Abelian.hpp

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#pragma once
#include "Utility/General.hpp"
 
 
namespace mackey
{
    template<typename T>
    class AbelianGroup {
    public:
 
        T group;
 
        AbelianGroup() = default;
 
        AbelianGroup(const T& a);
 
        bool istrivial() const;
 
        bool iscyclic() const;
 
        auto operator[](int i) const;
 
        auto& operator[](int i);
 
        int number_of_summands() const;
 
        bool operator == (const AbelianGroup<T>& G) const;
 
        bool operator != (const AbelianGroup<T>& G) const;
 
        AbelianGroup<T> operator+(const AbelianGroup<T>& G) const;
 
        int order() const;
 
        int order(const T& element) const;
 
        template<typename Scalar>
        void normalize(Eigen::Matrix<Scalar, -1, -1>& linmap) const;
 
        void normalize(T& element) const;
 
        auto span(const T& a, const std::vector<T>& b) const;
 
        int isMultiple(const T& a, const T& b) const;
 
        std::pair <std::vector<dense_t<T>>, std::vector<dense_t<T>>> all_automorphisms() const;
 
    private:
        void mod_normalize(T& element) const;
 
        template<typename S>
        bool check_isomorphism_p_group(int p, const S& a) const;
 
        std::vector<dense_t<T>> aut_p_group(int p) const;
 
        std::vector<dense_t<T>> inverses(const std::vector<dense_t<T>>& isos) const;
 
        static std::vector<int> primes(int n);
 
        int is_p_group() const;
 
        template<typename S>
        friend std::ostream& operator<<(std::ostream& os, const AbelianGroup<S>& A);
    };
    
    template<typename T>
    std::ostream& operator<<(std::ostream& os, const AbelianGroup<T>& A);
}
#include "impl/Abelian.ipp"