%% Created by Maple 15.00, Windows 7 %% Source Worksheet: p57.mw %% Generated: Tue May 08 12:00:20 CST 2012 \documentclass{article} \usepackage{maplestd2e} \usepackage{CJK} \def\emptyline{\vspace{12pt}} \begin{document} \begin{CJK}{}{} \pagestyle{empty} \DefineParaStyle{Maple Heading 1} \DefineParaStyle{Maple Text Output} \DefineParaStyle{Maple Dash Item} \DefineParaStyle{Maple Bullet Item} \DefineParaStyle{Maple Normal} \DefineParaStyle{Maple Heading 4} \DefineParaStyle{Maple Heading 3} \DefineParaStyle{Maple Heading 2} \DefineParaStyle{Maple Warning} \DefineParaStyle{Maple Title} \DefineParaStyle{Maple Error} \DefineCharStyle{Maple Hyperlink} \DefineCharStyle{Maple 2D Math} \DefineCharStyle{Maple Maple Input} \DefineCharStyle{Maple 2D Output} \DefineCharStyle{Maple 2D Input} \mapleinline{inert}{2d}{f1 := z = f(x+y, z+y)}{$\displaystyle {\it f1}\, := \,z=f \left( x+y,z+y \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{z = f(x+y, z+y)}{$\displaystyle z=f \left( x+y,z+y \right)$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{implicitdiff(f1, z, x, x)}{$\displaystyle {\it implicitdiff} \left( {\it f1},z,x,x \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2)/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{$\displaystyle -{\frac { \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}-2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) D_{{2}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}}{-1-3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}\\ \mbox{}+3\,D_{{2}} \left( f \right) \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{3}}}$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{implicitdiff(f1, z, x, y)-implicitdiff(f1, z, y, x)}{$\displaystyle {\it implicitdiff} \left( {\it f1},z,x,y \right) -{\it implicitdiff} \left( {\it f1},z,y,x \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{0}{$\displaystyle 0$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{implicitdiff(f1, z, x, y)}{$\displaystyle {\it implicitdiff} \left( {\it f1},z,x,y \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)-(D[1, 2](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 2](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y))/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{$\displaystyle -{\frac { \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}-2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) D_{{2}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}- \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{2}} \left( f \right) \left( x+y,z+y \right) + \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}}{-1-3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}+3\,D_{{2}} \left( f \right) \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{3}}}$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{implicitdiff(f1, z, y, y)}{$\displaystyle {\it implicitdiff} \left( {\it f1},z,y,y \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)^2-2*(D[1, 1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+(D[1, 1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)-2*(D[1, 2](f))(x+y, z+y)*(D[2](f))(x+y, z+y)+2*(D[1, 2](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)^2+2*(D[2, 2](f))(x+y, z+y)*(D[1](f))(x+y, z+y)+(D[2, 2](f))(x+y, z+y))/(-1-3*(D[2](f))(x+y, z+y)^2+3*(D[2](f))(x+y, z+y)+(D[2](f))(x+y, z+y)^3)}{$\displaystyle -{\frac { \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}-2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) D_{{2}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}-2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{2}} \left( f \right) \left( x+y,z+y \right) +2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}+2\, \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) D_{{1}} \left( f \right) \left( x+y,z+y \right) \\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y \right) }{-1-3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{2}+3\,D_{{2}} \left( f \right) \left( x+y,z+y \right) + \left( D_{{2}} \left( f \right) \left( x+y,z+y \right) \right) ^{3}\\ \mbox{}}}$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{f2 := f(x+y, z+y, z+x) = 0}{$\displaystyle {\it f2}\, := \,f \left( x+y,z+y,z+x \right) =0$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{f(x+y, z+y, z+x) = 0}{$\displaystyle f \left( x+y,z+y,z+x \right) =0$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{dx2 := simplify(implicitdiff(f2, z, x, x))}{$\displaystyle {\it dx2}\, := \,{\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,x,x \right) \\ \mbox{} \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-(2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)+(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2)/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{$\displaystyle -{\frac {2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}-2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}+2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}-2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}}{3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +3\,D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}+ \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}}}$} \end{maplelatex} \end{maplegroup} \mapleinline{inert}{2d}{latex(dx2)}{$\displaystyle {\it latex} \left( {\it dx2} \right)$} \begin{maplegroup} \mapleresult -\{\symbol{92}frac \{2\symbol{92}, \symbol{92}left( D\_\{\{1,1\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+ y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right)\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92},\symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left(f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right)\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92},\symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) + \symbol{92}left( D\_\{\{1,1\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{1,1\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left(D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}-2\symbol{92},\symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{2\}+2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left(D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+\symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{2\}\}\{3\symbol{92}, \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}right) \symbol{94}\{2\}D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) +3\symbol{92},D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right)\symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{3\}+ \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}right) \symbol{94}\{3\}\}\}\end{maplegroup} \begin{maplegroup} \mapleresult -\{\symbol{92}frac \{2\symbol{92}, \symbol{92}left( D\_\{\{1,1\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+ y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right)\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92},\symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left(f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) +2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right)\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left(x+y,z+y,z+x \symbol{92}right) -2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) -2\symbol{92},\symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) + \symbol{92}left( D\_\{\{1,1\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{2\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{1,1\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left(D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}-2\symbol{92},\symbol{92}left( D\_\{\{1,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{2\}+2\symbol{92}, \symbol{92}left( D\_\{\{1,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2,2\}\} \symbol{92}right) \symbol{92}left( f\symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right)\symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+2\symbol{92}, \symbol{92}left( D\_\{\{2,3\}\}\symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left( D\_\{\{1\}\}\symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+ \symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}left(D\_\{\{1\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right) \symbol{94}\{2\}+\symbol{92}left( D\_\{\{3,3\}\} \symbol{92}right) \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{2\}\}\{3\symbol{92}, \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}right) \symbol{94}\{2\}D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) +3\symbol{92},D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right) \symbol{92}right)\symbol{94}\{2\}+ \symbol{92}left( D\_\{\{2\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x \symbol{92}right)\symbol{92}right) \symbol{94}\{3\}+ \symbol{92}left( D\_\{\{3\}\} \symbol{92}left( f \symbol{92}right) \symbol{92}left( x+y,z+y,z+x\symbol{92}right) \symbol{92}right) \symbol{94}\{3\}\}\}\end{maplegroup} \begin{Maple Normal}{ \begin{Maple Normal}{ \mapleinline{inert}{2d}{}{$\displaystyle$} }\end{Maple Normal} }\end{Maple Normal} \mapleinline{inert}{2d}{simplify(implicitdiff(f2, z, x, y))}{$\displaystyle {\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,x,y\\ \mbox{} \right) \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-((D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2-(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2-(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x))/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{$\displaystyle -{\frac { \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}- \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}- \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}-2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) }{3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}+3\,D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}\\ \mbox{}+ \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}}}$} \end{maplelatex} \end{maplegroup} \begin{Maple Normal}{ \begin{Maple Normal}{ \mapleinline{inert}{2d}{Typesetting:-mover(Typesetting:-mo("→", family = "SimSun", size = "12", bold = "false", italic = "false", underline = "false", subscript = "false", superscript = "false", foreground = "[0,0,0]", background = "[255,255,255]", opaque = "false", executable = "false", readonly = "false", composed = "false", converted = "false", imselected = "false", placeholder = "false", selection-placeholder = "false", font_style_name = "2D Math", mathvariant = "normal", fence = "false", separator = "false", stretchy = "true", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mtext("to string", family = "SimSun", size = "12", bold = "false", italic = "false", underline = "false", subscript = "false", superscript = "false", foreground = "[0,0,0]", background = "[255,255,255]", opaque = "false", executable = "false", readonly = "false", composed = "false", converted = "false", imselected = "false", placeholder = "false", selection-placeholder = "false", font_style_name = "2D Math", mathvariant = "normal"), accent = "false")}{$\displaystyle \Mapleoverset{}{\rightarrow }$} }\end{Maple Normal} }\end{Maple Normal} \begin{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \begin{center} \mapleinline{inert}{2d}{"-(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)"}{$\displaystyle -(D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+D[1,1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[2,2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+2*D[2,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2+D[3,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)^2-D[3,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)^2+2*D[1,1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,2](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)-2*D[1,3](f)(x+y,z+y,z+x)*D[1](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)+2*D[2,3](f)(x+y,z+y,z+x)*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x))/(3*D[2](f)(x+y,z+y,z+x)^2*D[3](f)(x+y,z+y,z+x)+3*D[2](f)(x+y,z+y,z+x)*D[3](f)(x+y,z+y,z+x)^2+D[2](f)(x+y,z+y,z+x)^3+D[3](f)(x+y,z+y,z+x)^3)''$} \end{center} \end{center} \mapleinline{inert}{2d}{simplify(implicitdiff(f2, z, y, y))}{$\displaystyle {\it simplify} \left( {\it implicitdiff} \left( {\it f2},z,y,y \right) \\ \mbox{} \right)$} \begin{maplegroup} \mapleresult \begin{maplelatex} \mapleinline{inert}{2d}{-(2*(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[1, 2](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)-2*(D[2, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)+2*(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)+(D[1, 1](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[1, 1](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[1, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2-2*(D[1, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[2, 2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+2*(D[2, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[1](f))(x+y, z+y, z+x)^2+(D[3, 3](f))(x+y, z+y, z+x)*(D[2](f))(x+y, z+y, z+x)^2)/(3*(D[2](f))(x+y, z+y, z+x)^2*(D[3](f))(x+y, z+y, z+x)+3*(D[2](f))(x+y, z+y, z+x)*(D[3](f))(x+y, z+y, z+x)^2+(D[2](f))(x+y, z+y, z+x)^3+(D[3](f))(x+y, z+y, z+x)^3)}{$\displaystyle -{\frac {2\, \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}-2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}-2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) -2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +2\, \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \\ \mbox{}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{1,1}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{1,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}-2\, \left( D_{{1,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{2,2}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+2\, \left( D_{{2,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{1}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}+ \left( D_{{3,3}} \right) \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}}{3\, \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) +3\,D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{2}\\ \mbox{}+ \left( D_{{2}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}+ \left( D_{{3}} \left( f \right) \left( x+y,z+y,z+x \right) \right) ^{3}}}$} \end{maplelatex} \end{maplegroup} \begin{Maple Normal}{ \begin{Maple Normal}{ \mapleinline{inert}{2d}{}{$\displaystyle$} }\end{Maple Normal} }\end{Maple Normal} \end{CJK} \end{document}