FORM 4.0 (Jun 30 2012) 64-bits                   Run: Sat Aug  3 17:45:52 2013
    *   Title:  SMALL CHARGED SPHERE:  denominators
    *    File:  denoms.frm
    *  Author:  David N. Williams
    * License:  Creative Commons Attribution-Share Alike
    * Started:  November 8, 1987 (Schoonschip)
    *           July 8, 2012     (Form)
    * Revised:  July 8,9,28, 2012
    *
    * All parts of this program not in the public domain are:
    *
    *   Copyright (C) 1987, 2012 David N. Williams
    *
    * This work is licensed under the Creative Commons Attribution-
    * Share Alike 2.5 License.  To view a copy of this license, visit
    * http://creativecommons.org/licenses/by-sa/2.5/ or send a letter
    * to Creative Commons, 543 Howard Street, 5th Floor, San
    * Francisco, California, 94105, USA.
    *
    *   Input:  RdotU from rdotu.frm
    *  Output:  [1/RdotU^2], [1/RdotU^3] in denoms.sav
    *
    * We need two orders in [1/RdotU^2] and three in [1/RdotU^3] to
    * get the leading nonsingular term in the Lorentz force.
    
    *** DECLARATIONS
    
    off statistics;
    
    S eps;
    S c,snorm;
    V u,a,j,n;
    T d1y,d2y,d3y,d1u,d2u,d1a;
    Load rdotu.sav;
 RdotU loaded
    S x,i;
    
    *** MODULES
    
    * need 2 orders for leading nonsingular term
    * G [1/RdotU^2] = sum_(i,0,1,sign_(i)*x^i*binom_(2-1+i,i));
    G [1/RdotU^2] = 1 - 2*x;
    Id x = RdotU*eps^-1*snorm^-1*c^-1 - 1;
    Id eps^2 = 0;
    
    multiply eps^-2*snorm^-2*c^-2;
    
    .sort
    
    hide [1/RdotU^2];
    
    * need 3 orders for leading nonsingular term
    * G [1/RdotU^3] = sum_(i,0,2,sign_(i)*x^i*binom_(3-1+i,i));
    G [1/RdotU^3] = 1 - 3*x + 6*x^2;
    Id x = RdotU*eps^-1*snorm^-1*c^-1 - 1;
    Id eps^3 = 0;
    
    multiply eps^-3*snorm^-3*c^-3;
    .sort
    
    unhide [1/RdotU^2];
    b eps,snorm;
    print +s;
    .store

   [1/RdotU^2] =

       + eps^-2*snorm^-2 * (
          + c^-2
          )

       + eps^-1*snorm^-4 * (
          + d1y(u,n)*d1y(u,n)*d1y(a,n)*c^-6
          - 2*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-4
          - d1y(u,n)*d2y(u,n,n)*c^-4
          + d1y(N1_?,n)*d2y(N1_?,n,n)*c^-2
          )

       + eps^-1*snorm^-2 * (
          - d1y(a,n)*c^-4
          );

   [1/RdotU^3] =

       + eps^-3*snorm^-3 * (
          + c^-3
          )

       + eps^-2*snorm^-5 * (
          + 3/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*c^-7
          - 3*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-5
          - 3/2*d1y(u,n)*d2y(u,n,n)*c^-5
          + 3/2*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-3
          )

       + eps^-2*snorm^-3 * (
          - 3/2*d1y(a,n)*c^-5
          )

       + eps^-1*snorm^-7 * (
          + 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-11
          - 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*
         c^-9
          - 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-9
          + 15/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-7
          + 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(
         N2_?,n)*c^-7
          + 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-7
          + 15/8*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*c^-7
          - 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)*
         c^-5
          - 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)*
         c^-5
          - 15/4*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*c^-5
          + 15/8*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)*c^-3
          )

       + eps^-1*snorm^-6 * (
          - 3/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)*c^-4
          + 3/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)*c^-4
          )

       + eps^-1*snorm^-5 * (
          - 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*a.a*c^-11
          - 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*c^-9
          - 15/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*c^-9
          + 3/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*c^-7
          + 3/4*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*c^-7
          + 15/2*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*c^-7
          + 15/4*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*c^-7
          - 3/2*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*c^-5
          - 3/2*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*c^-5
          - 1/2*d1y(u,n)*d3y(u,n,n,n)*c^-5
          - 9/4*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*c^-5
          - 3/2*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*c^-5
          - 3/2*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*c^-5
          + 1/2*d1y(N1_?,n)*d3y(N1_?,n,n,n)*c^-3
          - 3/8*d2y(u,n,n)*d2y(u,n,n)*c^-5
          + 3/8*d2y(N1_?,n,n)*d2y(N1_?,n,n)*c^-3
          )

       + eps^-1*snorm^-3 * (
          + 3/4*d1y(u,n)*d1y(u,n)*a.a*c^-9
          + 3/2*d1y(u,n)*d1y(j,n)*c^-7
          + 15/8*d1y(a,n)*d1y(a,n)*c^-7
          - 3/2*d1y(N1_?,n)*d1a(N1_?,n)*c^-5
          - 3/4*d2y(a,n,n)*c^-5
          )

       + eps^-1*snorm^-2 * (
          + d1y(u,n)*a.a*c^-8
          + d1y(j,n)*c^-6
          )

       + eps^-1*snorm^-1 * (
          + 3/8*a.a*c^-7
          );

    
    save denoms.sav [1/RdotU^2],[1/RdotU^3];
    .end
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