next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
RandomComplexes :: testTimeForLLLonSyzygies

testTimeForLLLonSyzygies -- test timing for LLL on syzygies

Synopsis

Description

We randomly choose an r × 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}, .00171887, .00105829)

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

o4 = ({50, 2.30853e454, 98}, .00510556, .0450635)

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

o5 = {{.00562073, .0155383}, {.00533828, .0051976}, {.0416348, .00818361},
     ------------------------------------------------------------------------
     {.00606714, .0124354}, {.00614554, .0166726}, {.00867853, .0156773},
     ------------------------------------------------------------------------
     {.00574824, .0110869}, {.0165167, .00932374}, {.00501987, .0065006},
     ------------------------------------------------------------------------
     {.00685353, .00979812}}

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

o6 = .0107623381

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

o7 = .0110414232

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :