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Can someone help me on how to split the equation automatically using the WinEdt macros:

See sample below:

Original Code:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}

\begin{align}
\rho (v_{a}) &= \rho_{a}^{i}(x)\ e_{i}, \label{anch} \\[4pt]
\lbrack v_{a},v_{b}] &=  C_{ab}^{c}(\mathrm{x})\ v_{c} \label{liea}
\end{align}


\begin{align}
\widehat{\rho }_{a}^{j}e_{j}({}\widehat{\rho }_{b}^{i})-\widehat{\rho }_{b}^{j}e_{j}
(\widehat{\rho }_{a}^{i}) &= \widehat{\rho }_{e}^{j}\mathbf{C}_{ab}^{e},
\nonumber \\ \hspace*{-12pt}
\sum\limits_{cyclic(a,b,e)}\left( \widehat{\rho }_{a}^{j}e_{j}(
\mathbf{C}_{be}^{f})+\mathbf{C}_{ag}^{f}\mathbf{C}_{be}^{g}-\mathbf{C}
_{b^{\prime }e^{\prime }}^{f^{\prime }} \widehat{\rho }_{a}^{j}
\mathbf{Q}_{f^{\prime }bej}^{fb^{\prime }e^{\prime }}\right) &= 0, \label{lased}
\end{align}


\begin{align}
L_{b^{\prime }e^{\prime }}^{a^{\prime }} \;\;&=\;\; \left( \mathcal{D}_{e^{\prime }}
\mathbf{z}_{b^{\prime }}\right) \rfloor \mathbf{z}^{a^{\prime }},\quad L_{be^{\prime }}^{a}=\left( \mathcal{D}_{e^{\prime }}\mathbf{v}_{b}\right) \rfloor \mathbf{v}^{a} \label{hcov} \\
K_{b^{\prime }c}^{a^{\prime }} \;\;&=\;\; \left( \mathcal{D}_{c}\mathbf{z}_{b^{\prime }}\right) \rfloor \mathbf{z}^{a^{\prime }},\quad K_{bc}^{a}=\left( \mathcal{D}_{c}\mathbf{v}_{b}\right) \rfloor
\mathbf{v}^{a}. \label{vcov}
\end{align}


\begin{align}
A_{A}^{\underline{A}} \;\;&=\;\; \mathbf{e}_{A}^{\underline{A}}=\left[
\begin{array}{cc}
e_{a}^{\underline{a}} & N_{a}^{b}e_{b}^{\underline{a}} \\
0 & e_{a}^{\underline{a}}
\end{array}\right] , \label{vt1} \\ A_{\underline{B}}^{B} \;\;&=\;\; \mathbf{e}_{\underline{B}}^{B}=\left[
\begin{array}{cc}
e_{\underline{a}}^{a} & -N_{a}^{b} e_{\underline{a}}^{a} \\
0 & e_{\underline{a}}^{a}
\end{array}\right] ,
\label{vt2}
\end{align}


\begin{align}
R_{e^{\prime }b^{\prime }c^{\prime }}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime }}\rfloor \mathcal{R}\left( \mathbf{z}_{c^{\prime }},\mathbf{z}_{b^{\prime }}\right) \mathbf{z}_{e^{\prime }},
R_{ bb^{\prime }e^{\prime }}^{a}=v^{a}\rfloor \mathcal{R}\left( \mathbf{z}_{e^{\prime }},\mathbf{z}
_{b^{\prime }}\right) \mathbf{v}_{b}, \label{curvaturehv} \\
P_{ b^{\prime }c^{\prime }c}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime}}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{z}_{c^{\prime }}\right) \mathbf{z}_{b^{\prime }},~P_{ bc^{\prime}c}^{a}= \mathbf{v}^{a}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{z}_{c^{\prime }}\right)
\mathbf{v}_{b}, \nonumber \\
S_{b^{\prime }bc}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime }}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{v}_{b}\right) \mathbf{z}_{b^{\prime }}, S_{bcd}^{a}=\mathbf{v}^{a}\rfloor \mathcal{R}\left( \mathbf{v}_{d}, \mathbf{v}_{c}\right) \mathbf{v}_{b}. \nonumber
\end{align}

