On Nov 26, 2009, at 12:35 AM, Florent Hivert wrote:

>   Hi Nathann,
>
>> For Linear Programming, I need to create plenty of symbolic variables
>> which I use to represent linear functions.... To do it, I use the
>> class InfinitePolynomialRing which lets me create them easily ( and  
>> it
>> is really needed, as my colleagues often have to create Linear
>> Programs using 1000~2000 variables. This is not a problem for the
>> solvers, but Sage does not like it :
>> 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 ? 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 ) ?
>
> This is indeed a problem. I think I know the cause... Each time a  
> new variable
> is created, the ring itself is somehow changed. Therefore for each new
> variable in your sum, there is a big computation which convert the  
> former sum
> to the new ring. Though this could be improved by using a similar  
> trick than
> doubling the size of a list when appending element, I'm not sure  
> that's what
> we want.

I think this makes perfect sense...I'm actually surprised it's not  
implemented that way already.

> In the mean time. I have the following workaround: Just start by
> declaring your last variable:

If one knows how many variables one needs ahead of time, than what's  
the advantage of using the InfinitePolynomialRing over a finite one of  
the right size?

- Robert

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