PYTHON program not work

[robmio]

Thanks so much for your reply, Albert. Reflecting on the algorithm for the calculation of CDF_Roy, the obstacle is in the calculation of the determinant. The result varies according to the precision with which the values of the matrix “A” are calculated. For example: to obtain the true result of “CDF_Roy (8,15,5,0.959)”, it would take a calculation precision comprising several hundred values after the decimal point. In short, the values that make up the matrix "A" should have at least 100 or more decimal precision, so that the right result is obtained.
Even using your suggestion, which consists in calculating the beta function with continuous fractions and with “loggamma”, the problem arises again in the calculation of the determinant of the matrix “A” (see "RETURN √(DET(A));" at the bottom of the algorithm).

Code:

#cas
CDF_Roy(s,m,n,theta):=
BEGIN
LOCAL A, ii, j, b, a, adzero, aa, cc;
A:=MAKEMAT(0,s,s);
b:=MAKELIST(0,x,1,s);
cc(x):=sqrt(π)*Gamma((2*m+2*n+s+x+2)/
2)/(Gamma((2*m+x+1)/2)*Gamma((2*n+x+
1)/2)*Gamma(x/2));
FOR ii FROM 1 TO s DO
b:=REPLACE(b,ii,{(Beta(m+ii,n+1,theta)
^2)/2});
FOR j FROM ii TO s-1 DO
b:=REPLACE(b,j+1,{(m+j)/(m+j+n+1)*
b(j)-Beta(2*m+ii+j,2*n+2,theta)/
(m+j+n+1)});
a:=(Beta(m+ii,n+1,theta)*Beta(m+j+1,
n+1,theta)-2*b(j+1))*cc(ii)*
cc(j+1);
A:=REPLACE(A,{ii,j+1},[[a]]);
END;
END;
aa:={};
FOR ii FROM 1 TO s DO
aa:=CONCAT(aa,{Beta(m+ii,n+1,theta)*
cc(ii)});
END;
aa:=ListToMat(aa);
adzero:=MAKELIST(0,x,1,s+1,1);
adzero:=ListToMat(adzero);
IF odd(s)==1 THEN
A:=ADDCOL(A,aa,s+1);
A:=ADDROW(A,adzero,s+1);
END;
A:=A-TRN(A);
RETURN √(DET(A));
END;
#end

However, in this post, my question is: “how can I get the result of a program written with PYTHON in an HPPPL environment without going through 'the terminal'?”.
Best regards, Roberto