\begin{align}
R_{e^{\prime }b^{\prime }c^{\prime }}^{a^{\prime }} \;\;&=\;\; \mathbf{z}
_{c^{\prime }}(L_{.e^{\prime }b^{\prime }}^{a^{\prime }})-\mathbf{z}
_{b^{\prime }}(L_{.e^{\prime }c^{\prime }}^{a^{\prime }})+L_{.e^{\prime
}b^{\prime }}^{d^{\prime }}L_{d^{\prime }c^{\prime }}^{a^{\prime
}}-L_{.e^{\prime }c^{\prime }}^{d^{\prime }}L_{d^{\prime }b^{\prime
}}^{a^{\prime }}-K_{.e^{\prime }a}^{a^{\prime }}\Omega_{.b^{\prime
}c^{\prime }}^{a}, \label{dcurv} \\
R_{ bb^{\prime }e^{\prime }}^{a} \;\;&=\;\; \mathbf{z}_{e^{\prime }}(L_{.bb^{\prime
}}^{a})-\mathbf{z}_{b^{\prime }}(L_{.be^{\prime }}^{a})+L_{.bb^{\prime
}}^{c}L_{.ce^{\prime }}^{a}-L_{.be^{\prime }}^{c}L_{.cb^{\prime
}}^{a}-K_{.bc}^{a} \Omega_{.b^{\prime }e^{\prime }}^{c}, \nonumber \\
P_{ e^{\prime }b^{\prime }a}^{a^{\prime }} \;\;&=\;\; \mathbf{v}_{a}(L_{.e^{\prime
}b^{\prime }}^{a^{\prime }})-(\mathbf{z}_{b^{\prime }}(K_{.e^{\prime
}a}^{a^{\prime }})+L_{.d^{\prime }b^{\prime }}^{a^{\prime }}K_{.e^{\prime
}a}^{d^{\prime }}-L_{.e^{\prime }b^{\prime }}^{d^{\prime }}K_{.d^{\prime
}a}^{a^{\prime }}-L_{.ab^{\prime }}^{c}K_{.e^{\prime }c}^{a^{\prime }}) \nonumber \\
&\quad\;\; +K_{.e^{\prime }b}^{a^{\prime }}T_{.b^{\prime }a}^{b}, \nonumber \\
P_{ ba^{\prime }a}^{c} \;\;&=\;\; \mathbf{v}_{a}(L_{.ba^{\prime }}^{c})-\left(
\mathbf{z}_{a^{\prime }}(K_{.ba}^{c})+L_{.da^{\prime
}}^{c\,}K_{.ba}^{d}-L_{.ba^{\prime }}^{d}K_{.da}^{c}-L_{.aa^{\prime}}^{d}K_{.bd}^{c}\right) \nonumber \\
&\quad\;\; +K_{.bd}^{c}T_{.a^{\prime }a}^{d}, \nonumber \\
S_{ b^{\prime }bc}^{a^{\prime }} \;\;&=\;\; S_{ jbc}^{i}=\mathbf{v}
_{c}(K_{.b^{\prime }b}^{a^{\prime }})-\mathbf{v}_{b}(K_{.b^{\prime
}c}^{a^{\prime }})+K_{.b^{\prime }b}^{e^{\prime }}K_{.e^{\prime
}c}^{a^{\prime }}-K_{.b^{\prime }c}^{e^{\prime }}K_{e^{\prime }b}^{a^{\prime }}, \nonumber \\
S_{ bcd}^{a} \;\;&=\;\; \mathbf{v}_{d}(K_{.bc}^{a})-\mathbf{v}_{c}(K_{.bd}^{a}) + K_{.bc}^{e}K_{.ed}^{a}-K_{.bd}^{e}K_{.ec}^{a}. \nonumber
\end{align}
\end{document}

