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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}, .00121947, .000649184)

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

o4 = ({50, 2.30853e454, 98}, .00340133, .0302936)

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

o5 = {{.00354203, .0106402}, {.00383128, .00365222}, {.0230721, .00646176},
     ------------------------------------------------------------------------
     {.00404019, .00972304}, {.0037331, .013157}, {.00463209, .0106123},
     ------------------------------------------------------------------------
     {.00368809, .00716356}, {.00430927, .00694876}, {.0232526, .00569321},
     ------------------------------------------------------------------------
     {.00461698, .00802099}}

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

o6 = .0078717703

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

o7 = .0082073005

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.