- testwiki

General

Display information for equation id:math.1971.19 on revision:1971

* Page found: Poisson- Klammern (eq math.1971.19)

Occurrences on the following pages:

Poisson- Klammern Eq: math.1979.19

Hash: 3f711fa7c94d8abf3b30a71660d3b2b6

TeX (original user input):

\begin{align}
  & \frac{\partial f}{\partial {{x}_{i}}}=\sum\limits_{k}{\frac{\partial f}{\partial {{y}_{k}}}\frac{\partial {{y}_{k}}}{\partial {{x}_{i}}}=}\sum\limits_{k}{{{M}_{ki}}^{-1}\frac{\partial f}{\partial {{y}_{k}}}\Leftrightarrow {{{\bar{f}}}_{x}}={{\left( {{M}^{-1}} \right)}^{T}}{{{\bar{f}}}_{y}}\Leftrightarrow {{{\bar{f}}}_{x}}^{T}={{{\bar{f}}}_{y}}^{T}\left( {{M}^{-1}} \right)} \\ 
 & {{{\bar{f}}}_{x}}^{T}J{{{\bar{g}}}_{x}}={{{\bar{f}}}_{y}}^{T}\left( {{M}^{-1}} \right)J{{\left( {{M}^{-1}} \right)}^{T}}{{{\bar{g}}}_{y}}={{{\bar{f}}}_{y}}^{T}J{{{\bar{g}}}_{y}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial f}{\partial {{x}_{i}}}}=\sum \limits _{k}{{\frac {\partial f}{\partial {{y}_{k}}}}{\frac {\partial {{y}_{k}}}{\partial {{x}_{i}}}}=}\sum \limits _{k}{{{M}_{ki}}^{-1}{\frac {\partial f}{\partial {{y}_{k}}}}\Leftrightarrow {{\bar {f}}_{x}}={{\left({{M}^{-1}}\right)}^{T}}{{\bar {f}}_{y}}\Leftrightarrow {{\bar {f}}_{x}}^{T}={{\bar {f}}_{y}}^{T}\left({{M}^{-1}}\right)}\\&{{\bar {f}}_{x}}^{T}J{{\bar {g}}_{x}}={{\bar {f}}_{y}}^{T}\left({{M}^{-1}}\right)J{{\left({{M}^{-1}}\right)}^{T}}{{\bar {g}}_{y}}={{\bar {f}}_{y}}^{T}J{{\bar {g}}_{y}}\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (4.824 KB / 538 B) :

\begin{matrix} \frac{\partial f}{\partial x_{i}} = \sum_{k} \frac{\partial f}{\partial y_{k}} \frac{\partial y_{k}}{\partial x_{i}} = \sum_{k} {M_{k i}}^{- 1} \frac{\partial f}{\partial y_{k}} \Leftrightarrow {\bar{f}}_{x} = {(M^{- 1})}^{T} {\bar{f}}_{y} \Leftrightarrow {\bar{f}}_{x}^{T} = {\bar{f}}_{y}^{T} (M^{- 1}) \\ {\bar{f}}_{x}^{T} J {\bar{g}}_{x} = {\bar{f}}_{y}^{T} (M^{- 1}) J {(M^{- 1})}^{T} {\bar{g}}_{y} = {\bar{f}}_{y}^{T} J {\bar{g}}_{y} \end{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>f</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><munder><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></munder><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>f</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo></mrow><munder><mo form="prefix" movablelimits="false" stretchy="false">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msup><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>i</mi></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>f</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>y</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo stretchy="false">⇔</mo><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mo stretchy="false">⇔</mo><msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo stretchy="false">=</mo><msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mi>J</mi><msub><mover><mi>g</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">=</mo><msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>J</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><msub><mover><mi>g</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mo stretchy="false">=</mo><msup><msub><mover><mi>f</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mi>J</mi><msub><mover><mi>g</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$f$

$x_{i}$

$k$

$f$

$y_{k}$

$y_{k}$

$x_{i}$

$k$

$M_{k i}$

$f$

$y_{k}$

${\bar{f}}_{x}$

$M$

$T$

${\bar{f}}_{y}$

${\bar{f}}_{x}$

$T$

${\bar{f}}_{y}$

$T$

$M$

${\bar{f}}_{x}$

$T$

$J$

${\bar{g}}_{x}$

${\bar{f}}_{y}$

$T$

$M$

$J$

$M$

$T$

${\bar{g}}_{y}$

${\bar{f}}_{y}$

$T$

$J$

${\bar{g}}_{y}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search