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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}, .003328, 0)

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

o4 = ({50, 2.30853e454, 98}, .00210923, .0232746)

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

o5 = {{.00480732, .00842549}, {.00332631, .00332692}, {.00331832, .00332771},
     ------------------------------------------------------------------------
     {.00332866, .00341095}, {.00332848, .0071605}, {.00448399, .00665135},
     ------------------------------------------------------------------------
     {.00333094, .00332241}, {.0033286, .00664931}, {.00333136, .00331547},
     ------------------------------------------------------------------------
     {.00330436, .00664157}}

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

o6 = .0035888346

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

o7 = .00522316819999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.