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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}, .00183353, .00093035)

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

o4 = ({50, 2.30853e454, 98}, .00537953, .0415055)

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

o5 = {{.0336527, .0142899}, {.00653353, .00504569}, {.00623642, .00705821},
     ------------------------------------------------------------------------
     {.00597547, .0104901}, {.017988, .0139156}, {.00642576, .0130903},
     ------------------------------------------------------------------------
     {.00543404, .00934793}, {.00661167, .00822899}, {.00584338, .00668947},
     ------------------------------------------------------------------------
     {.014481, .00979284}}

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

o6 = .0109181917

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

o7 = .00979489709999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.