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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}, .00398993, .00106109)

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

o4 = ({50, 2.30853e454, 98}, .00873811, .082157)

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

o5 = {{.011882, .0270499}, {.0110855, .00876604}, {.0128362, .0172968},
     ------------------------------------------------------------------------
     {.0615813, .0242468}, {.0105694, .0311405}, {.0123105, .0306267},
     ------------------------------------------------------------------------
     {.0120521, .0206576}, {.00500033, .018992}, {.00431917, .00614694},
     ------------------------------------------------------------------------
     {.00526842, .008352}}

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

o6 = .0146905058999999

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

o7 = .0193275252

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.