Output should look like the data below:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{align}
\rho (v_{a}) &= \rho_{a}^{i}(x)\ e_{i}, \label{anch} [4pt]
\end{align}
\begin{align}
\lbrack v_{a},v_{b}] &=  C_{ab}^{c}(\mathrm{x})\ v_{c} \label{liea}
\end{align}


\begin{align}
\widehat{\rho }_{a}^{j}e_{j}({}\widehat{\rho }_{b}^{i})-\widehat{\rho }_{b}^{j}e_{j}
(\widehat{\rho }_{a}^{i}) &= \widehat{\rho }_{e}^{j}\mathbf{C}_{ab}^{e},
\nonumber \hspace*{-12pt}
\end{align}
\begin{align}
\sum\limits_{cyclic(a,b,e)}\left( \widehat{\rho }_{a}^{j}e_{j}(
\mathbf{C}_{be}^{f})+\mathbf{C}_{ag}^{f}\mathbf{C}_{be}^{g}-\mathbf{C}
_{b^{\prime }e^{\prime }}^{f^{\prime }} \widehat{\rho }_{a}^{j}
\mathbf{Q}_{f^{\prime }bej}^{fb^{\prime }e^{\prime }}\right) &= 0, \label{lased}
\end{align}


\begin{align}
L_{b^{\prime }e^{\prime }}^{a^{\prime }} \;\;&=\;\; \left( \mathcal{D}_{e^{\prime }}
\mathbf{z}_{b^{\prime }}\right) \rfloor \mathbf{z}^{a^{\prime }},\quad L_{be^{\prime }}^{a}=\left( \mathcal{D}_{e^{\prime }}\mathbf{v}_{b}\right) \rfloor \mathbf{v}^{a} \label{hcov}
\end{align}
\begin{align}
K_{b^{\prime }c}^{a^{\prime }} \;\;&=\;\; \left( \mathcal{D}_{c}\mathbf{z}_{b^{\prime }}\right) \rfloor \mathbf{z}^{a^{\prime }},\quad K_{bc}^{a}=\left( \mathcal{D}_{c}\mathbf{v}_{b}\right) \rfloor
\mathbf{v}^{a}. \label{vcov}
\end{align}


\begin{align}
A_{A}^{\underline{A}} \;\;&=\;\; \mathbf{e}_{A}^{\underline{A}}=\left[
\begin{array}{cc}
e_{a}^{\underline{a}} & N_{a}^{b}e_{b}^{\underline{a}} \\
0 & e_{a}^{\underline{a}}
\end{array}\right] , \label{vt1}
\end{align}
\begin{align}
 A_{\underline{B}}^{B} \;\;&=\;\; \mathbf{e}_{\underline{B}}^{B}=\left[
\begin{array}{cc}
e_{\underline{a}}^{a} & -N_{a}^{b} e_{\underline{a}}^{a} \\
0 & e_{\underline{a}}^{a}
\end{array}\right] ,
\label{vt2}
\end{align}


\begin{align}
R_{e^{\prime }b^{\prime }c^{\prime }}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime }}\rfloor \mathcal{R}\left( \mathbf{z}_{c^{\prime }},\mathbf{z}_{b^{\prime }}\right) \mathbf{z}_{e^{\prime }},
R_{ bb^{\prime }e^{\prime }}^{a}=v^{a}\rfloor \mathcal{R}\left( \mathbf{z}_{e^{\prime }},\mathbf{z}
_{b^{\prime }}\right) \mathbf{v}_{b}, \label{curvaturehv}
\end{align}
\begin{align}
P_{ b^{\prime }c^{\prime }c}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime}}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{z}_{c^{\prime }}\right) \mathbf{z}_{b^{\prime }},~P_{ bc^{\prime}c}^{a}= \mathbf{v}^{a}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{z}_{c^{\prime }}\right)
\mathbf{v}_{b}, \nonumber
\end{align}
\begin{align}
S_{b^{\prime }bc}^{a^{\prime }} \;\;&=\;\; \mathbf{z}^{a^{\prime }}\rfloor \mathcal{R}\left( \mathbf{v}_{c},\mathbf{v}_{b}\right) \mathbf{z}_{b^{\prime }}, S_{bcd}^{a}=\mathbf{v}^{a}\rfloor \mathcal{R}\left( \mathbf{v}_{d}, \mathbf{v}_{c}\right) \mathbf{v}_{b}. \nonumber
\end{align}

