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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}, .00190629, .00123741)

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

o4 = ({50, 2.30853e454, 98}, .00618844, .083685)

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

o5 = {{.00687025, .0232192}, {.00574725, .00687068}, {.0271413, .0121516},
     ------------------------------------------------------------------------
     {.00720279, .0190313}, {.0069335, .0273289}, {.00914694, .0261636},
     ------------------------------------------------------------------------
     {.00601695, .0139864}, {.0300021, .0132747}, {.00549206, .00957613},
     ------------------------------------------------------------------------
     {.00819906, .0149215}}

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

o6 = .0112752183

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

o7 = .0166524063

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :