Symmetric_Basis.hpp

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#pragma once
#include "Polynomials.hpp"
#include "Generators.hpp"
 
 
namespace symmp
{
 
    template <class T = int64_t, class _deg = int64_t>
    struct StandardVariables : public std::vector<T>
    {
        using std::vector<T>::vector;
        typedef _deg deg_t; 
 
        deg_t degree() const;
 
        static std::string name(int i, int n);
 
        StandardVariables operator+(const StandardVariables &b) const;
 
        size_t operator()() const;
    };
 
    template <class T = int64_t, class _deg = int64_t>
    struct ElementarySymmetricVariables : public StandardVariables<T, _deg>
    {
        using StandardVariables<T, _deg>::StandardVariables;
        typedef _deg deg_t; 
 
        deg_t degree() const;
 
        static std::string name(int i, int n);
    };
 
    template <class spec_t, class orig_poly_t, class new_poly_t>
    class PolynomialBasis
    {
    public:
        new_poly_t operator()(orig_poly_t a) const;
 
        orig_poly_t operator()(const new_poly_t &a) const;
 
        PolynomialBasis(int num);
 
        const std::vector<orig_poly_t> &generators() const;
 
        const std::vector<typename new_poly_t::deg_t> &dimensions() const;
 
        const std::vector<std::string> &names() const;
 
        const int number_of_variables;
 
    protected:
        std::vector<orig_poly_t> _generators;
 
        std::vector<typename new_poly_t::deg_t> generator_dimensions;
 
        std::vector<std::string> generator_names;
 
    private:
        orig_poly_t compute_product(const typename new_poly_t::exp_t &exponent) const;
    };
 
    template <class x_poly_t, class e_poly_t>
    class SymmetricBasis : public PolynomialBasis<SymmetricBasis<x_poly_t, e_poly_t>, x_poly_t, e_poly_t>
    {
    public:
        SymmetricBasis(int num);
 
    private:
        using PolynomialBasis<SymmetricBasis<x_poly_t, e_poly_t>, x_poly_t, e_poly_t>::number_of_variables;
        using PolynomialBasis<SymmetricBasis<x_poly_t, e_poly_t>, x_poly_t, e_poly_t>::_generators;
        typedef typename x_poly_t::exp_t x_t;
        typedef typename e_poly_t::exp_t e_t;
        x_poly_t get_elementary_symmetric(int i) const;
        auto find_exponent(const x_t &term) const -> e_t;
 
        friend class PolynomialBasis<SymmetricBasis<x_poly_t, e_poly_t>, x_poly_t, e_poly_t>;
    };
}
#include "impl/Symmetric_Basis.ipp"