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}, .00400313, .00400439)

o3 : Sequence

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

o4 = ({50, 2.30853e454, 98}, .00799626, .0511073)

o4 : Sequence

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

o5 = {{.0118591, .0191793}, {.0120032, .00799534}, {.0155979, .00963873},
     ------------------------------------------------------------------------
     {.0121831, .0199519}, {.0160084, .0233362}, {.0122242, .0191492},
     ------------------------------------------------------------------------
     {.00883759, .0126397}, {.00789794, .0083288}, {.00960415, .00916745},
     ------------------------------------------------------------------------
     {.0169402, .015225}}

o5 : List

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

o6 = .0123155782

o6 : RR (of precision 53)

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

o7 = .0144611626

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

testTimeForLLLonSyzygies(ZZ,ZZ)

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.