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testTimeForLLLonSyzygies -- test timing for LLL on syzygies

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";
 -- setting random seed to 12638458417381289481402307077
i2 : r=10,n=20

o2 = (10, 20)

o2 : Sequence
i3 : (m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11)

o3 = ({5, 2.91596e52, 9}, .000990842, 0)

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

o4 = ({50, 2.30853e454, 98}, .00297076, .0297387)

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

o5 = {{.00394252, .00990524}, {.00296993, .00295215}, {.00397491, .00592473},
     ------------------------------------------------------------------------
     {.00395238, .00791746}, {.0049663, .0108989}, {.00496414, .00989296},
     ------------------------------------------------------------------------
     {.00397346, .00594322}, {.00496966, .00593881}, {.00296039, .00396488},
     ------------------------------------------------------------------------
     {.0039628, .00692927}}

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

o6 = .004063647500000034

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

o7 = .007026758599999905

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

  • testTimeForLLLonSyzygies(ZZ,ZZ)

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.


The source of this document is in RandomComplexes.m2:492:0.