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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}, 0, .00400076)

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

o4 = ({50, 2.30853e454, 98}, .00800928, .0359289)

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

o5 = {{.00559775, .011817}, {.0079998, .00399999}, {.00399944, .00796965},
     ------------------------------------------------------------------------
     {.00599355, .0108761}, {.00400075, .0159474}, {.00400053, .0119982},
     ------------------------------------------------------------------------
     {.00400113, .00799904}, {.00400095, .00399973}, {.00799944, .00399884},
     ------------------------------------------------------------------------
     {.00799744, .0079988}}

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

o6 = .005559078500000014

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

o7 = .008660482499999933

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.