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You declare R.<x>=RR[] but this invokes the normal polynomial ring with positive integer exponents.
You should use symbolics for your numeric purposes, as tmonteil has shown to you.
In fact, in mathematics there exist polynomial rings with other type of exponents:
- from ZZ: Laurent polynomials
from QQ: Puiseux polynomials
https://en.wikipedia.org/wiki/Polynomial_ring
- https://en.wikipedia.org/wiki/Laurent_polynomial
