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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}, .0019784, .0009858)

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

o4 = ({50, 2.30853e454, 98}, .0049304, .0568332)

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

o5 = {{.00690932, .0159054}, {.00594016, .00494816}, {.00692484, .00793768},
     ------------------------------------------------------------------------
     {.00692388, .0139335}, {.0079236, .019912}, {.00791576, .01992},
     ------------------------------------------------------------------------
     {.00595044, .009938}, {.00693456, .00893612}, {.00585088, .00595692},
     ------------------------------------------------------------------------
     {.00790672, .0109229}}

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

o6 = .006918015999999927

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

o7 = .011831068

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.