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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}, .00205533, .00100161)

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

o4 = ({50, 2.30853e454, 98}, .0060142, .0354561)

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

o5 = {{.00739761, .0128073}, {.00644677, .00435228}, {.00934741, .00697136},
     ------------------------------------------------------------------------
     {.0624939, .0102679}, {.00649541, .0135955}, {.00749624, .0125613},
     ------------------------------------------------------------------------
     {.00682132, .00884183}, {.00631742, .0078353}, {.00514141, .00565771},
     ------------------------------------------------------------------------
     {.00788031, .00838431}}

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

o6 = .0125837746

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

o7 = .0091274842

o7 : RR (of precision 53)

Ways to use testTimeForLLLonSyzygies :

For the programmer

The object testTimeForLLLonSyzygies is a method function with options.