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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}, .00151106, .00108772)

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

o4 = ({50, 2.30853e454, 98}, .00425164, .0776173)

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

o5 = {{.00575473, .0217449}, {.0045445, .0066718}, {.0243089, .0107745},
     ------------------------------------------------------------------------
     {.00482875, .0169872}, {.00494068, .0253291}, {.00555174, .024866},
     ------------------------------------------------------------------------
     {.00438131, .0130586}, {.0228592, .0120511}, {.00410281, .00799339},
     ------------------------------------------------------------------------
     {.00535844, .0144382}}

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

o6 = .0086631074

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

o7 = .0153914814

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :