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Display information for equation id:math.1108.9 on revision:1108

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TeX (original user input): 

d{{\sigma }^{2}}={{\left( d{{x}^{1}} \right)}^{2}}+{{\left( d{{x}^{2}} \right)}^{2}}+{{\left( d{{x}^{3}} \right)}^{2}}={{\left( dx{{'}^{1}} \right)}^{2}}+{{\left( dx{{'}^{2}} \right)}^{2}}+{{\left( dx{{'}^{3}} \right)}^{2}}=d\sigma {{'}^{2}}

TeX (checked): 

d{{\sigma }^{2}}={{\left(d{{x}^{1}}\right)}^{2}}+{{\left(d{{x}^{2}}\right)}^{2}}+{{\left(d{{x}^{3}}\right)}^{2}}={{\left(dx{{'}^{1}}\right)}^{2}}+{{\left(dx{{'}^{2}}\right)}^{2}}+{{\left(dx{{'}^{3}}\right)}^{2}}=d\sigma {{'}^{2}}

LaTeXML (experimental; uses MathML) rendering

MathML (15.23 KB / 1.973 KB) :

d σ 2 = ( d x 1 ) 2 + ( d x 2 ) 2 + ( d x 3 ) 2 = ( d x ) ′ 1 2 + ( d x ) ′ 2 2 + ( d x ) ′ 3 2 = d σ 2 ′ fragments d superscript 𝜎 2 superscript fragments ( d superscript 𝑥 1 ) 2 superscript fragments ( d superscript 𝑥 2 ) 2 superscript fragments ( d superscript 𝑥 3 ) 2 superscript fragments ( d x superscript superscript ) 1 ′ 2 superscript fragments ( d x superscript superscript ) 2 ′ 2 superscript fragments ( d x superscript superscript ) 3 ′ 2 d σ superscript superscript absent 2 ′ {\displaystyle{\displaystyle d{{\sigma}^{2}}={{\left(d{{x}^{1}}\right)}^{2}}+{% {\left(d{{x}^{2}}\right)}^{2}}+{{\left(d{{x}^{3}}\right)}^{2}}={{\left(dx{{{}^% {\prime}}^{1}}\right)}^{2}}+{{\left(dx{{{}^{\prime}}^{2}}\right)}^{2}}+{{\left% (dx{{{}^{\prime}}^{3}}\right)}^{2}}=d\sigma{{{}^{\prime}}^{2}}}} 
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    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle d{{\sigma}^{2}}={{\left(d{{x}^{1}}\right)}^{2}}+{%
{\left(d{{x}^{2}}\right)}^{2}}+{{\left(d{{x}^{3}}\right)}^{2}}={{\left(dx{{{}^%
{\prime}}^{1}}\right)}^{2}}+{{\left(dx{{{}^{\prime}}^{2}}\right)}^{2}}+{{\left%
(dx{{{}^{\prime}}^{3}}\right)}^{2}}=d\sigma{{{}^{\prime}}^{2}}}}</annotation>
  </semantics>
</math>

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dσ2=(dx1)2+(dx2)2+(dx3)2=(dx'1)2+(dx'2)2+(dx'3)2=dσ'2
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>d</mi><msup><mi>&#x03C3;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><msup><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><mi>x</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mi>d</mi><mi>&#x03C3;</mi><msup><mi>'</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle></mrow></math>

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