Half_Idempotent.hpp

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#pragma once
#include "Symmetric_Basis.hpp"
#include <sstream>
 
 
namespace symmp
{
 
    template <class T, size_t N = 0>
    struct ArrayVectorWrapper;
 
    template <class T = int64_t, class _deg = int64_t, size_t N = 0>
    struct HalfIdempotentVariables : public ArrayVectorWrapper<T, N>
    {
        using ArrayVectorWrapper<T, N>::ArrayVectorWrapper;
 
        HalfIdempotentVariables operator+(const HalfIdempotentVariables &b) const;
 
        HalfIdempotentVariables operator-(const HalfIdempotentVariables &b) const;
 
        typedef _deg deg_t; 
 
        deg_t degree() const;
 
        static std::string name(int i, int num);
 
        size_t operator()() const;
    };
 
    template <class T = int64_t, class _deg = int64_t>
    struct TwistedChernVariables : public std::vector<T>
    {
        using std::vector<T>::vector;
        typedef _deg deg_t; 
 
        TwistedChernVariables operator+(const TwistedChernVariables &b) const;
 
        size_t operator()() const;
    };
 
    template <class xy_poly_t, class chern_poly_t>
    class TwistedChernBasis : public PolynomialBasis<TwistedChernBasis<xy_poly_t, chern_poly_t>, xy_poly_t, chern_poly_t>
    {
    public:
        TwistedChernBasis(int n);
 
        const std::vector<chern_poly_t> &relations() const;
 
        const xy_poly_t &generator(int s, int j) const;
 
        friend class PolynomialBasis<TwistedChernBasis<xy_poly_t, chern_poly_t>, xy_poly_t, chern_poly_t>;
 
    private:
        typedef typename xy_poly_t::exp_t xy_t;
        typedef typename chern_poly_t::exp_t chern_t;
        using PolynomialBasis<TwistedChernBasis<xy_poly_t, chern_poly_t>, xy_poly_t, chern_poly_t>::_generators;
        using PolynomialBasis<TwistedChernBasis<xy_poly_t, chern_poly_t>, xy_poly_t, chern_poly_t>::generator_names;
        using PolynomialBasis<TwistedChernBasis<xy_poly_t, chern_poly_t>, xy_poly_t, chern_poly_t>::generator_dimensions;
 
        const int n;                    //Half the variable number
        const int number_of_generators; //Number of c_{s,j}
        std::vector<chern_poly_t> _relations;
 
        //Takes (s,j) to the index in the _generators vector
        std::map<std::array<int, 2>, int> generator_double_index;
        //Transforms index (s,j) of c_{s,j} into the corresponding index in the generators vector.
        int index(int s, int j) const;
        auto create_generator(int s, int i);
        void set_generators();
        void set_relations();
        auto find_exponent(const xy_t &term) const;
        void find_exponent_recursive(const xy_t &term, chern_t &exponent) const;
    };
 
    template <class xy_poly_t, class chern_poly_t>
    void print_half_idempotent_relations(int n, bool print = 1, bool verify = 1, bool verify_verbose = 1);
 
}
#include "impl/Half_Idempotent.ipp"