function [Aeq,Beq,Ain,Bin] = abmetric(N)
% linear constraints for a metric on N points

% symmetry, d(x,x)=0
Aeq = zeros(0,N^2);
Beq = zeros(0,1);
rind = 0;
for i=1:N
  rind = rind+1;
  colii = coord2ind([i i],[N N]);
  Aeq(rind,colii) = 1;
  Beq(rind,1) = 0;
  for j=i+1:N
    rind = rind+1;
    colij = coord2ind([i j],[N N]);
    colji = coord2ind([j i],[N N]);
    Aeq(rind,colij) =  1;
    Aeq(rind,colji) = -1;
    Beq(rind,1) = 0;
  end
end

% triangle inequality
Ain = zeros(0,N^2);
Bin = zeros(0,1);
rind = 0;
for i=1:N
  for j=i+1:N
    for k=setdiff(1:N,[i j])
      rind = rind+1;
      colij = coord2ind([i j],[N N]);
      colik = coord2ind([i k],[N N]);
      colkj = coord2ind([k j],[N N]);
      Ain(rind,colij) =  1;
      Ain(rind,colik) = -1;      
      Ain(rind,colkj) = -1;            
      Bin(rind,1) = 0;      
    end
  end
end
% nonnegativity is enforced elsewhere
return