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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}, .00629646, .00254046)

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

o4 = ({50, 2.30853e454, 98}, .0186102, .112346)

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

o5 = {{.019711, .0351788}, {.0191304, .0121071}, {.0198098, .0189954},
     ------------------------------------------------------------------------
     {.0807329, .02893}, {.0206647, .0399063}, {.0217909, .0391962},
     ------------------------------------------------------------------------
     {.0201693, .0231434}, {.0210983, .021384}, {.0163931, .0158461},
     ------------------------------------------------------------------------
     {.0844557, .0243393}}

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

o6 = .0323956080000001

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

o7 = .025902662

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :