Hi Waldek, (and all others interested in this topic)
first of all, thanks for looking into it.
Yes, I cannot read/interpret the profile report.
> There are other ways to speed up factorization.
> I am not sure if they would help in this case.
> Anyway, before looking at other tricks one should
> invest in fast low-level implementation as
> this would give biggest speedup and decide if
> anything more is really needed/helpful.
Honestly, after Dima mentioned NTL, I think that would be the better way
to go. Unfortunately, I feel unable to program a general interfact to
NTL. (In fact, it would be nice to have a simple way to call external
libraries, wouldn't it?)
NTL comes with Debian. If we could simply call functions from the
dynamic library, that would be great. I don't know yet how memory
allocation for NTL-polynomials (Z_p[x]) would work, but I guess, that
can be done.
I just need an example how I would call one NTL function from FriCAS. I
can probably do the rest.
Actually my intend is to program something like AlgebraicNumber, but
with the property that in cases like the one below at least one of the
zero tests returns true. Actually, already programmed. It relies on
keeping a projection into a finite field with enough roots (i.e. it has
to be dynamically extended, similar to being the closure of a prime field).
Only for that I need such a high degree finite field (and of course,
factorization of univariate polynomials over that field).
Ralf
(1) -> a2: AN := 2
(1) 2
Type: AlgebraicNumber
(2) -> a3: AN := 3
(2) 3
Type: AlgebraicNumber
(3) -> r2 := sqrt(a2)
+-+
(3) \|2
Type: AlgebraicNumber
(4) -> r3 := sqrt(a3)
+-+
(4) \|3
Type: AlgebraicNumber
(5) -> r6 := sqrt(a2*a3)
+-+
(5) \|6
Type: AlgebraicNumber
(6) -> zero?(r6 - r2*r3)
(6) false
Type: Boolean
(7) -> zero?(r6 + r2*r3)
(7) false
Type: Boolean
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