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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}, .00329833, .00172825)

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

o4 = ({50, 2.30853e454, 98}, .00950127, .0671133)

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

o5 = {{.0105114, .0216402}, {.00984645, .00717147}, {.0288526, .0116959},
     ------------------------------------------------------------------------
     {.0101529, .0172899}, {.0106653, .0243056}, {.0120157, .0238515},
     ------------------------------------------------------------------------
     {.0112398, .0142693}, {.0127523, .0131769}, {.0255504, .009263},
     ------------------------------------------------------------------------
     {.0114088, .0144688}}

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

o6 = .0142995775

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

o7 = .0157132425

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.