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RandomComplexes :: testTimeForLLLonSyzygies

testTimeForLLLonSyzygies -- test timing for LLL on syzygies

Synopsis

Description

We randomly choose an r × 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}, .0061251, .00251162)

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

o4 = ({50, 2.30853e454, 98}, .0178941, .111825)

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

o5 = {{.0194329, .0352453}, {.0194114, .0121673}, {.0216202, .0190721},
     ------------------------------------------------------------------------
     {.0200377, .0285058}, {.0205166, .0398944}, {.0214742, .039171},
     ------------------------------------------------------------------------
     {.0186337, .0233067}, {.0209659, .0213225}, {.0170491, .0151508},
     ------------------------------------------------------------------------
     {.0230288, .0240229}}

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

o6 = .020217042

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

o7 = .025785882

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :