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Display information for equation id:math.357.0 on revision:357

* Page found: Kovariante Ableitung (eq math.357.0)

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Kovariante Ableitung Eq: math.357.0

Hash: 2b2ded49e72e3d49744cf8a170dc9832

TeX (original user input):

\begin{align}
T_{{\color{Orange}rs...}; \color{Red}l}^{\color{Blue}ik...}
 =
T_{{\color{Orange}rs...}, \color{Red}l}^{\color{Blue} ik...}&
 +
\Gamma _{ m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{m\color{Blue}k...}\quad&&
 +
\Gamma _{m\color{Red}l}^{\color{Blue}i}T_{\color{Orange}rs...}^{{\color{Blue}r}m\color{Blue}...}... &\quad&
{\color{Blue}\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden oberen Index}} \\
 & +
\Gamma _{\color{Orange}r\color{Red}l}^{m}T_{m\color{Orange}s...}^{ \color{Blue}ik...}\quad&&
+
\Gamma _{\color{Orange}r\color{Red}l}^{m}T_{{\color{Orange}r}m\color{Orange}...}^{ \color{Blue}ik...}...&&
\color{Orange}{\text{f }\!\!\ddot{\mathrm{u}}\!\!\text{ r jeden unteren Index}} \\
\end{align}

TeX (checked):

{\begin{aligned}T_{{\color {Orange}rs...};\color {Red}l}^{\color {Blue}ik...}=T_{{\color {Orange}rs...},\color {Red}l}^{\color {Blue}ik...}&+\Gamma _{m\color {Red}l}^{\color {Blue}i}T_{\color {Orange}rs...}^{m\color {Blue}k...}\quad &&+\Gamma _{m\color {Red}l}^{\color {Blue}i}T_{\color {Orange}rs...}^{{\color {Blue}r}m\color {Blue}...}...&\quad &{\color {Blue}{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden oberen Index}}}\\&+\Gamma _{\color {Orange}r\color {Red}l}^{m}T_{m\color {Orange}s...}^{\color {Blue}ik...}\quad &&+\Gamma _{\color {Orange}r\color {Red}l}^{m}T_{{\color {Orange}r}m\color {Orange}...}^{\color {Blue}ik...}...&&\color {Orange}{{\text{f }}\!\!{\ddot {\mathrm {u} }}\!\!{\text{ r jeden unteren Index}}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

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MathML (7.018 KB / 625 B) :

\begin{aligned} T_{r s . . .; l}^{i k . . .} = T_{r s . . ., l}^{i k . . .} & + Γ_{m l}^{i} T_{r s . . .}^{m k . . .} & + Γ_{m l}^{i} T_{r s . . .}^{r m . . .} . . . & f \ddot{u} r jeden oberen Index \\ + Γ_{r l}^{m} T_{m s . . .}^{i k . . .} & + Γ_{r l}^{m} T_{r m . . .}^{i k . . .} . . . & f \ddot{u} r jeden unteren Index \end{aligned}

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mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle></mrow></mrow></msubsup><mo>=</mo><msubsup><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>r</mi></mstyle><mstyle mathcolor="#F58137"><mi>s</mi></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle></mrow><mo>,</mo><mstyle mathcolor="#ED1B23"><mi>l</mi></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mi>i</mi></mstyle><mstyle mathcolor="#2D2F92"><mi>k</mi></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle></mrow></mrow></msubsup></mtd><mtd><mo>+</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow 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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mstyle mathcolor="#ED1B23"><mi>l</mi></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mi>i</mi></mstyle></mrow></mrow></msubsup><msubsup><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>r</mi></mstyle><mstyle mathcolor="#F58137"><mi>s</mi></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mi>r</mi></mstyle></mrow><mi>m</mi><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle></mrow></mrow></msubsup><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd><mspace width="1em"></mspace></mtd><mtd><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mrow data-mjx-texclass="ORD"><mtext>f&#xA0;</mtext></mrow></mstyle><mstyle mathcolor="#2D2F92"><mspace width="-0.167em"></mspace></mstyle><mstyle mathcolor="#2D2F92"><mspace width="-0.167em"></mspace></mstyle><mstyle mathcolor="#2D2F92"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow></mstyle><mstyle mathcolor="#2D2F92"><mspace width="-0.167em"></mspace></mstyle><mstyle mathcolor="#2D2F92"><mspace width="-0.167em"></mspace></mstyle><mstyle mathcolor="#2D2F92"><mrow data-mjx-texclass="ORD"><mtext>&#xA0;r jeden oberen Index</mtext></mrow></mstyle></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>+</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>r</mi></mstyle><mstyle mathcolor="#ED1B23"><mi>l</mi></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msubsup><msubsup><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mstyle mathcolor="#F58137"><mi>s</mi></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mi>i</mi></mstyle><mstyle mathcolor="#2D2F92"><mi>k</mi></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle></mrow></mrow></msubsup><mspace width="1em"></mspace></mtd><mtd></mtd><mtd><mo>+</mo><msubsup><mi mathvariant="normal">&#x0393;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>r</mi></mstyle><mstyle mathcolor="#ED1B23"><mi>l</mi></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msubsup><msubsup><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#F58137"><mi>r</mi></mstyle></mrow><mi>m</mi><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle><mstyle mathcolor="#F58137"><mo>.</mo></mstyle></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mstyle mathcolor="#2D2F92"><mi>i</mi></mstyle><mstyle mathcolor="#2D2F92"><mi>k</mi></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle><mstyle mathcolor="#2D2F92"><mo>.</mo></mstyle></mrow></mrow></msubsup><mo>.</mo><mo>.</mo><mo>.</mo></mtd><mtd></mtd><mtd><mstyle mathcolor="#F58137"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>f&#xA0;</mtext></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mtext>&#xA0;r jeden unteren Index</mtext></mrow></mrow></mstyle></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$T$

$r$

$s$

$l$

$i$

$k$

$T$

$r$

$s$

$l$

$i$

$k$

$Γ$

$m$

$l$

$i$

$T$

$r$

$s$

$m$

$k$

$Γ$

$m$

$l$

$i$

$T$

$r$

$s$

$r$

$m$

$\ddot{u}$

$Γ$

$r$

$l$

$m$

$T$

$m$

$s$

$i$

$k$

$Γ$

$r$

$l$

$m$

$T$

$r$

$m$

$i$

$k$

$\ddot{u}$

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