On Wednesday, December 18, 2013 9:58:15 AM UTC-8, vdelecroix wrote:
>
> Users of polynomials should worry about the coefficient ring. What do 
> someone should expect of 
>
>     sage: (6*x^2 - 12).factor() 
>
> The answers are different in ZZ[x], QQ[x] and RR[x]. For a symbolic 
> polynomial there is no way to make it coherent... 
>
It's worse: SR isn't even an exact ring (and it has zero divisors; 
seehttp://trac.sagemath.org/ticket/11126#comment:2) , so a lot of 
polynomial arithmetic you'd normally expect to work, doesn't in general.

So yes we can define polynomial rings with coefficients in SR:

sage: SR['x']
Univariate Polynomial Ring in x over Symbolic Ring
sage: (1+sin(2))*x-2.3
(sin(2) + 1)*x - 2.30000000000000

but any nontrivial computation in it will be problematic (I take this as 
definition of nontrivial here).
 

> And I guess a long term goal of Sage would be to make it disappear. 
>

It IS good for some things: integration strategies and some symbolic 
differential equation solving methods do benefit from the loose approach 
that SR takes with mathematical expressions.
I think a more attainable goal is to allow the user to avoid SR in as many 
cases as possible.

-- 
You received this message because you are subscribed to the Google Groups 
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/groups/opt_out.

Reply via email to