testTimeForLLLonSyzygies -- test timing for LLL on syzygies

Synopsis

Usage:

(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>100)
Inputs:
- r, an integer,
- n, an integer,
Optional inputs:
- Height => an integer, default value 11, the sizes of the random integers used
Outputs:
- m, a list, of maximal absolute values of the entries of A, B and the LLL basis of B
- t1, a real number, the time in seconds to compute B = ker A
- t2, a real number, the time to compute the LLL basis of B

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}, .00399238, .00399242)

o3 : Sequence

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

o4 = ({50, 2.30853e454, 98}, .0119679, .0823252)

o4 : Sequence

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

o5 = {{.0117603, .027712}, {.0119731, .00803996}, {.0119013, .0165625},
     ------------------------------------------------------------------------
     {.0155925, .0199846}, {.0119887, .0331237}, {.0116323, .0314746},
     ------------------------------------------------------------------------
     {.0117297, .020008}, {.012008, .0160042}, {.00799906, .0120129},
     ------------------------------------------------------------------------
     {.0120004, .0221592}}

o5 : List

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

o6 = .01185853899999998

o6 : RR (of precision 53)

i7 : 1/10*sum(L,t->t_1)

o7 = .02070816799999999

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

testTimeForLLLonSyzygies(ZZ,ZZ)

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.