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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}, .00175294, .000865413)

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

o4 = ({50, 2.30853e454, 98}, .00518477, .0352547)

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

o5 = {{.0367858, .0122874}, {.00555417, .00414138}, {.00629169, .00661691},
     ------------------------------------------------------------------------
     {.00625531, .00987907}, {.0224559, .0131262}, {.00687662, .0124527},
     ------------------------------------------------------------------------
     {.00572725, .00798097}, {.00616528, .00744592}, {.00491147, .00535296},
     ------------------------------------------------------------------------
     {.0194797, .00813626}}

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

o6 = .0120503228

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

o7 = .00874196619999998

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.