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}, .00128716, .000713423)

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

o4 = ({50, 2.30853e454, 98}, .00414227, .0289821)

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

o5 = {{.00445241, .0100266}, {.00410818, .00344861}, {.00449458, .00589275},
     ------------------------------------------------------------------------
     {.00488974, .00843493}, {.00464055, .0110269}, {.0056853, .0104263},
     ------------------------------------------------------------------------
     {.00518494, .00676431}, {.0230155, .00722852}, {.00435713, .00469806},
     ------------------------------------------------------------------------
     {.00547657, .00683744}}

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

o6 = .00663048889999999

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

o7 = .0074784479

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.