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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}, .0038911, .0015413)

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

o4 = ({50, 2.30853e454, 98}, .0116812, .0715212)

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

o5 = {{.0127874, .0225181}, {.0124063, .00750025}, {.0521884, .0120901},
     ------------------------------------------------------------------------
     {.0131118, .0179729}, {.0136388, .0254193}, {.0145248, .0253012},
     ------------------------------------------------------------------------
     {.0120811, .0144758}, {.0528401, .0135415}, {.0111722, .00952718},
     ------------------------------------------------------------------------
     {.0152792, .0153639}}

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

o6 = .0210030125

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

o7 = .0163710275

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :