%RUN_UCONJ_EXT_JAC

%Checks the extended Stenger conjecture for Jacobi
%polynomials

tic
global a b ab ab0 
%for b=[[-.9:.6:.9] [1.7:.7:3.8] [4.7:.9:7.4]]
for b=37/4
  ab0=r_jacobi(300,0,b); 
%  for a=[[-.9:.6:.9] [1.7:.7:3.8] [4.7:.9:7.4]]
  for a=b
    [a b]
    if a>10, error('a exceeds 10'); end
    ab=r_jacobi(30,a,b);
    for n=[5 15 30]
      if n>30, error('n exceeds 15'); end
      dig=32; [U,d]=Uconj_ext_jac(dig,n); 
      d
%      plot(d,'k*','MarkerSize',16);set(gca,'FontSize',24) 
      semilogx(d,'k*','MarkerSize',16);set(gca,'FontSize',24)
%      axis([10^(-3) 10 -.25 .25])
      for i=1:n
        if real(d(i))<=0, error('conjecture is false'); end
      end
      disp('conjecture is true')
    end
  end
end
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