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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}, .00182048, .00081863)

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

o4 = ({50, 2.30853e454, 98}, .0048964, .0349622)

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

o5 = {{.00540629, .0121297}, {.00565081, .00416231}, {.00573386, .00655663},
     ------------------------------------------------------------------------
     {.00570927, .00994153}, {.00552402, .0134238}, {.0230393, .012486},
     ------------------------------------------------------------------------
     {.00538566, .00801059}, {.00544942, .00750408}, {.00473703, .00527862},
     ------------------------------------------------------------------------
     {.00604951, .00805216}}

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

o6 = .00726851400000001

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

o7 = .008754547

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.