#include "axiom"

CyclicGroup(n:PositiveInteger,g:Symbol): Group with {
        1: %;
        
        coerce : % -> OutputForm;
        
        one?: % -> Boolean;
        
        coerce:Symbol -> %;

        genrtr: %;

} == add {
        Rep == Integer;

        import from Integer;
        1:% == per 0;

        genrtr: % == per (address@hidden);
        
        coerce(x:%):OutputForm ==  {
                zero? rep x => outputForm(address@hidden); 
                z where {import from Fraction Polynomial Integer; import from Polynomial Integer;
                        z:OutputForm := ((g::Polynomial Integer)::Fraction Polynomial Integer^(rep x))::OutputForm;
                }
        };


        coerce(x:Symbol):% ==  {
                x ~= g => error "wrong symbol";
                per (address@hidden);
        }
        
        
        (x:%) * (y:%): % == per addmod(rep x,rep y,n::Integer);
        
        (x:%) = (y:%): Boolean == rep x = rep y;
        
        one?(x:%):Boolean == zero? rep x;

        inv(x:%):% == { one? x => 1; per( n::Integer - rep x)};
        
}