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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}, .00146381, .000990814)

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

o4 = ({50, 2.30853e454, 98}, .00419536, .0754786)

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

o5 = {{.00461368, .0209427}, {.0044215, .0063344}, {.00476819, .0102663},
     ------------------------------------------------------------------------
     {.0181246, .016463}, {.00465073, .0243577}, {.00517271, .0239806},
     ------------------------------------------------------------------------
     {.00454481, .0125462}, {.00473394, .0114967}, {.00378874, .00761121},
     ------------------------------------------------------------------------
     {.00504613, .0139071}}

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

o6 = .00598650590000001

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

o7 = .0147905834

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :