Macaulay2 » Documentation
Packages » RandomComplexes :: testTimeForLLLonSyzygies
next | previous | forward | backward | up | index | toc

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}, .00200008, .00100026)

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

o4 = ({50, 2.30853e454, 98}, .00700148, .0359422)

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

o5 = {{.00698594, .0119966}, {.00698669, .00396817}, {.00700119, .00699774},
     ------------------------------------------------------------------------
     {.00830052, .0101381}, {.0060025, .0130111}, {.00600103, .0129373},
     ------------------------------------------------------------------------
     {.00497913, .00799893}, {.00600068, .00799642}, {.00494467, .00601667},
     ------------------------------------------------------------------------
     {.00600017, .00899556}}

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

o6 = .006320253699999912

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

o7 = .009005657100000031

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies:

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.