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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}, .00197728, .000994477)

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

o4 = ({50, 2.30853e454, 98}, .00594677, .0358618)

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

o5 = {{.00496611, .0109217}, {.00496165, .00397195}, {.00595875, .00595458},
     ------------------------------------------------------------------------
     {.00594403, .00895481}, {.00595665, .0129284}, {.00695576, .0129251},
     ------------------------------------------------------------------------
     {.00592686, .00695817}, {.00595739, .00695725}, {.00495619, .00496741},
     ------------------------------------------------------------------------
     {.00696102, .00794381}}

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

o6 = .00585444169999999

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

o7 = .00824831539999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.