1.2.15 `sm1.appell1'
--------------------

sm1.appell1(A|proc=P)
     ::  Returns the Appell hypergeometric system F_1 or F_D.

RETURN
     List

P
     Number

A
     List

   * Returns the hypergeometric system for the Lauricella function
     F_D(a,b1,b2,...,bn,c;x1,...,xn) where A =(a,c,b1,...,bn).  When
     n=2, the Lauricella function is called the Appell function F_1.
     The parameters a, c, b1, ..., bn may be rational numbers.

   * It does not call sm1 function appell1. As a concequence, when
     parameters are rational or symbolic, this function also works as
     well as integral parameters.


     [281] sm1.appell1([1,2,3,4]);
     [[((-x1+1)*x2*dx1-3*x2)*dx2+(-x1^2+x1)*dx1^2+(-5*x1+2)*dx1-3,
       (-x2^2+x2)*dx2^2+((-x1*x2+x1)*dx1-6*x2+2)*dx2-4*x1*dx1-4,
       ((-x2+x1)*dx1+3)*dx2-4*dx1],       equations
      [x1,x2]]                            the list of variables

     [282] sm1.gb(@);
     [[((-x2+x1)*dx1+3)*dx2-4*dx1,((-x1+1)*x2*dx1-3*x2)*dx2+(-x1^2+x1)*dx1^2
       +(-5*x1+2)*dx1-3,(-x2^2+x2)*dx2^2+((-x2^2+x1)*dx1-3*x2+2)*dx2
       +(-4*x2-4*x1)*dx1-4,
       (x2^3+(-x1-1)*x2^2+x1*x2)*dx2^2+((-x1*x2+x1^2)*dx1+6*x2^2
      +(-3*x1-2)*x2+2*x1)*dx2-4*x1^2*dx1+4*x2-4*x1],
      [x1*dx1*dx2,-x1^2*dx1^2,-x2^2*dx1*dx2,-x1*x2^2*dx2^2]]

     [283] sm1.rank(sm1.appell1([1/2,3,5,-1/3]));
     3

     [285] Mu=2$ Beta = 1/3$
     [287] sm1.rank(sm1.appell1([Mu+Beta,Mu+1,Beta,Beta,Beta]));
     4

