function [U,d]=sConj_lag(n)
%SCONJ_LAG The Stenger conjecture.  
%   Tests the validity of the Stenger conjecture for
%   a Laguerre weight function in variable-precision
%   arithmetic

global dig a ab0 ab1
digits(dig); sym0=vpa(0); 
m1=ceil(n/2);
m0=ceil((n+double(a))/2);
if m0>75, error('a exceeds 75'); end
U=vpa(zeros(n));
ab1n=ab1(1:n,:); 
ab0m=ab0(1:m0,:); ab1m=ab1(1:m1,:);
xw1n=sgauss(dig,n,ab1n); x1n=xw1n(:,1);
xw0m=sgauss(dig,m0,ab0m); x0m=xw0m(:,1); w0m=xw0m(:,2);
xw1m=sgauss(dig,m1,ab1m); x1m=xw1m(:,1); w1m=xw1m(:,2);
for j=1:n
  for k=1:n
    s1=sym0;
    for i=1:m1
      x=x1m(i);
      lag=slagrange(dig,n,x1n,x);
      s1=s1+w1m(i)*lag(k);
    end
    s0=sym0;
    for i=1:m0
      x=x1n(j)+x0m(i);
      lag=slagrange(dig,n,x1n,x);
      s0=s0+w0m(i)*lag(k)*x^a;
    end 
    U(j,k)=s1-exp(-x1n(j))*s0;
  end
end
d=eig(U);
