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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}, .000984918, .000987204)

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

o4 = ({50, 2.30853e454, 98}, .00395855, .0327803)

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

o5 = {{.00396711, .0109205}, {.00396602, .00396543}, {.00396799, .00595089},
     ------------------------------------------------------------------------
     {.00397463, .0751487}, {.00298182, .0119087}, {.00298163, .0119084},
     ------------------------------------------------------------------------
     {.00397248, .00694519}, {.00396567, .00694071}, {.00397012, .00495868},
     ------------------------------------------------------------------------
     {.00396871, .0069457}}

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

o6 = .003771618599999949

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

o7 = .01455929299999996

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.