function [U,d]=Uconj_jac(dig,n)
%UCONJ_JAC The Stenger conjecture.  
%   Tests the validity of the Stenger U-onjecture for
%   a Jacobi weight function

global a b ab0 ab00 
m=ceil((n+a)/2);
C=zeros(n);
ab0n=ab0(1:n,:); ab00m=ab00(1:m,:); 
xw0n=gauss(n,ab0n); x0n=xw0n(:,1);
xw00m=gauss(m,ab00m); x00m=xw00m(:,1); w00m=xw00m(:,2);
for j=1:n
  cn=x0n(j);
  const=((1+cn)/2)^(a+b+1);
  for k=1:n
    s=0;
    for i=1:m
      x=((1+cn)/2)*x00m(i)-((1-cn)/2);
      lag=lagrange(n,x0n,x);
      s=s+w00m(i)*lag(k)*((3-cn)/(1+cn)-x00m(i))^a;
    end
    C(j,k)=const*s;
  end
end
%C
if n==5
  for k=1:5
    PS=prestable(C,k);
  end
  disp('C is prestable for n=5')
end
digits(dig);
D=zeros(n);
U=vpa(C);
d=eig(U);
d=double(d);
U=double(U);
