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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}, .00151051, .00083048)

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

o4 = ({50, 2.30853e454, 98}, .00442003, .0345297)

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

o5 = {{.00487266, .0119476}, {.00459098, .00403372}, {.00493623, .0063271},
     ------------------------------------------------------------------------
     {.00486973, .00967588}, {.00500769, .0129405}, {.0055429, .0122369},
     ------------------------------------------------------------------------
     {.00532118, .00779023}, {.00559028, .00727135}, {.00419256, .00517873},
     ------------------------------------------------------------------------
     {.00537668, .00778993}}

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

o6 = .005030091

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

o7 = .00851919339999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.