next | previous | forward | backward | up | top | index | toc | packages | Macaulay2 website
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}, .00272721, .00115331)

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

o4 = ({50, 2.30853e454, 98}, .00607044, .0489604)

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

o5 = {{.00667782, .0236886}, {.00672069, .00555691}, {.00674189, .00896197},
     ------------------------------------------------------------------------
     {.00706151, .0135315}, {.00688496, .0179867}, {.0166567, .0167215},
     ------------------------------------------------------------------------
     {.00626127, .0109063}, {.00651103, .0101229}, {.0060696, .0071841},
     ------------------------------------------------------------------------
     {.00753702, .0107986}}

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

o6 = .00771225170000002

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

o7 = .0125459084

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.