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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}, .00198491, .000991851)

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

o4 = ({50, 2.30853e454, 98}, .00695565, .0447806)

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

o5 = {{.00694984, .015921}, {.00595412, .00594169}, {.00794882, .0089347},
     ------------------------------------------------------------------------
     {.00794819, .0832628}, {.00594795, .0168998}, {.00596417, .0159049},
     ------------------------------------------------------------------------
     {.00497016, .00994455}, {.00595892, .00994733}, {.00496436, .0069597},
     ------------------------------------------------------------------------
     {.00695207, .00990201}}

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

o6 = .006355858599999964

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

o7 = .01836184189999996

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.