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LLL-based Algorithms

An LLL-based minimal polynomial algorithm is found in most computer algebra systems. We have received quite comparable results for the following three systems. For all three systems the tests were performed on an R4600 SGI workstation running at 132 MHz. Maple and Mathematica are leading commercial computer algebra products. PARI-GP can be obtained by anonymous ftp to megrez.math.u-bordeaux.fr.


software precision time function
system needed needed used
Maple 5.5 235(310)* 27 min* minpoly
Mathematica 3.0 170 33.5 min NumberTheory`Recognize`
PARI-GP 1.39 175(265)* 27.5 min* lindep2


Comments:


* The notation d1(d2) means that the first correct result is received at the precision of d1 decimal digits but a steady stream of correct results (when incrementing the precision by 5 digits in one step) only starts at d2 digits. In this case, the timing in the third column is for the run at the precision of d1 digits.


next up previous
Next: The PSLQ Algorithm Up: Implementations Previous: A Test Example
Agnes Szanto
2000-05-10