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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}, .00440115, .00172431)

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

o4 = ({50, 2.30853e454, 98}, .0126998, .0649362)

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

o5 = {{.0135611, .0227265}, {.0138443, .00839892}, {.0204486, .0125415},
     ------------------------------------------------------------------------
     {.0135, .0181907}, {.0142539, .025433}, {.0153085, .0220478}, {.014031,
     ------------------------------------------------------------------------
     .0162103}, {.0147338, .0151005}, {.0192857, .0128853}, {.022785,
     ------------------------------------------------------------------------
     .019338}}

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

o6 = .0161751874

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

o7 = .017287254

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.