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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}, .00717084, .00348856)

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

o4 = ({50, 2.30853e454, 98}, .0257853, .203612)

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

o5 = {{.0279898, .061899}, {.0256856, .0183315}, {.0271505, .030351},
     ------------------------------------------------------------------------
     {.0277125, .169706}, {.0218211, .0682573}, {.0243794, .0678935},
     ------------------------------------------------------------------------
     {.0207347, .0366959}, {.0219039, .0331952}, {.0189853, .0239535},
     ------------------------------------------------------------------------
     {.0248031, .0394808}}

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

o6 = .0241166

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

o7 = .054976402

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :