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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}, .00198932, .00096924)

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

o4 = ({50, 2.30853e454, 98}, .0056926, .0585632)

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

o5 = {{.00588652, .0168726}, {.00580832, .00499808}, {.00607988, .00828772},
     ------------------------------------------------------------------------
     {.00636696, .0133335}, {.00628744, .0198633}, {.0135646, .0200898},
     ------------------------------------------------------------------------
     {.00593212, .009977}, {.00620512, .00908204}, {.00523468, .0058904},
     ------------------------------------------------------------------------
     {.007078, .0113654}}

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

o6 = .00684436799999999

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

o7 = .011975984

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.