I would be for dropping 'x' as the only "default" variable (defined at 
start time).
Sage is unique in this sense AFAIK; there are CASes which don't require 
declaration of any variable, 
there are ones that don't have any special variables like Sage's 'x'.


On Wednesday, February 28, 2018 at 8:00:34 AM UTC, Simon King wrote:
>
> Hi Ralf, 
>
> On 2018-02-28, Ralf Stephan <gtr...@gmail.com <javascript:>> wrote: 
> > The reason is apparently that the polynomial ring was not created by the 
> > user on the command line but by the charpoly() code. 
>
> The parent of the pre-defined variable x wasn't created by the user 
> either, so, please don't blame polynomial rings or the 
> minpoly()/charpoly() code for it. 
>
>  sage: QQbar(sqrt(2)).minpoly().parent() 
>  Univariate Polynomial Ring in x over Rational Field 
>  sage: x.parent() 
>  Symbolic Ring 
>
>
> > i would consider this a high priority bug. Is there a ticket? 
>
> Not in the way you think, IMHO. 
>
> One problem that I see is the fact that it is possible to create rings 
> in which one variable name occurs twice, such as here: 
>   sage: RR['x']['x'] 
>   Univariate Polynomial Ring in x over Univariate Polynomial Ring in x 
>   over Real Field with 53 bits of precision 
>   sage: RR['x'].gen()-RR['x']['x'].gen() 
>   -x + x 
>   sage: _==0 
>   False 
>
> So, we have two x with different roles. It would make sense to disallow 
> the creation of such rings. 
>
> Also, I belive it is a bug that x is pre-defined as a symbolic variable; 
> we should finally drop that pseudo-courtesy. Users mistake FAR too often 
> symbolics with polynomials; by pre-defining x, we let the users believe 
> that x is good for *all* computations. So, I believe it would be better 
> to let the user create x him/herself, for the specific application that 
> he/she has in mind. However, I am aware that I belong to a minority with 
> that opinion. 
>
> Best regards, 
> Simon 
>
>

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