Hello,
Le sam. 11 mai 2024 à 21:25, Waldek Hebisch <[email protected]> a écrit :
>
> On Sat, May 04, 2024 at 09:30:51AM +0200, Grégory Vanuxem wrote:
> > As a matter of fact, use of FLINT in FriCAS:
> >
> > (21) -> x:=x::NUP(NINT,"x")
> >
> > (21) x
> > Type:
> > NemoUnivariatePolynomial(NemoInteger,x)
> > Time: 0
> > sec
> > (22) -> p:=2*x+2*x^5+13*x^9
> >
> > (22) 13*x^9 + 2*x^5 + 2*x
> > Type:
> > NemoUnivariatePolynomial(NemoInteger,x)
> > Time: 0
> > sec
> > (23) -> p:=p^5;
> >
> > Type:
> > NemoUnivariatePolynomial(NemoInteger,x)
> > Time: 0
> > sec
> > (24) -> degree(p^750)
> >
> > (24) 33750
> > Type:
> > PositiveInteger
> > Time: 0.09 (EV) = 0.09
> > sec
> > (25) -> degree(p^750)
> >
> > (25) 33750
> > Type:
> > PositiveInteger
> > Time: 0.06 (EV) = 0.06
> > sec
>
> Hmm, I wonder what you are computing here. Could you give result
> (time and resulting number) for
>
> reduce(_+, map(length, coefficients(p^750)))
>
> assuming that 'length' and 'coefficients' are available for Nemo
> integeres/polynomials. Also, I wonder if you can monitor actual CPU time
> for this computation. I mean, if computation is delegated to a separate
> process then FriCAS will not know about time spent in another process
> and just report interface time. And one can split such computation
> into multiple cores, that reduces real time (if you have enough
> cores).
Looking more carefully. I have not implemented coefficients since
coefficients in Nemo/AbstractAlgebra returns an iterator. But if you
want a "list" as in LISP you can use collect on this iterator. The
problem is that polynomial of degree, say 9, will return all
coefficients;:
julia> p
13*x^9 + 2*x^5 + 2*x
julia> collect(coefs)
10-element Vector{ZZRingElem}:
0
2
0
0
0
2
0
0
0
13
So in principle, in FriCAS, the default 'coefficients' operation is used:
(8) -> coefficients(p)
(8) [13, 2, 2]
Type: List(NemoInteger)
But I have also not implemented length for NemoInteger since Nemo does
not have it unless doing low level stuff I guess (it's a GMP mpz_t as
far as I know), so for your question (not first powered):
(6) -> p
(6) 13*x^9 + 2*x^5 + 2*x
Type: NemoUnivariatePolynomial(NemoInteger,x)
Time: 0 sec
(7) -> pp
9 5
(7) 13 y + 2 y + 2 y
Type: UnivariatePolynomial(y,Integer)
Time: 0 sec
(8) -> reduce(_+,map(length, coefficients(p^750)::List(INT)))
(8) 3672690
Type: PositiveInteger
Time: 0.30 (IN) + 1.47 (EV) = 1.78 sec
(9) -> reduce(_+,map(length, coefficients(pp^750)::List(INT)))
(9) 3672690
Type: PositiveInteger
Time: 0.20 (EV) + 0.01 (GC) = 0.22 sec
What you're asking is too costly for my actual implementation. I
should not have used the word "arithmetic" this morning, my mistake,
sorry, what I meant is that I have not implemented all
_primitive_routines, all polynomial manipulation/information routines.
With p^5^750, and the different coercions, FriCAS silently stop and
the process returns to the bash shell :-(
And for your question about the number of threads used the Nemo
documentation says:
-----------------------------------------------------
Experimental threading support for flint
Enabling a threaded version of flint can be done by setting the
environment variable NEMO_THREADED=1. To set the actual number of
threads, use Nemo.flint_set_num_threads($numberofthreads).
If you need more information, please let me know.
-----------------------------------------------------
https://nemocas.github.io/Nemo.jl/latest/#Experimental-threading-support-for-flint
Using it:
-- Execute a julia command directly in FriCAS and displa its returned value
(11) -> )jud Nemo.flint_set_num_threads(1)
To use threaded flint, julia has to be started with NEMO_THREADED=1
(11) ->
And time given by FriCAS seems good, that's extremely fast.
- Greg
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