1.1.2 `dsolv_starting_term'
---------------------------

dsolv_starting_term(F,V,W)
     ::  Find the starting term of the solutions of the regular
     holonomic system F to the direction W.

RETURN
     List

F, V, W
     List

   * Find the starting term of the solutions of the regular holonomic
     system F to the direction W.

   * The return value is of the form [[E1, E2, ...],  [S1, S2, ...]]
     where E1 is an exponent vector and S1 is the corresponding
     solution set, and so on.

   * If you set `Dsolv_message_starting_term' to 1, then this function
     outputs messages during the computation.

Algorithm: Saito, Sturmfels, Takayama, Grobner Deformations of
Hypergeometric Differential Equations ([SST]), Chapter 2.

     [1076]   F = sm1_gkz( [ [[1,1,1,1,1],[1,1,0,-1,0],[0,1,1,-1,0]], [1,0,0]]);
     [[x5*dx5+x4*dx4+x3*dx3+x2*dx2+x1*dx1-1,-x4*dx4+x2*dx2+x1*dx1,
       -x4*dx4+x3*dx3+x2*dx2,
       -dx2*dx5+dx1*dx3,dx5^2-dx2*dx4],[x1,x2,x3,x4,x5]]
     [1077]  A= dsolv_starting_term(F[0],F[1],[1,1,1,1,0])$
     Computing the initial ideal.
     Done.
     Computing a primary ideal decomposition.
     Primary ideal decomposition of the initial Frobenius ideal
     to the direction [1,1,1,1,0] is
     [[[x5+2*x4+x3-1,x5+3*x4-x2-1,x5+2*x4+x1-1,3*x5^2+(8*x4-6)*x5-8*x4+3,
        x5^2-2*x5-8*x4^2+1,x5^3-3*x5^2+3*x5-1],
      [x5-1,x4,x3,x2,x1]]]

     ----------- root is [ 0 0 0 0 1 ]
     ----------- dual system is
     [x5^2+(-3/4*x4-1/2*x3-1/4*x2-1/2*x1)*x5+1/8*x4^2
      +(1/4*x3+1/4*x1)*x4+1/4*x2*x3-1/8*x2^2+1/4*x1*x2,
      x4-2*x3+3*x2-2*x1,x5-x3+x2-x1,1]

     [1078] A[0];
     [[ 0 0 0 0 1 ]]
     [1079] map(fctr,A[1][0]);
     [[[1/8,1],[x5,1],[log(x2)+log(x4)-2*log(x5),1],
               [2*log(x1)-log(x2)+2*log(x3)+log(x4)-4*log(x5),1]],
      [[1,1],[x5,1],[-2*log(x1)+3*log(x2)-2*log(x3)+log(x4),1]],
      [[1,1],[x5,1],[-log(x1)+log(x2)-log(x3)+log(x5),1]],
      [[1,1],[x5,1]]]

