Parent structures for Infinite Polynomials over rings with operators

File for the ring structure of Differential polynomials

This file contains all the parent structures for Differential polynomials and all the coercion associated classes. Mainly, this module provides the class DifferentialPolynomialRing_dense, which is the main parent class defining a ring of differential polynomials.

EXAMPLES:

sage: from dalgebra import *
sage: R.<y> = DifferentialPolynomialRing(QQ['x']) 
sage: x = R.base().gens()[0] 
sage: p = x^2*y[1]^2 - y[2]*y[1]; p
-y_2*y_1 + x^2*y_1^2
sage: R
Ring of operator polynomials in (y) over Differential Ring [[Univariate Polynomial Ring 
in x over Rational Field], (d/dx,)]
sage: p.derivative()
-y_3*y_1 - y_2^2 + 2*x^2*y_2*y_1 + 2*x*y_1^2

AUTHORS:

• Antonio Jimenez-Pastor (2021-05-19): initial version

dalgebra.rwo_polynomial.rwo_polynomial_ring.DifferentialPolynomialRing(base, *names, **kwds)

dalgebra.rwo_polynomial.rwo_polynomial_ring.DifferencePolynomialRing(base, *names, **kwds)

dalgebra.rwo_polynomial.rwo_polynomial_ring.is_RWOPolynomialRing(element)

Method to check whether an object is a ring of infinite polynomial with an operator.