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RandomComplexes :: testTimeForLLLonSyzygies

testTimeForLLLonSyzygies -- test timing for LLL on syzygies

Synopsis

Description

We randomly choose an $r \times\ n$ 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}, .00247668, .000957)

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

o4 = ({50, 2.30853e454, 98}, .00624412, .0590919)

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

o5 = {{.0068138, .0171653}, {.0062694, .0050866}, {.00663216, .00846804},
     ------------------------------------------------------------------------
     {.006972, .0135191}, {.0067712, .0201662}, {.0202414, .0202577},
     ------------------------------------------------------------------------
     {.00639812, .0102669}, {.00646216, .0093174}, {.00560336, .0060782},
     ------------------------------------------------------------------------
     {.00775868, .0116584}}

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

o6 = .007992224

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

o7 = .01219838

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.