FORM 4.0 (Jun 30 2012) 64-bits Run: Sat Aug 3 17:45:57 2013 * Title: SMALL CHARGED SPHERE: Lorentz force * F(mu,nu)*U(nu) leading regular order * File: lfreg.frm * Author: David N. Williams * License: Creative Commons Attribution-Share Alike * Started: November 7, 1987 (Schoonschip) * July 10, 2012 (Form) * Revised: July 10,28,29, 2012 * Revised: August 5, 2012 * * All parts of this program not in the public domain are: * * Copyright (C) 1987-1990, 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: TAU1, TAU2, TAU3 from dtau.sav * RdotA from rdota.sav * [1/RdotU^2], [1/RdotU^3] from denoms.sav * Output: lfreg in lfreg.sav *** DECLARATIONS * set to "1" to kill odd n terms in lfreg #define KILLODDN "0" OFF statistics; S eps; S c,snorm; V u,a,j,n; T d1y,d2y,d3y,d1u,d2u,d1a; T eta; Load dtau.sav; TAU1 loaded TAU2 loaded TAU3 loaded Load rdota.sav; RdotA loaded Load denoms.sav; [1/RdotU^2] loaded [1/RdotU^3] loaded S dtau; S [1/d^2],[1/d^3]; I mu,nu,la,l,m; CF R,U,A; CF [d1y*d1y]; S p; *** DEBUGGING #procedure try .sort B eps,snorm; print +s; .end #endprocedure *** MODULES * leading nonsingular order in this section: eps^3 L F(mu,nu) = ( R(mu)*U(nu) - R(nu)*U(mu) ) * [1/d^3] * ( c^2 - RdotA ) + ( R(mu)*A(nu) - R(nu)*A(mu) ) * [1/d^2]; Id R(mu?) = - d1y(mu,n)*eps - d2y(mu,n,n)*eps^2/2 - d3y(mu,n,n,n)*eps^3/6 - u(mu)*dtau - d1u(mu,n)*eps*dtau - d2u(mu,n,n)*eps^2*dtau/2 - a(mu)*dtau^2/2 - d1a(mu,n)*eps*dtau^2/2 - j(mu)*dtau^3/6; Id U(mu?) = u(mu) + d1u(mu,n)*eps + d2u(mu,n,n)*eps^2/2 + a(mu)*dtau + d1a(mu,n)*eps*dtau + j(mu)*dtau^2/2; Id A(mu?) = a(mu) + d1a(mu,n)*eps + j(mu)*dtau; Id eps^4 = 0; .sort * Lorentz force density G lfreg = F(mu,nu)*u(nu)/c; Id eps^4 = 0; Id eps^3 * dtau = 0; Id eps^2 * dtau^2 = 0; Id eps * dtau^3 = 0; Id dtau^4 = 0; Id u.u = c^2; Id u.a = 0; Id u.j = -a.a; Id d1u(u,l?) = 0; Id d1a(u,l?) = -d1u(a,l); Id, d2u(u,l?,m?) = -d1u(la,l)*d1u(la,m); Sum la; Id dtau = TAU1*eps + TAU2*eps^2 + TAU3*eps^3; Id eps^4 = 0; .sort Id [1/d^2] = [1/RdotU^2]; Id [1/d^3] = [1/RdotU^3]; .sort * kill superfluous order from RdotA Id eps = 0; * kill singular orders Id eps^-1 = 0; Id d1y(mu,n) = eta(mu,n) + d1y(u,n)*u(mu)*c^-2; .sort hide F; * kill odd powers of n #if `KILLODDN' if ( count(n,1) == 7 ) discard; if ( count(n,1) == 5 ) discard; if ( count(n,1) == 3 ) discard; if ( count(n,1) == 1 ) discard; #endif Id d1y(mu?,n)*d1y(nu?,n) = [d1y*d1y](mu,nu); .sort * kill symmetric times antisymmetric symmetrize [d1y*d1y]; Id [d1y*d1y](mu?,nu?) = d1y(mu,n)*d1y(nu,n); .sort unhide F; b eps,snorm; print +s; .store F(mu,nu) = + snorm^-7 * ( - 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n )*u(mu)*u(nu)*c^-11 + 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*d1y(nu, n)*u(mu)*c^-9 - 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*eta(mu, n)*u(nu)*c^-9 + 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u( N1_?,n)*u(mu)*u(nu)*c^-9 + 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*u(mu) *u(nu)*c^-9 - 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d1y(N1_?,n)* d1u(N1_?,n)*u(mu)*c^-7 - 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d2y(u,n,n)* u(mu)*c^-7 - 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n) *u(mu)*u(nu)*c^-7 + 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)* eta(mu,n)*u(nu)*c^-7 + 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*eta(mu,n)* u(nu)*c^-7 - 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n )*d1u(N2_?,n)*u(mu)*u(nu)*c^-7 - 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n) *u(mu)*u(nu)*c^-7 - 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*u(mu)*u(nu)* c^-7 + 15/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d1y(N1_?,n)*d2y(N1_?,n,n )*u(mu)*c^-5 - 15/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*eta(mu,n )*u(nu)*c^-5 + 15/2*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?, n)*d1u(N2_?,n)*u(mu)*c^-5 + 15/2*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n )*u(mu)*c^-5 + 15/8*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d2y(u,n,n)*d2y(u,n,n)*u(mu)*c^-5 + 15/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u( N2_?,n)*u(mu)*u(nu)*c^-5 + 15/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u( N1_?,n)*u(mu)*u(nu)*c^-5 - 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u( N2_?,n)*eta(mu,n)*u(nu)*c^-5 + 15/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*u(mu)* u(nu)*c^-5 - 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*eta(mu,n )*u(nu)*c^-5 - 15/8*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*eta(mu,n)*u(nu)*c^-5 - 15/4*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u( N2_?,n)*u(mu)*c^-3 - 15/4*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u( N1_?,n)*u(mu)*c^-3 - 15/4*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*u(mu) *c^-3 - 15/8*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)* u(mu)*u(nu)*c^-3 + 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* eta(mu,n)*u(nu)*c^-3 + 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* eta(mu,n)*u(nu)*c^-3 + 15/4*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*eta(mu,n)*u(nu) *c^-3 + 15/8*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n) *u(mu)*c^-1 - 15/8*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)*eta(mu,n) *u(nu)*c^-1 ) + snorm^-6 * ( + 3/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* u(mu)*u(nu)*c^-4 - 3/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* u(mu)*u(nu)*c^-4 - 3/4*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* u(mu)*c^-2 + 3/4*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* u(mu)*c^-2 + 3/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)*eta(mu,n)* u(nu)*c^-2 - 3/4*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)*eta(mu,n)* u(nu)*c^-2 ) + snorm^-5 * ( + 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*u(mu)*u(nu)*a.a* c^-11 + 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*u(mu)*a(nu)*c^-9 + 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*u(nu)*a(mu)*c^-9 + 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*u(mu)*u(nu)*c^-9 - 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(nu,n)*u(mu)*a.a*c^-9 + 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*eta(mu,n)*u(nu)*a.a*c^-9 + 9/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*u(mu)*u(nu)*c^-9 - 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(nu,n)*a(mu)*c^-7 - 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1u(nu,n)*u(mu)*c^-7 + 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*eta(mu,n)*a(nu)*c^-7 - 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*d1y(nu,n)*u(mu)*c^-7 + 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*eta(mu,n)*u(nu)*c^-7 - 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(mu)*a(nu) *c^-7 - 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(nu)*a(mu) *c^-7 - 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*u(mu)*u(nu) *c^-7 - 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*u(mu)*a(nu)*c^-7 - 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*u(nu)*a(mu)*c^-7 - 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*u(mu)*u(nu)*c^-7 - 9/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*d1y(nu,n)*u(mu)*c^-7 + 9/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*eta(mu,n)*u(nu)*c^-7 + 3/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d1u(mu,n)*c^-5 - 9/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(mu)*u(nu) *c^-7 - 9/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*u(mu)*u(nu)*c^-7 - 3/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(mu,n,n)*u(nu)*c^-5 + 3/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(nu,n,n)*u(mu)*c^-5 - 3/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1u(nu,n)*eta(mu,n)*c^-5 + 3*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1u(N1_?,n)*a(mu)*c^-5 + 3/2*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1a(N1_?,n)*u(mu)*c^-5 + 3/2*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d2y(u,n,n)*a(mu)*c^-5 + 3/4*d1y(u,n)*d1y(u,n)*d1y(nu,n)*d2y(a,n,n)*u(mu)*c^-5 + 3/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*u(mu)*a(nu)*c^-5 + 3/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*u(nu)*a(mu)*c^-5 + 3*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(nu,n)*d1u(N1_?,n)*u(mu)*c^-5 - 3*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*eta(mu,n)*a(nu)*c^-5 + 3/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*u(mu)*u(nu)*c^-5 - 3/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*eta(mu,n)*u(nu)*c^-5 + 3/2*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d1u(nu,n)*u(mu)*c^-5 - 3/2*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*eta(mu,n)*a(nu)*c^-5 - 3/4*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*eta(mu,n)*u(nu)*c^-5 + 3/2*d1y(u,n)*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*u(mu)*u(nu)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d3y(u,n,n,n)*u(mu)*u(nu)*c^-5 + 9/2*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(mu)*c^-5 + 9/4*d1y(u,n)*d1y(a,n)*d1y(nu,n)*d2y(u,n,n)*u(mu)*c^-5 + 3/4*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*u(mu)*u(nu)*c^-5 - 9/2*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*eta(mu,n)*u(nu)*c^-5 - 9/4*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*eta(mu,n)*u(nu)*c^-5 - 3/2*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*a(mu)*c^-3 - 3*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d1u(mu,n)*d1u(N1_?,n)*c^-3 - 3/2*d1y(u,n)*d1y(nu,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*u(mu)*c^-3 - 3/2*d1y(u,n)*d1y(nu,n)*d2y(u,n,n)*d1u(mu,n)*c^-3 - 3/2*d1y(u,n)*d1y(nu,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*u(mu)*c^-3 - 1/2*d1y(u,n)*d1y(nu,n)*d3y(u,n,n,n)*u(mu)*c^-3 + 3/2*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*u(mu) *u(nu)*c^-5 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*u(mu)*u(nu)*c^-5 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(mu,n,n)*d1u(N1_?,n)*u(nu)*c^-3 - 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(nu,n,n)*d1u(N1_?,n)*u(mu)*c^-3 - 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*d1u(nu,n)*u(mu)*c^-3 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*eta(mu,n)*a(nu)*c^-3 - 1/2*d1y(u,n)*d1y(N1_?,n)*d3y(N1_?,n,n,n)*u(mu)*u(nu)*c^-3 + 3*d1y(u,n)*d1y(N1_?,n)*d1u(nu,n)*d1u(N1_?,n)*eta(mu,n)*c^-3 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*eta(mu,n)*u(nu)*c^-3 + 3/8*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*u(mu)*u(nu)*c^-5 + 3/4*d1y(u,n)*d2y(u,n,n)*d2y(mu,n,n)*u(nu)*c^-3 - 3/4*d1y(u,n)*d2y(u,n,n)*d2y(nu,n,n)*u(mu)*c^-3 + 3/2*d1y(u,n)*d2y(u,n,n)*d1u(nu,n)*eta(mu,n)*c^-3 - 3/8*d1y(u,n)*d2y(N1_?,n,n)*d2y(N1_?,n,n)*u(mu)*u(nu)*c^-3 + 3/2*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*eta(mu,n)*u(nu)*c^-3 + 1/2*d1y(u,n)*d3y(u,n,n,n)*eta(mu,n)*u(nu)*c^-3 - 3/4*d1y(a,n)*d1y(nu,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*u(mu)*c^-3 + 3/4*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*eta(mu,n)*u(nu)*c^-3 - 3/2*d1y(nu,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)* u(mu)*c^-3 - 3/2*d1y(nu,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*u(mu)*c^-3 + 3/2*d1y(nu,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*d1u(mu,n)*c^-1 + 1/2*d1y(nu,n)*d1y(N1_?,n)*d3y(N1_?,n,n,n)*u(mu)*c^-1 - 3/8*d1y(nu,n)*d2y(u,n,n)*d2y(u,n,n)*u(mu)*c^-3 + 3/8*d1y(nu,n)*d2y(N1_?,n,n)*d2y(N1_?,n,n)*u(mu)*c^-1 + 3/2*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*eta(mu,n)* u(nu)*c^-3 + 3/2*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*eta(mu,n)*u(nu)*c^-3 - 3/4*d1y(N1_?,n)*d2y(mu,n,n)*d2y(N1_?,n,n)*u(nu)*c^-1 + 3/4*d1y(N1_?,n)*d2y(nu,n,n)*d2y(N1_?,n,n)*u(mu)*c^-1 - 3/2*d1y(N1_?,n)*d2y(N1_?,n,n)*d1u(nu,n)*eta(mu,n)*c^-1 - 1/2*d1y(N1_?,n)*d3y(N1_?,n,n,n)*eta(mu,n)*u(nu)*c^-1 + 3/8*d2y(u,n,n)*d2y(u,n,n)*eta(mu,n)*u(nu)*c^-3 - 3/8*d2y(N1_?,n,n)*d2y(N1_?,n,n)*eta(mu,n)*u(nu)*c^-1 ) + snorm^-3 * ( - 1/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*u(mu)*u(nu)*a.a*c^-9 - 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*u(mu)*j(nu)*c^-7 - 1/3*d1y(u,n)*d1y(u,n)*d1y(u,n)*u(nu)*j(mu)*c^-7 - 3/2*d1y(u,n)*d1y(u,n)*d1y(a,n)*u(nu)*a(mu)*c^-7 - 1/2*d1y(u,n)*d1y(u,n)*d1y(j,n)*u(mu)*u(nu)*c^-7 + 1/4*d1y(u,n)*d1y(u,n)*d1y(nu,n)*u(mu)*a.a*c^-7 + 1/2*d1y(u,n)*d1y(u,n)*d1y(nu,n)*j(mu)*c^-5 - 1/2*d1y(u,n)*d1y(u,n)*d1u(mu,n)*a(nu)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d1u(nu,n)*a(mu)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d1a(mu,n)*u(nu)*c^-5 + 1/2*d1y(u,n)*d1y(u,n)*d1a(nu,n)*u(mu)*c^-5 - 1/4*d1y(u,n)*d1y(u,n)*eta(mu,n)*u(nu)*a.a*c^-7 - 1/2*d1y(u,n)*d1y(u,n)*eta(mu,n)*j(nu)*c^-5 - 3/8*d1y(u,n)*d1y(a,n)*d1y(a,n)*u(mu)*u(nu)*c^-7 + 3/2*d1y(u,n)*d1y(a,n)*d1y(nu,n)*a(mu)*c^-5 + 1/2*d1y(u,n)*d1y(a,n)*d1u(nu,n)*u(mu)*c^-5 - 3/2*d1y(u,n)*d1y(a,n)*eta(mu,n)*a(nu)*c^-5 + 1/2*d1y(u,n)*d1y(j,n)*d1y(nu,n)*u(mu)*c^-5 - 1/2*d1y(u,n)*d1y(j,n)*eta(mu,n)*u(nu)*c^-5 - d1y(u,n)*d1y(nu,n)*d1a(mu,n)*c^-3 - 1/2*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(mu)*a(nu)*c^-5 + 3/2*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*u(nu)*a(mu)*c^-5 + 1/2*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*u(mu)*u(nu)*c^-5 - 1/4*d1y(u,n)*d2y(u,n,n)*u(mu)*a(nu)*c^-5 + 3/4*d1y(u,n)*d2y(u,n,n)*u(nu)*a(mu)*c^-5 + 1/4*d1y(u,n)*d2y(a,n,n)*u(mu)*u(nu)*c^-5 + 1/2*d1y(u,n)*d2y(mu,n,n)*a(nu)*c^-3 - 1/2*d1y(u,n)*d2y(nu,n,n)*a(mu)*c^-3 - 1/2*d1y(u,n)*d2u(nu,n,n)*u(mu)*c^-3 + d1y(u,n)*d1a(nu,n)*eta(mu,n)*c^-3 + 3/8*d1y(a,n)*d1y(a,n)*d1y(nu,n)*u(mu)*c^-5 - 3/8*d1y(a,n)*d1y(a,n)*eta(mu,n)*u(nu)*c^-5 - 1/2*d1y(a,n)*d1y(nu,n)*d1u(mu,n)*c^-3 + 1/4*d1y(a,n)*d2y(mu,n,n)*u(nu)*c^-3 - 1/4*d1y(a,n)*d2y(nu,n,n)*u(mu)*c^-3 + 1/2*d1y(a,n)*d1u(nu,n)*eta(mu,n)*c^-3 - d1y(nu,n)*d1y(N1_?,n)*d1u(N1_?,n)*a(mu)*c^-3 - 1/2*d1y(nu,n)*d1y(N1_?,n)*d1a(N1_?,n)*u(mu)*c^-3 - 1/2*d1y(nu,n)*d2y(u,n,n)*a(mu)*c^-3 - 1/4*d1y(nu,n)*d2y(a,n,n)*u(mu)*c^-3 + 1/2*d1y(nu,n)*d2u(mu,n,n)*c^-1 + 1/4*d1y(N1_?,n)*d2y(N1_?,n,n)*u(mu)*a(nu)*c^-3 - 1/4*d1y(N1_?,n)*d2y(N1_?,n,n)*u(nu)*a(mu)*c^-3 + d1y(N1_?,n)*d1u(N1_?,n)*eta(mu,n)*a(nu)*c^-3 + 1/2*d1y(N1_?,n)*d1a(N1_?,n)*eta(mu,n)*u(nu)*c^-3 + 1/2*d2y(u,n,n)*eta(mu,n)*a(nu)*c^-3 + 1/4*d2y(a,n,n)*eta(mu,n)*u(nu)*c^-3 - 1/2*d2y(mu,n,n)*d1u(nu,n)*c^-1 + 1/2*d2y(nu,n,n)*d1u(mu,n)*c^-1 - 1/6*d3y(mu,n,n,n)*u(nu)*c^-1 + 1/6*d3y(nu,n,n,n)*u(mu)*c^-1 - 1/2*d2u(nu,n,n)*eta(mu,n)*c^-1 ) + snorm^-1 * ( + 1/8*d1y(u,n)*u(mu)*u(nu)*a.a*c^-7 - 1/2*d1y(u,n)*u(mu)*j(nu)*c^-5 + d1y(u,n)*u(nu)*j(mu)*c^-5 - 3/4*d1y(a,n)*u(mu)*a(nu)*c^-5 + 3/4*d1y(a,n)*u(nu)*a(mu)*c^-5 - 1/8*d1y(nu,n)*u(mu)*a.a*c^-5 - 1/2*d1y(nu,n)*j(mu)*c^-3 + 1/2*d1u(mu,n)*a(nu)*c^-3 - 1/2*d1u(nu,n)*a(mu)*c^-3 - 1/2*d1a(mu,n)*u(nu)*c^-3 + 1/2*d1a(nu,n)*u(mu)*c^-3 + 1/8*eta(mu,n)*u(nu)*a.a*c^-5 + 1/2*eta(mu,n)*j(nu)*c^-3 ) - 2/3*u(mu)*j(nu)*c^-4 + 2/3*u(nu)*j(mu)*c^-4 ; lfreg = + snorm^-7 * ( - 15/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*eta(mu, n)*c^-8 + 15/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)* eta(mu,n)*c^-6 + 15/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*eta(mu,n)*c^-6 - 15/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*eta(mu,n )*c^-4 - 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u( N2_?,n)*eta(mu,n)*c^-4 - 15/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*eta(mu,n )*c^-4 - 15/8*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*eta(mu,n)*c^-4 + 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d1u(N2_?,n)* eta(mu,n)*c^-2 + 15/4*d1y(u,n)*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N2_?,n,n)*d1u(N1_?,n)* eta(mu,n)*c^-2 + 15/4*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*eta(mu,n)*c^-2 - 15/8*d1y(N1_?,n)*d1y(N2_?,n)*d2y(N1_?,n,n)*d2y(N2_?,n,n)*eta(mu,n) ) + snorm^-5 * ( - 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*a(mu)*c^-8 + 1/8*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(u,n)*eta(mu,n)*a.a*c^-8 + 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1u(mu,n)*c^-6 + 1/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(j,n)*eta(mu,n)*c^-6 + 3/2*d1y(u,n)*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*a(mu)*c^-6 + 3/4*d1y(u,n)*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*a(mu)*c^-6 + 9/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d1y(a,n)*eta(mu,n)*c^-6 + 3/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*u(mu)*c^-6 - 3/4*d1y(u,n)*d1y(u,n)*d1y(a,n)*d2y(mu,n,n)*c^-4 - 3/4*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*a(mu)*c^-4 - 3*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1u(mu,n)*d1u(N1_?,n)*c^-4 - 3/2*d1y(u,n)*d1y(u,n)*d1y(N1_?,n)*d1a(N1_?,n)*eta(mu,n)*c^-4 - 3/2*d1y(u,n)*d1y(u,n)*d2y(u,n,n)*d1u(mu,n)*c^-4 - 3/4*d1y(u,n)*d1y(u,n)*d2y(a,n,n)*eta(mu,n)*c^-4 - 9/2*d1y(u,n)*d1y(a,n)*d1y(N1_?,n)*d1u(N1_?,n)*eta(mu,n)*c^-4 - 9/4*d1y(u,n)*d1y(a,n)*d2y(u,n,n)*eta(mu,n)*c^-4 - 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*u(mu)*c^-4 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(mu,n,n)*d1u(N1_?,n)*c^-2 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*d1u(mu,n)*c^-2 + 3/2*d1y(u,n)*d1y(N1_?,n)*d2u(N1_?,n,n)*eta(mu,n)*c^-2 - 3/4*d1y(u,n)*d2y(u,n,n)*d2y(u,n,n)*u(mu)*c^-4 + 3/4*d1y(u,n)*d2y(u,n,n)*d2y(mu,n,n)*c^-2 + 3/2*d1y(u,n)*d2y(N1_?,n,n)*d1u(N1_?,n)*eta(mu,n)*c^-2 + 1/2*d1y(u,n)*d3y(u,n,n,n)*eta(mu,n)*c^-2 + 3/4*d1y(a,n)*d1y(N1_?,n)*d2y(N1_?,n,n)*eta(mu,n)*c^-2 + 3/2*d1y(N1_?,n)*d1y(N2_?,n)*d1u(N1_?,n)*d1u(N2_?,n)*eta(mu,n)*c^-2 + 3/4*d1y(N1_?,n)*d2y(u,n,n)*d2y(N1_?,n,n)*u(mu)*c^-2 + 3/2*d1y(N1_?,n)*d2y(u,n,n)*d1u(N1_?,n)*eta(mu,n)*c^-2 - 3/4*d1y(N1_?,n)*d2y(mu,n,n)*d2y(N1_?,n,n) - 1/2*d1y(N1_?,n)*d3y(N1_?,n,n,n)*eta(mu,n) + 3/8*d2y(u,n,n)*d2y(u,n,n)*eta(mu,n)*c^-2 - 3/8*d2y(N1_?,n,n)*d2y(N1_?,n,n)*eta(mu,n) ) + snorm^-3 * ( + 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*u(mu)*a.a*c^-8 + 1/6*d1y(u,n)*d1y(u,n)*d1y(u,n)*j(mu)*c^-6 - 1/2*d1y(u,n)*d1y(u,n)*d1u(a,n)*u(mu)*c^-6 - 1/2*d1y(u,n)*d1y(u,n)*d1a(mu,n)*c^-4 + 1/4*d1y(u,n)*d1y(u,n)*eta(mu,n)*a.a*c^-6 - 1/2*d1y(u,n)*d1y(a,n)*d1u(mu,n)*c^-4 - 1/2*d1y(u,n)*d1y(j,n)*eta(mu,n)*c^-4 + 1/2*d1y(u,n)*d1y(N1_?,n)*d1u(N1_?,n)*a(mu)*c^-4 - 1/4*d1y(u,n)*d2y(u,n,n)*a(mu)*c^-4 - d1y(u,n)*d1u(a,n)*eta(mu,n)*c^-4 + 1/2*d1y(u,n)*d1u(N1_?,n)*d1u(N1_?,n)*u(mu)*c^-4 + 1/2*d1y(u,n)*d2u(mu,n,n)*c^-2 - 3/8*d1y(a,n)*d1y(a,n)*eta(mu,n)*c^-4 - 1/4*d1y(a,n)*d2y(u,n,n)*u(mu)*c^-4 + 1/4*d1y(a,n)*d2y(mu,n,n)*c^-2 - 1/4*d1y(N1_?,n)*d2y(N1_?,n,n)*a(mu)*c^-2 + 1/2*d1y(N1_?,n)*d1a(N1_?,n)*eta(mu,n)*c^-2 + 1/2*d2y(u,n,n)*d1u(mu,n)*c^-2 + 1/4*d2y(a,n,n)*eta(mu,n)*c^-2 + 1/6*d3y(u,n,n,n)*u(mu)*c^-2 - 1/6*d3y(mu,n,n,n) + 1/2*d1u(N1_?,n)*d1u(N1_?,n)*eta(mu,n)*c^-2 ) + snorm^-1 * ( + 1/2*d1y(u,n)*u(mu)*a.a*c^-6 + 1/2*d1y(u,n)*j(mu)*c^-4 + 3/4*d1y(a,n)*a(mu)*c^-4 - 1/2*d1u(a,n)*u(mu)*c^-4 - 1/2*d1a(mu,n)*c^-2 - 3/8*eta(mu,n)*a.a*c^-4 ) + 2/3*u(mu)*a.a*c^-5 + 2/3*j(mu)*c^-3 ; save lfreg.sav; .end 5.20 sec out of 5.21 sec