next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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}, .00497937, .00190845)

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

o4 = ({50, 2.30853e454, 98}, .0142445, .0702928)

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

o5 = {{.0158812, .0242419}, {.0159871, .00894861}, {.0170874, .0138712},
     ------------------------------------------------------------------------
     {.0343019, .0199215}, {.0161021, .0265032}, {.0173218, .0250365},
     ------------------------------------------------------------------------
     {.0157454, .0166527}, {.0170787, .0155181}, {.0141065, .011451},
     ------------------------------------------------------------------------
     {.0180056, .0276791}}

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

o6 = .0181617598

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

o7 = .0189823784

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :