BPASRecursivePolynomial.hpp

#ifndef _BPAS_RECURSIVE_POLY_H_
#define _BPAS_RECURSIVE_POLY_H_

#include "BPASMultivarPolynomial.hpp"

/**
 * An abstract class defining the interface of a multivariate polynomial that can be viewed recursively.
 * That is, it can be viewed as a univariate polynomial with multivariate polynomial coefficients.
 */
template <class Ring, class Derived>
class BPASRecursivelyViewedPolynomial : public virtual BPASMultivariatePolynomial<Ring,Derived>
{
    public:

        /**
         * Get the initial, or leading coefficient, with respect to the main variable of
         * this polynomial.
         *
         * @return the initial of this polynomial.
         */
        virtual Derived initial() const = 0;

        /**
         * Get the main variable of this polynomial, that is, the one
         * which is most significant under its variable ordering.
         *
         * @return the main variable of the polynomial.
         */
        virtual Symbol mainVariable() const = 0;

        /**
         * Get the main degree of this polynomial, that is, the
         * partial degree of the main variable.
         *
         * @return the main degree of the polynomial.
         */
        virtual int mainDegree() const = 0;

        /**
         * Get the rank of this polynomial, that is, the
         * main variable of this polynomial raised to the main degree.
         * This this returns a monomial.
         *
         * @return the rank of this polynomial.
         */
        virtual Derived rank() const = 0;

        /**
         * Get the tail of this polynomial, that is,
         * this polynomial after removing its leading term.
         * It is equivalent to the reductum of this polynomial, viewing
         * it as a univariate polynomial in its main variable.
         *
         * @return the tail of this polynomial.
         */
        virtual Derived tail() const = 0;

        /**
         * Get the head of this polynomial, that is,
         * the leading term of this polynomial.
         * It is equivalent to the initial of this polynomial
         * multiplied by its rank.
         *
         * @return the head of this polynomial.
         */
        virtual Derived head() const = 0;

        /**
         * Get the separant of this polynomial, that is,
         * its derivative with respect to the main variable.
         *
         * @return the separant of this polynomial.
         */
        virtual Derived separant() const = 0;

        // virtual SparseUnivariatePolynomial<Derived> convertToSUP() const = 0;

};

#endif