next | previous | forward | backward | up | top | index | toc | Macaulay2 website
RandomComplexes :: testTimeForLLLonSyzygies

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}, .00415836, .00170385)

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

o4 = ({50, 2.30853e454, 98}, .0124453, .0636)

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

o5 = {{.0137611, .0223411}, {.0137042, .00912857}, {.0223062, .0210258},
     ------------------------------------------------------------------------
     {.0183593, .0198093}, {.0127519, .0229275}, {.024833, .0225347},
     ------------------------------------------------------------------------
     {.0132716, .0151579}, {.0137954, .014219}, {.0119102, .0108607},
     ------------------------------------------------------------------------
     {.0153264, .0153006}}

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

o6 = .0160019468

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

o7 = .0173305154

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.