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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}, .00251023, .0011011)

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

o4 = ({50, 2.30853e454, 98}, .00597021, .0455032)

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

o5 = {{.00667255, .0157205}, {.00645049, .00755861}, {.00713632, .00846098},
     ------------------------------------------------------------------------
     {.0070991, .0128935}, {.00696719, .0172938}, {.0245293, .0157621},
     ------------------------------------------------------------------------
     {.00654048, .0104369}, {.00675361, .00965625}, {.00589796, .00695092},
     ------------------------------------------------------------------------
     {.00753141, .0104988}}

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

o6 = .00855784199999998

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

o7 = .0115232421

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.