/*-*-macsyma-*-*/
base(pol):=if atom(pol) or inpart(pol,0) # "^" then pol else inpart(pol,1)$

rateigenvectors(mat,[var]):=
     block([scalarmatrixp:false,
	    listarith:algebraic:inflag:true,
	    ans:[],
	    tellrats:tellrat(),
	    id:ident(length(mat))],
	   var:if var=[] then 'lambda else var[1],
	   for pol in 'false*factor(charpoly(mat,var)) do
	    if not(freeof(var,pol))
	     then (rat(base(pol),var),
		   tellrat(%%/coeff(%%,var,hipow(%%,var))),
		   ans:cons(cons(pol,args(transpose(%rateig(echelon(mat-var*id),id)))),
			    ans)),
	   apply('tellrat,tellrats),
	   ans)$

%rateig(mat,id):=
      if mat=-mat then id
 else if mat*id=id then zeromatrix(length(mat),0)
 else if mat[1,1]=0 then addcol(col(id,1),
				 (id:submatrix(id,1))
				.
				 %rateig(submatrix(rest(mat,-1),1),
					 rest(id)))
 else  addrow(matrix(-rest(mat[1])),id:submatrix(1,id,1))
      .
       %rateig(submatrix(1,mat,1),id)$