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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}, .00199755, .00100288)

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

o4 = ({50, 2.30853e454, 98}, .00799949, .0358704)

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

o5 = {{.00900069, .0129802}, {.00699867, .0039981}, {.00879858, .00699341},
     ------------------------------------------------------------------------
     {.00899956, .0110001}, {.0100009, .0140016}, {.00998778, .0129976},
     ------------------------------------------------------------------------
     {.0080005, .00899798}, {.00899924, .00899769}, {.00687104, .00599886},
     ------------------------------------------------------------------------
     {.00999876, .00798517}}

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

o6 = .0087655763

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

o7 = .00939506490000003

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.