Hi all!

On ticket http://trac.sagemath.org/ticket/9706 for the orthogonal 
Polynomials Jeroen Demeyer came up with the the idea of a 
SymbolicPolynomial class. I think that's a great idea, because, if well 
designed, such a class has much potential to give very much comfort to the 
handling of sage. Because many algorithms that deal with Polynomials have 
to be called from external programs and libraries.

I already have two things which should be added to such a class:

The // operator should enforce polynomial division and return the result, 
while the % operator should return the remainder of the division.
E.g:

(x^2 - 2)//(x+1) returns x-1 and (x^2 - 2) % (x+1) returns -1

+ we could add features for polynomial algebra

More input welcome 

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