On Wednesday, February 28, 2018 at 2:42:26 PM UTC, Ralf Stephan wrote:
>
> It might not be necessary to (re)assign the global variable. Only if the
> user wants to do operations with the polynomial he wants an x to be that
> poly variable, and certainly not another x. So, the parser can do the part
> of figuring out what x is meant, maybe by checking all generator names.
> Example:
>
> sage: ....charpoly()
> x + 1
> sage: _ - x
> (parser sees underscore and operation, and an unassigned global, so it
> checks the object referred by the underscore for variable names)
>
I don't think this would be a job for the parser. You'd want x bound to
something like "UniversalCoercingNamedGenerator('x')" which would be an
object that happily coerces into any parent P via essentially P('x'), but
it could do something more fancy.
In order for 1+UniversalCoercingNamedGenerator('x') to work some more
magic for finding common covering parents would be necessary. Mind you:
you'd end up with a polynomial over ZZ then, not a symbolic expression. For
that you'd need
sin(1)+UniversalCoercingNamedGenerator('x')-sin(1)+1
It could be a fun exercise to write such an object, and I think it would be
possible. However, I wouldn't be in favour of including it in sage. Its
behaviour would be too magical to be reliable for a medium to expert level
user, and a novice would probably be able to find all kinds of unexpected
edge cases.
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