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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}, .00399997, 0)

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

o4 = ({50, 2.30853e454, 98}, .00400295, .0359259)

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

o5 = {{.00400181, .0148947}, {.00366175, .00400023}, {.00400003, .00799972},
     ------------------------------------------------------------------------
     {.00400269, .007998}, {.00400372, .0119803}, {.00589711, .0119926},
     ------------------------------------------------------------------------
     {.00273579, .00801078}, {.0086054, .00557576}, {.00400576, .00400068},
     ------------------------------------------------------------------------
     {.00615017, .00799862}}

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

o6 = .004706422199999993

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

o7 = .008445134499999929

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.