\begin{align}
R_{e^{\prime }b^{\prime }c^{\prime }}^{a^{\prime }} \;\;&=\;\; \mathbf{z}
_{c^{\prime }}(L_{.e^{\prime }b^{\prime }}^{a^{\prime }})-\mathbf{z}
_{b^{\prime }}(L_{.e^{\prime }c^{\prime }}^{a^{\prime }})+L_{.e^{\prime
}b^{\prime }}^{d^{\prime }}L_{d^{\prime }c^{\prime }}^{a^{\prime
}}-L_{.e^{\prime }c^{\prime }}^{d^{\prime }}L_{d^{\prime }b^{\prime
}}^{a^{\prime }}-K_{.e^{\prime }a}^{a^{\prime }}\Omega_{.b^{\prime
}c^{\prime }}^{a}, \label{dcurv}
\end{align}
\begin{align}
R_{ bb^{\prime }e^{\prime }}^{a} \;\;&=\;\; \mathbf{z}_{e^{\prime }}(L_{.bb^{\prime
}}^{a})-\mathbf{z}_{b^{\prime }}(L_{.be^{\prime }}^{a})+L_{.bb^{\prime
}}^{c}L_{.ce^{\prime }}^{a}-L_{.be^{\prime }}^{c}L_{.cb^{\prime
}}^{a}-K_{.bc}^{a} \Omega_{.b^{\prime }e^{\prime }}^{c}, \nonumber
\end{align}
\begin{align}
P_{ e^{\prime }b^{\prime }a}^{a^{\prime }} \;\;&=\;\; \mathbf{v}_{a}(L_{.e^{\prime
}b^{\prime }}^{a^{\prime }})-(\mathbf{z}_{b^{\prime }}(K_{.e^{\prime
}a}^{a^{\prime }})+L_{.d^{\prime }b^{\prime }}^{a^{\prime }}K_{.e^{\prime
}a}^{d^{\prime }}-L_{.e^{\prime }b^{\prime }}^{d^{\prime }}K_{.d^{\prime
}a}^{a^{\prime }}-L_{.ab^{\prime }}^{c}K_{.e^{\prime }c}^{a^{\prime }}) \nonumber
\end{align}
\begin{align}
&\quad\;\; +K_{.e^{\prime }b}^{a^{\prime }}T_{.b^{\prime }a}^{b}, \nonumber
\end{align}
\begin{align}
P_{ ba^{\prime }a}^{c} \;\;&=\;\; \mathbf{v}_{a}(L_{.ba^{\prime }}^{c})-\left(
\mathbf{z}_{a^{\prime }}(K_{.ba}^{c})+L_{.da^{\prime
}}^{c\,}K_{.ba}^{d}-L_{.ba^{\prime }}^{d}K_{.da}^{c}-L_{.aa^{\prime}}^{d}K_{.bd}^{c}\right) \nonumber
\end{align}
\begin{align}
&\quad\;\; +K_{.bd}^{c}T_{.a^{\prime }a}^{d}, \nonumber
\end{align}
\begin{align}
S_{ b^{\prime }bc}^{a^{\prime }} \;\;&=\;\; S_{ jbc}^{i}=\mathbf{v}
_{c}(K_{.b^{\prime }b}^{a^{\prime }})-\mathbf{v}_{b}(K_{.b^{\prime
}c}^{a^{\prime }})+K_{.b^{\prime }b}^{e^{\prime }}K_{.e^{\prime
}c}^{a^{\prime }}-K_{.b^{\prime }c}^{e^{\prime }}K_{e^{\prime }b}^{a^{\prime }}, \nonumber
\end{align}
\begin{align}
S_{ bcd}^{a} \;\;&=\;\; \mathbf{v}_{d}(K_{.bc}^{a})-\mathbf{v}_{c}(K_{.bd}^{a}) + K_{.bc}^{e}K_{.ed}^{a}-K_{.bd}^{e}K_{.ec}^{a}. \nonumber
\end{align}
\end{document}
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Try a find/replace tool. Select the environment and replace \\[4pt] by \end{align}\begin{align}. Be careful, check if the replace only selected is your case. –  Sigur Oct 15 '12 at 14:08
    
but not all the data after the "\\" has measurement. –  jeecabz Oct 15 '12 at 14:20
    
So first, replace [4pt] by nothing and then replace again. Take care of selection. –  Sigur Oct 15 '12 at 14:29
    
Your formulas would be more readable if all ^{\prime } are replaced by ' (a straight apostrophe). You're using \; in places where it's wrong; also \left and \right are in most cases redundant. The term "cyclic" should be input as \text{cyclic} –  egreg Oct 15 '12 at 14:42
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2 Answers

up vote 1 down vote accepted
+50

Take the following WinEdt macro as an approach. You should extend the macro to check if you found the string in an environment where it is not useful to replace the string like in the array-environment in your example.

