%==========================================================================
%
%       Labeled groups with a fixed identity.
%       Is enumerated by EIS A058163 (1,1,1,4,6,80,120,2760,7560,108864,...)
%
% See also:
%
% http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A058163
% http://www.iki.fi/~kartturi/matikka/ModFin/
%
% http://arp.anu.edu.au/~jks/finder.html
%
%==========================================================================

sort {
        int
        cardinality = 4
}


function i: int -> int.      % Inverse of each element.

function o: int,int -> int   % The group composition.
{
        row_bijective
        column_bijective
        no_priority
}




clause {
        o(x,0) = x.                 % Right-mult with neutral elem fixes.
        o(0,x) = x.                 % Left-mult with neutral elem fixes.
        o(x,i(x)) = 0.              % Right-mult with inverse gives neutral.
        o(i(x),x) = 0.              % Left-mult with inverse gives neutral.
        o(x,o(y,z)) = o(o(x,y),z).  % The composition is associative.
}

setting {
        verbosity stats: full
        stack: maximal
}


end