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A question on finite field package performance

  • To: mathgroup at
  • Subject: [mg49540] A question on finite field package performance
  • From: Sergey Afonin <serg at>
  • Date: Fri, 23 Jul 2004 05:59:27 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

I have tried to expand a product of two polynomials over a finite
field using the FiniteFields package and found that it works *very* 
slow. It seems that this an old problem:

but from my point of view the problem is outside FiniteFields package.
Consider the following example:

p = 127;
n = 18;
rv = Table[GF[p][{Random[Integer, {0, p - 1}]}], {n}];
Print@Timing[Fold[Times, First[rv], Rest[rv]]];
Print@Timing[Times @@ rv];

The results are as follows:

{0. Second, result}, {11.43 Second, result} for n=18, and
{0. Second, result}, {108.4 Second, result} for n=21.

(a+a+a)+(a+a+a) is also faster then (a+a+a+a+a+a+a) for GF objects.

I have tried to rewrite addition of GF objects, but without any success:
the delay is related to function call (pattern matching for Plus?), not 
evaluation. If function name is other then Plus, say xPlus, then 
everything is ok.

Can anyone suggest a solution for this problem?

Thanks in advance,
Sergey Afonin

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