On 26-Nov-09, at 12:23 PM, Florent Hivert wrote:

>>> On Thu, Nov 26, 2009 at 08:30:53AM -0800, YannLC wrote:
>>>> Just a toy implementation as a very thin layer over dict (at  
>>>> least it
>>>> should be fast)
>>>
>>> That's precisely what CombinatorialFreeModule elements are :-)
>>>
>>> Further optimizations to it are most welcome (For example, I am not
>>> sure += is implemented there)!
>>>
>>> Yes, the name is bad: there is nothing combinatorial to it. Merging
>>> this into FreeModule so that one could do FreeModule(QQ,  
>>> Objects()) is
>>> part of the future plan.
>>
>> I have been an observer of the sage-combinat process since its
>> inception and, I must say, I have been mildly skeptical (very  
>> mildly).
>
> Could you elaborate ? What's makes you skeptical ?

Two things, mostly.  The huge amount of code that wasn't being merged  
-- that appears to now be merged :)  And the whole categories/generic  
code effort: while I support the ends, I'm worried that the system  
will become so slow that it is unusable in practice.  Which is  
strange, because I'm not usually the one arguing for efficiency over  
clarity!

>> But if you guys allow me to view a multivariate polynomial ring as a
>> module over its base ring I will be very grateful.
>
> Of course they are ! I have no clue about why you say that ? Could  
> you explain
> yourself ? So what ?

I know they are mathematically, but at the moment it's very hard to  
take QQ['x', 'y'] and view it as a vector space over QQ.  Essentially,  
it's not easy to say that monomials x^i*y^j are the basis for some  
free module over QQ, and have sage convert back and forth.  But it  
sounds like you can do that too!

Nick

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