function [ismag, whynot] = ismagic(square)
%  function [ismag, whynot] = ismagic(square)
%  square: square to be checked for "magicness"
%  ismag: 1 if magical, 0 if not
%  whynot: if ismag == 0, then
%    whynot returns the reason why ismagic fails
%    whynot = 1 : not all elements from 1 to n^2 uniquely used.
%           = 2 : not all rows and columns add up to the same number

dim = size(square,1);
elems = unique(square);
nelems = length(elems);
if ( ~(elems(1) == 1 & elems(nelems) == nelems & nelems == size(square,1)^2) )
	whynot = 1;
	ismag = 0;
	return;	
end
colsums = unique(sum(square,1));
rowsums = unique(sum(square,2));
diagsums = unique([sum(diag(square)), sum(diag(rot90(square)))]);
if ( ~(length(colsums) == 1 & length(rowsums) == 1 & length(diagsums) == 1) )
	whynot = 2;
	ismag = 0;
	return;
end
if ( ~(colsums == rowsums & colsums == diagsums) )
	whynot = 2;
	ismag = 0;
	return;
end
ismag = 1;
whynot = [];
return;