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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}, .00242984, .000963415)

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

o4 = ({50, 2.30853e454, 98}, .00539876, .0364323)

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

o5 = {{.0059123, .0118712}, {.00542278, .00397394}, {.00555019, .00630331},
     ------------------------------------------------------------------------
     {.00545815, .00963814}, {.00547801, .0132608}, {.0178535, .0124986},
     ------------------------------------------------------------------------
     {.00531976, .00776248}, {.00556362, .00712592}, {.00483627, .0050384},
     ------------------------------------------------------------------------
     {.0062157, .0080711}}

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

o6 = .00676103009999999

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

o7 = .00855438599999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.