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}, .00349303, .00172873)

o3 : Sequence

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

o4 = ({50, 2.30853e454, 98}, .00890225, .0653445)

o4 : Sequence

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

o5 = {{.00978126, .0229921}, {.0104088, .00774003}, {.010322, .0119556},
     ------------------------------------------------------------------------
     {.0105834, .0179259}, {.0102687, .0241449}, {.0364017, .0217175},
     ------------------------------------------------------------------------
     {.0094837, .0140227}, {.00953647, .0126296}, {.00847103, .00893416},
     ------------------------------------------------------------------------
     {.0107524, .0134113}}

o5 : List

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

o6 = .0126009451

o6 : RR (of precision 53)

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

o7 = .0155473815

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

"testTimeForLLLonSyzygies(ZZ,ZZ)"

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.