {.0120387, .0327794}, {.012774, .0507646}, {.0769592, .0462744},
     ------------------------------------------------------------------------
     {.0085954, .0202097}, {.00912892, .0182032}, {.00855956, .0113745},
     ------------------------------------------------------------------------
     {.010659, .0267332}}

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

o6 = .0172878039

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

o7 = .0279714

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :