Lanczos:=proc(p,alpha,beta,n)
  local k,q,x; p:=array(0..n); alpha:=array(1..n); beta:=array(1..n-1);
  p[0]:=1/ sqrt(2);
  alpha[1]:=int(x*p[0]*p[0],x=-1..1);
  q:=(x-alpha[1])*p[0];
  for k from 2 to n do
    beta[k-1]:=sqrt(int(q*q,x=-1..1));
    p[k-1]:=expand(q/beta[k-1]);
    alpha[k]:=int(x*p[k-1]*p[k-1],x=-1..1);
    q:=(x-alpha[k])*p[k-1]-beta[k-1]*p[k-2];
  od;
  RETURN(NULL);     # results are returned in the variables passed in
end;