SetSearchForward(1);
SetSearchCaseSensitive(0);
SetSearchEntire(1);
SetSearchCyclic(1);
SetSearchRelaxed(0);
SetSearchWholeWords(1);
SetSearchInline(1);
SetSearchCurrentDoc;
SetNotFoundNotify(0);
SetReplacePrompt(0);
SetRegEx(0);

SetFindStr("\\");
SearchReset;
BeginGroup;
SetTracking(0);

Loop(!|Find;IfOK(!"Call('Format');",!"JMP('Done');");|);

:Format::
    Backspace(2);
    GoToEndOfLine;
    NewLine;
    InsText("\end{align}");
    NewLine;
    InsText("\begin{align}");
    Return;

:Done::
    EndGroup;
    SetTracking(1);
    RestoreFind;
End;   
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You can do many improvements to your equations. I assume that they are blocks from various parts of your document.

  1. The ^{\prime} bits make the formulas less readable; use ' in its place.

  2. A \widehat{\rho} clashes with the exponent: \widehat{\rho}_{a}^{\,j} is better.

  3. Consecutive align environments should not be used, nor, in general, consecutive general alignment environments. Use equation for a single numbered equation, equation* for a non numbered one; use gather for sequences of centered equations.

  4. \left(...\right) should be used only when really needed; definitely not with all parentheses pairs. If it's WinEdt that adds \left and \right, tell it not to.

  5. Spacing \; around equals signs are wrong.

  6. For multiple alignment points use alignat or alignedat; or even align. With alignat you can control the spacing between the columns.

  7. You can control the interrow spacing with the usual optional argument to \\.

Here is a modified version of your input

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}
\begin{gather}
\rho (v_{a}) = \rho_{a}^{i}(x)\ e_{i}, \label{anch}
\\[4pt]
\lbrack v_{a},v_{b}] =  C_{ab}^{c}(\mathrm{x})\ v_{c} \label{liea}
\end{gather}

\begin{equation*}
\widehat{\rho}_{a}^{\,j}e_{j}({}\widehat{\rho}_{b}^{\,i})-\widehat{\rho}_{b}^{j}e_{j}
(\widehat{\rho}_{a}^{\,i}) = \widehat{\rho}_{e}^{\,j}\mathbf{C}_{ab}^{e},
\end{equation*}

\begin{equation}
\sum_{\text{cyclic}(a,b,e)}
  \bigl(\widehat{\rho}_{a}^{\,j}e_{j}
  (\mathbf{C}_{be}^{f})+\mathbf{C}_{ag}^{f}\mathbf{C}_{be}^{g}-\mathbf{C}_{b'e'}^{f'} \widehat{\rho}_{a}^{\,j}
  \mathbf{Q}_{f'bej}^{fb'e'}\bigr) = 0, \label{lased}
\end{equation}

\begin{alignat}{2}
L_{b'e'}^{a'} &= (\mathcal{D}_{e'}\mathbf{z}_{b'}) \rfloor \mathbf{z}^{a'},
\quad &
L_{be'}^{a} &=(\mathcal{D}_{e'}\mathbf{v}_{b}) \rfloor \mathbf{v}^{a} \label{hcov}
\\
K_{b'c}^{a'} &= (\mathcal{D}_{c}\mathbf{z}_{b'}) \rfloor \mathbf{z}^{a'},
\quad &
K_{bc}^{a} &= (\mathcal{D}_{c}\mathbf{v}_{b}) \rfloor\mathbf{v}^{a}. \label{vcov}
\end{alignat}

\begin{align}
A_{A}^{\underline{A}} &=
\mathbf{e}_{A}^{\underline{A}}=
\begin{bmatrix}
e_{a}^{\underline{a}} & N_{a}^{b}e_{b}^{\underline{a}} \\
0 & e_{a}^{\underline{a}}
\end{bmatrix}, \label{vt1}
\\
A_{\underline{B}}^{B} &=
\mathbf{e}_{\underline{B}}^{B}=
\begin{bmatrix}
e_{\underline{a}}^{a} & -N_{a}^{b} e_{\underline{a}}^{a} \\
0 & e_{\underline{a}}^{a}
\end{bmatrix}, \label{vt2}
\end{align}


