BPASMultivarPolynomial.hpp

#ifndef _BPAS_MULTIVAR_POLYNOMIAL_H_
#define _BPAS_MULTIVAR_POLYNOMIAL_H_


#include "BPASPolynomial.hpp"
#include <vector>


/**
 * An abstract class defining the interface of a multivariate polynomial over an arbitrary BPASRing.
 *
 * This class is automatically determined to be an integral domain, GCD domain, etc.
 * depending on the template specialization of Ring.
 */
template <class Ring, class Derived>
class BPASMultivariatePolynomial : public virtual BPASPolynomial<Ring, Derived>
{
    // Monomials are the abelian free monoid generated by Symbols
    public:
        // virtual void setPolynomialRing(const std::vector<Symbol>& v) = 0;
        // virtual std::vector<Symbol> polynomialRing() = 0;


        /**
         * Differentiate this polynomial, with respect to a particular
         * variable, setting itself to its derivative.
         *
         * @param var: the variable to derive with respect to.
         */
        virtual void differentiate(const Symbol& var) = 0;

        /**
         * Differentiate this polynomial k times, with respect to a particular
         * variable, setting itself to its derivative.
         *
         * @param var: the variable to derive with respect to.
         * @param k: the number of times to differentiate.
         */
        virtual void differentiate(const Symbol& var, int k) = 0;

        /**
         * Differentiate this polynomial, with respect to a particular
         * variable, setting itself to its derivative.
         *
         * @param var: the variable to derive with respect to.
         *
         * @return the derivative.
         */
        virtual Derived derivative(const Symbol&) const = 0;

        /**
         * Differentiate this polynomial k times, with respect to a particular
         * variable, setting itself to its derivative.
         *
         * @param var: the variable to derive with respect to.
         * @param k: the number of times to differentiate.
         *
         * @return the derivative.
         */
        virtual Derived derivative(const Symbol&, int) const = 0;

        // TODO
        // virtual void integrate(const Symbol&) = 0;
        // virtual void integrate(const Symbol&, int) = 0;
        // virtual Derived integral(const Symbol&) const = 0;
        // virtual Derived integral(const Symbol&, int) const = 0;

        /**
         * Evaluate this polynomial by substituting the input ring
         * elements elems for the variables vars, such that
         * vars[i] = elems[i].
         *
         * @param n: the size of the vars and elems arrays.
         * @param vars: the variables to evaluate.
         * @param elems: the ring elements to substitute for the varibales.
         * @return the evaluation of this polynomial for the variables in vars.
         */
        virtual Derived evaluate(int n, const Symbol* vars, const Ring* elems) const = 0;

        /**
         * Evaluate this polynomial by substituting the input ring
         * elements elems for the variables vars, such that
         * vars[i] = elems[i].
         *
         * @param vars: the variables to evaluate.
         * @param elems: the ring elements to substitute for the varibales.
         * @return the evaluation of this polynomial for the variables in vars.
         */
        virtual Derived evaluate(const std::vector<Symbol>& vars, const std::vector<Ring>& elems) const = 0;

        /**
         * Get the number of variables in this multivariate polynomial
         * which have positive degree.
         *
         * @return the number of variables.
         */
        virtual int numberOfVariables() const = 0;

        /**
         * Get the number of variables defined for the poylnomial ring of this
         * polynomial, that is, in the ambient space of this polynomial.
         *
         * @return the number variables in the polynomial ring of this polynomial.
         */
        virtual int numberOfRingVariables() const = 0;

        /**
         * Get the partial degree of this polynomial with respect to
         * the variable v.
         *
         * @return the partial degree w.r.t to variable v.
         */
        virtual Integer degree(const Symbol& v) const = 0;

        // virtual unsigned int degree(const Symbol& v) const = 0;

        /**
         * Get the coefficient of this polynomial with respect to the
         * monomial defined by exponent vector exps of size n.
         * The exponent vector should be defined over all variables in the
         * polynomial ring.
         *
         * @param n: the size of the exponent vector
         * @param exps: the exponent vector
         */
        virtual Ring coefficient(int n, const int* exps) const = 0;

        /**
         * Get the coefficient of this polynomial with respect to the
         * monomial defined by exponent vector exps.
         * The exponent vector should be defined over all variables in the
         * polynomial ring.
         *
         * @param exps: the exponent vector
         */
        virtual Ring coefficient(const std::vector<int>& exps) const = 0;


        /**
         * Set the coefficient of this polynomial for the
         * monomial defined by exponent vector exps, of size n, to r.
         * The exponent vector should be defined over all variables in the
         * polynomial ring.
         *
         * @param n: the size of the exponent vector
         * @param exps: the exponent vector
         * @param r: the ring element to set as coefficient.
         */
        virtual void setCoefficient(int n, const int*, const Ring& r) = 0;

        /**
         * Set the coefficient of this polynomial for the
         * monomial defined by exponent vector exps to r.
         * The exponent vector should be defined over all variables in the
         * polynomial ring.
         *
         * @param exps: the exponent vector
         * @param r: the ring element to set as coefficient.
         */
        virtual void setCoefficient(const std::vector<int>& v, const Ring& r) = 0;

        /**
         * Set the variables in the polynomial ring to xs.
         * This can change be used to change the symbols of the variables
         * as well as to increase or decrease the dimension of this polynomial ring.
         * On a decrease, this polynomial may be invalidated if it has
         * positive degree in a variable being removed.
         *
         * @param xs: the vector of new symbols for the polynomial ring.
         */
        virtual void setRingVariables (const std::vector<Symbol>& xs) = 0;


        /**
         * Get all the variables in the polynomial ring.
         *
         * @return a vector of all the variables in this polynomial's ring.
         */
        virtual std::vector<Symbol> ringVariables() const = 0;

        /**
         * Get all the variables in this polynomial with positive degree.
         *
         * @return a vector of all the variables in this polynomial with positive degree.
         */
        virtual std::vector<Symbol> variables() const = 0;

        // virtual Derived content(const std::vector<Symbol>& v) const = 0;
        // virtual Derived primitivePart(const std::vector<Symbol>& v) const = 0;
        // virtual Derived primitivePart(const std::vector<Symbol>& v, Derived& content) const = 0;
};




#endif