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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}, .00145938, .00105347)

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

o4 = ({50, 2.30853e454, 98}, .00415631, .0755781)

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

o5 = {{.00461632, .0212012}, {.00447069, .00613342}, {.0046604, .0104701},
     ------------------------------------------------------------------------
     {.019216, .0164891}, {.00461912, .0246921}, {.00557035, .0244245},
     ------------------------------------------------------------------------
     {.00453358, .0128577}, {.00471786, .0116368}, {.00371731, .00800005},
     ------------------------------------------------------------------------
     {.00573663, .014288}}

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

o6 = .00618582719999998

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

o7 = .0150192884

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :