In my developement version I switched polynomial factorization
over prime fields to use new factorizer. That gives substantial
speedup. However, profiling showed that in my test case (which
was polynomial with 84 linear factors) abut 10% time was spent
in multiplying factors, of of which 8.4% went into comparing
exponents (POLYCAT-;smaller?)
One trouble is that comparizons of polynomials are expensive.
Second, multiplying factor-by-factor triggers quadratic
behaviour in Factored. For use in factorizers this can
be fixed by passing list of factors to 'makeFr'.
We probably should have specialized comparizon routine
in SMP.
It is not entirely clear to me what to do with Factored.
Ordering can be used to speed up computations only when
we have true order, otherwise we may get wrong results.
Additionally, ordering factors gives speedup only when
all or most factors is prime, for other factors we need
to use quadratic method anyway. My conclusion is that
we can not have really efficient operations with
generality offered by Factored, so probably should
not care too much about speed of Factored.
--
Waldek Hebisch
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