\begin{equation}
\label{curvaturehv}
\begin{alignedat}{2}
R_{e'b'c'}^{a'} &= \mathbf{z}^{a'}\rfloor \mathcal{R}(\mathbf{z}_{c'},\mathbf{z}_{b'}) \mathbf{z}_{e'},
\quad &
R_{bb'e'}^{a}&=v^{a}\rfloor \mathcal{R}(\mathbf{z}_{e'},\mathbf{z}_{b'}) \mathbf{v}_{b},
\\
P_{b'c'c}^{a'} &= \mathbf{z}^{a'}\rfloor \mathcal{R}(\mathbf{v}_{c},\mathbf{z}_{c'}) \mathbf{z}_{b'},
\quad &
P_{bc^{\prime}c}^{a} &= \mathbf{v}^{a}\rfloor \mathcal{R}(\mathbf{v}_{c},\mathbf{z}_{c'})\mathbf{v}_{b},
\\
S_{b'bc}^{a'} &= \mathbf{z}^{a'}\rfloor \mathcal{R}(\mathbf{v}_{c},\mathbf{v}_{b}) \mathbf{z}_{b'},
\quad &
S_{bcd}^{a} &= \mathbf{v}^{a}\rfloor \mathcal{R}( \mathbf{v}_{d}, \mathbf{v}_{c}) \mathbf{v}_{b}.
\end{alignedat}
\end{equation}

\begin{equation}
\begin{aligned}
R_{e'b'c'}^{a'} &= \mathbf{z}_{c'}(L_{.e'b'}^{a'})-\mathbf{z}_{b'}(L_{.e'c'}^{a'})
  +L_{.e'b'}^{d'}L_{d'c'}^{a'}-L_{.e'c'}^{d'}L_{d'b'}^{a'}-K_{.e'a}^{a'}\Omega_{.b'c'}^{a}, \label{dcurv}
\\
R_{bb'e'}^{a} &= \mathbf{z}_{e'}(L_{.bb'}^{a})-\mathbf{z}_{b'}(L_{.be'}^{a})
  +L_{.bb'}^{c}L_{.ce'}^{a}-L_{.be'}^{c}L_{.cb'}^{a}-K_{.bc}^{a} \Omega_{.b'e'}^{c},
\\
P_{e'b'a}^{a'} &= \mathbf{v}_{a}(L_{.e'b'}^{a'})-(\mathbf{z}_{b'}(K_{.e'a}^{a'})
  +L_{.d'b'}^{a'}K_{.e'a}^{d'}-L_{.e'b'}^{d'}K_{.d'a}^{a'}-L_{.ab'}^{c}K_{.e'c}^{a'})
  \\&\qquad{}+K_{.e'b}^{a'}T_{.b'a}^{b},
\\
P_{ba'a}^{c} &= \mathbf{v}_{a}(L_{.ba'}^{c})
  -(\mathbf{z}_{a'}(K_{.ba}^{c})+L_{.da'}^{c\,}K_{.ba}^{d}-L_{.ba'}^{d}K_{.da}^{c}-L_{.aa'}^{d}K_{.bd}^{c})
  \\&\qquad{}+K_{.bd}^{c}T_{.a'a}^{d},
\\
S_{b'bc}^{a'} &= S_{jbc}^{i}=\mathbf{v}_{c}(K_{.b'b}^{a'})-\mathbf{v}_{b}(K_{.b'c}^{a'})
  +K_{.b'b}^{e'}K_{.e'c}^{a'}-K_{.b'c}^{e'}K_{e'b}^{a'},
\\
S_{bcd}^{a} &= \mathbf{v}_{d}(K_{.bc}^{a})-\mathbf{v}_{c}(K_{.bd}^{a}) 
  +K_{.bc}^{e}K_{.ed}^{a}-K_{.bd}^{e}K_{.ec}^{a}.
\end{aligned}
\end{equation}
\end{document}

enter image description here

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