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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}, .00199893, .00100127)

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

o4 = ({50, 2.30853e454, 98}, .00400027, .0349871)

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

o5 = {{.00599995, .0129898}, {.00499999, .00399912}, {.00691611, .00699949},
     ------------------------------------------------------------------------
     {.00698939, .00999972}, {.0070003, .0139994}, {.00800052, .0119822},
     ------------------------------------------------------------------------
     {.0070004, .00799876}, {.0069997, .00799926}, {.00500017, .00499854},
     ------------------------------------------------------------------------
     {.00799273, .00899384}}

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

o6 = .006689924600000063

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

o7 = .008996006499999921

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.