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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}, .0071186, .00286713)

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

o4 = ({50, 2.30853e454, 98}, .0204499, .106974)

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

o5 = {{.0227944, .0374329}, {.023011, .0143483}, {.0819374, .021754},
     ------------------------------------------------------------------------
     {.0230603, .0313904}, {.0242889, .0409006}, {.0242985, .0369777},
     ------------------------------------------------------------------------
     {.0218073, .0261829}, {.0430423, .0245045}, {.0203621, .0185597},
     ------------------------------------------------------------------------
     {.02685, .0256413}}

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

o6 = .0311452252

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

o7 = .0277692096

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :