Simon King wrote:
> Dear Jason,
> 
> On Dec 3, 7:54 pm, Jason Grout <[EMAIL PROTECTED]> wrote:
>> Wow, Sage will redefine symbols that are already existing to accommodate
>> what should be a dummy variable?  This looks seriously wrong and looks
>> like it could really mess things up.
> 
> I don't think so. Admittedly I don't like that x is pre-defined, but
> here it is something else.
> There are Sage constructions which define various things in one line.
> For example,
>  sage: R.<z>=QQ[]
> both defines R *and* z (the latter of type Polynomial_rational_dense).

In this case, z is not being used as a dummy variable.  I think it makes 
a lot of sense to define z globally when z is on the right, versus 
defining z just locally when you have R = QQ['z']


> 
> Similarly, doing
>  sage: R(z)=sin(z)
> both defines R *and* z (the latter of type SymbolicVariable).

In this case, mathematical convention says that z is a dummy variable; 
it should not matter what I call the thing inside the parentheses, and 
it certainly shouldn't affect stuff outside of the function.

Maybe part of the huge difference in my mind is that R(z) = sin(z) tries 
to follow a deeply-ingrained mathematical convention, while R.<z> is 
defining new notation.

Jason


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