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}, .00296667, .000994088)

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

o4 = ({50, 2.30853e454, 98}, .00696179, .0448062)

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

o5 = {{.00795356, .0159274}, {.00695712, .00596799}, {.0069416, .00796305},
     ------------------------------------------------------------------------
     {.0079554, .012944}, {.00695662, .0168862}, {.00795468, .0149321},
     ------------------------------------------------------------------------
     {.00788183, .00995608}, {.00795925, .00995198}, {.00596931, .00696885},
     ------------------------------------------------------------------------
     {.007959, .0109535}}

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

o6 = .00744883640000001

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

o7 = .0112451171

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.