funcprot(0)

function [x]=degreebound1(a)
  [m,n] = size(a);
  if m~=n then
    error("This matrix can not be accepted!");
  end;
  b=degree(a); 
  [i,j]=find(a==0);
  for k=1:n,
    cols=j(k==i);
    if size(cols,2)==n then
      x=-%inf;
      return;
    end;
    b(k,cols)=-%inf;
  end;
  for k=1:n,
    cols=i(k==j);
    if size(cols,2)==n then
      x=-%inf;
      return;
    end;
    b(cols,k)=-%inf;
  end;
  maxb=max(b);
  c=maxb*ones(m,n)-b;
  f=hungarian(c);
  x=sum(b(mtlb_logical(sparse([f;1:n]',ones(1,n)))));
endfunction

function [x]=degreebound2(a)
  n=size(a,1);
  d=max(degree(a));
  nd=n*d;
  nd0=n*(d-1);
  u=zeros(nd,nd);
  v=zeros(nd,nd);
  for i=1:nd0,
     u(i,i+n)=1;
  end;
  for i=1:nd0,
     v(i,i)=1;
  end;
  [qs,rs,es]=qr(coeff(a,d));	
  for j=0:d-1,
    f=qs'*coeff(a,j)*es;
    u(nd0+[1:n],j*n+[1:n])=-f(:,:);
  end;
  v(nd0+[1:n],nd0+[1:n])=rs(:,:);
  [alpha,beta]=spec(u,v);
  x=[nd,size(find(beta<>0),2)];
endfunction