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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}, .00153769, .000773931)

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

o4 = ({50, 2.30853e454, 98}, .00437929, .0344087)

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

o5 = {{.00482808, .0117343}, {.00462456, .00397779}, {.0178866, .00634608},
     ------------------------------------------------------------------------
     {.0049959, .00958963}, {.0052456, .0127051}, {.00599295, .0120714},
     ------------------------------------------------------------------------
     {.00514963, .0077852}, {.00559255, .00717644}, {.0168001, .00519738},
     ------------------------------------------------------------------------
     {.00562607, .00773409}}

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

o6 = .0076742042

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

o7 = .0084317459

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.