Hi Nathann!
On Nov 26, 8:18 am, Nathann Cohen <nathann.co...@gmail.com> wrote:
[...]
> To understand my problem, just try this code :
>
> X.<x> = InfinitePolynomialRing(RR)
> sum([x[i] for i in range(200)])
>
> Don't you think it is a bit long just to generate a sum ? I have to
> admit I do not know how this class is coded, and the slowness may be
> required for applications different from mine.. But wouldn't there be
> a way to speed this up ?
InfinitePolynomialRing has an underlying *finite* polynomial ring,
that changes whenever you need a variable that is not in the finite
ring.
Therefore,
sum([x[199-i] for i in range(200)])
is much faster.
Reason:
InfinitePolynomialRing has a dense and a sparse implementation, that
both have advantages and disadvantages. The default is "dense". It
means: If x[199] is called, then a polynomial ring with all variables
ranging from x0 to x199 is created. So, if you start the sum with x
[199] then the ring can be kept.
In the sparse implementation, both summation orders would be slow. The
advantage of the sparse implementation is that you can have x[100000]
without creating a ring with 100000 generators.
> If not, do you know of any way to generate
> many symbolic variables ( they do not need to be polynomial, just
> linear in my case ) ?
Well, you know that InfinitePolynomialRing does not yield symbolic
variables.
I would consider creating the variable names that you need, and create
symbolic variables explicitely:
sum([var('x'+str(i)) for i in range(200)])
is fast enough, I guess.
Cheers,
Simon
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