next | previous | forward | backward | up | top | index | toc | packages | 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}, .00149304, .000707456)

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

o4 = ({50, 2.30853e454, 98}, .00345146, .0301827)

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

o5 = {{.00379512, .0101252}, {.00360037, .00336888}, {.00362536, .00534998},
     ------------------------------------------------------------------------
     {.00363309, .00814665}, {.00350855, .0110396}, {.0188195, .0104733},
     ------------------------------------------------------------------------
     {.00343339, .00648073}, {.00355419, .00598869}, {.00315315, .00432432},
     ------------------------------------------------------------------------
     {.00418799, .00693692}}

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

o6 = .00513107360000001

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

o7 = .00722342669999998

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.