Jump to navigation Jump to search

General

Display information for equation id:math.240185.2 on revision:240185

* Page found: Cartan's equivalence method (eq math.240185.2)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: baf83f5d27e35e8bed59808e502590df

TeX (original user input):

\phi^*\gamma^i(y)=g^i_j(x)\theta^j(x),\ (g^i_j)\in G

TeX (checked):

\phi ^{*}\gamma ^{i}(y)=g_{j}^{i}(x)\theta ^{j}(x),\ (g_{j}^{i})\in G

LaTeXML (experimental; uses MathML) rendering

MathML (6.683 KB / 1.08 KB) :

ϕ * γ i ( y ) = g j i ( x ) θ j ( x ) , ( g j i ) G formulae-sequence superscript ϕ superscript γ i y superscript subscript g j i x superscript θ j x superscript subscript g j i G {\displaystyle\phi^{*}\gamma^{i}(y)=g_{j}^{i}(x)\theta^{j}(x),\ (g_{j}^{i})\in G}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\phi^{*}\gamma^{i}(y)=g_{j}^{i}(x)\theta^{j}(x),\ (g_{j}^{i})\in&#10;G}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.29" xref="p1.1.m1.1.29.1.cmml">
      <mrow id="p1.1.m1.1.29.2" xref="p1.1.m1.1.29.1.cmml">
        <mrow id="p1.1.m1.1.29.2.1" xref="p1.1.m1.1.29.1.cmml">
          <msup id="p1.1.m1.1.29.2.1.2" xref="p1.1.m1.1.29.1.cmml">
            <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">ϕ</mi>
            <mo id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">*</mo>
          </msup>
          <mo id="p1.1.m1.1.29.2.1.1" xref="p1.1.m1.1.29.2.1.1.cmml"></mo>
          <msup id="p1.1.m1.1.29.2.1.3" xref="p1.1.m1.1.29.1.cmml">
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">γ</mi>
            <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">i</mi>
          </msup>
          <mo id="p1.1.m1.1.29.2.1.1a" xref="p1.1.m1.1.29.2.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.29.2.1.4">
            <mo stretchy="false" id="p1.1.m1.1.5">(</mo>
            <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">y</mi>
            <mo stretchy="false" id="p1.1.m1.1.7">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">=</mo>
        <mrow id="p1.1.m1.1.29.2.2" xref="p1.1.m1.1.29.1.cmml">
          <msubsup id="p1.1.m1.1.29.2.2.2" xref="p1.1.m1.1.29.1.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">g</mi>
            <mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">j</mi>
            <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">i</mi>
          </msubsup>
          <mo id="p1.1.m1.1.29.2.2.1" xref="p1.1.m1.1.29.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.29.2.2.3">
            <mo stretchy="false" id="p1.1.m1.1.12">(</mo>
            <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">x</mi>
            <mo stretchy="false" id="p1.1.m1.1.14">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.29.2.2.1a" xref="p1.1.m1.1.29.2.2.1.cmml"></mo>
          <msup id="p1.1.m1.1.29.2.2.4" xref="p1.1.m1.1.29.1.cmml">
            <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">θ</mi>
            <mi id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">j</mi>
          </msup>
          <mo id="p1.1.m1.1.29.2.2.1b" xref="p1.1.m1.1.29.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.29.2.2.5">
            <mo stretchy="false" id="p1.1.m1.1.17">(</mo>
            <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">x</mi>
            <mo stretchy="false" id="p1.1.m1.1.19">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo rspace="7.5pt" id="p1.1.m1.1.20" xref="p1.1.m1.1.29.1a.cmml">,</mo>
      <mrow id="p1.1.m1.1.29.3" xref="p1.1.m1.1.29.1.cmml">
        <mrow id="p1.1.m1.1.29.3.1" xref="p1.1.m1.1.29.3.1.2.cmml">
          <mo stretchy="false" id="p1.1.m1.1.22">(</mo>
          <msubsup id="p1.1.m1.1.29.3.1.2" xref="p1.1.m1.1.29.3.1.2.cmml">
            <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">g</mi>
            <mi id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">j</mi>
            <mi id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">i</mi>
          </msubsup>
          <mo stretchy="false" id="p1.1.m1.1.26">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml"></mo>
        <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">G</mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.29.1.cmml" xref="p1.1.m1.1.29">
        <csymbol cd="ambiguous" id="p1.1.m1.1.29.1a.cmml" xref="p1.1.m1.1.20">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.29.2.cmml" xref="p1.1.m1.1.29">
          <eq id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
          <apply id="p1.1.m1.1.29.2.1.cmml" xref="p1.1.m1.1.29">
            <times id="p1.1.m1.1.29.2.1.1.cmml" xref="p1.1.m1.1.29.2.1.1"/>
            <apply id="p1.1.m1.1.29.2.1.2.cmml" xref="p1.1.m1.1.29">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.1.2.1.cmml">superscript</csymbol>
              <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">ϕ</ci>
              <times id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1"/>
            </apply>
            <apply id="p1.1.m1.1.29.2.1.3.cmml" xref="p1.1.m1.1.29">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.1.3.1.cmml">superscript</csymbol>
              <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">γ</ci>
              <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">i</ci>
            </apply>
            <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">y</ci>
          </apply>
          <apply id="p1.1.m1.1.29.2.2.cmml" xref="p1.1.m1.1.29">
            <times id="p1.1.m1.1.29.2.2.1.cmml" xref="p1.1.m1.1.29.2.2.1"/>
            <apply id="p1.1.m1.1.29.2.2.2.cmml" xref="p1.1.m1.1.29">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.2.2.1.cmml">superscript</csymbol>
              <apply id="p1.1.m1.1.29.2.2.2.2.cmml" xref="p1.1.m1.1.29">
                <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.2.2.2.1.cmml">subscript</csymbol>
                <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">g</ci>
                <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">j</ci>
              </apply>
              <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">i</ci>
            </apply>
            <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">x</ci>
            <apply id="p1.1.m1.1.29.2.2.4.cmml" xref="p1.1.m1.1.29">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.2.2.4.1.cmml">superscript</csymbol>
              <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">θ</ci>
              <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">j</ci>
            </apply>
            <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">x</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.29.3.cmml" xref="p1.1.m1.1.29">
          <in id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27"/>
          <apply id="p1.1.m1.1.29.3.1.2.cmml" xref="p1.1.m1.1.29.3.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.1.2.1.cmml">superscript</csymbol>
            <apply id="p1.1.m1.1.29.3.1.2.2.cmml" xref="p1.1.m1.1.29.3.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.29.3.1.2.2.1.cmml">subscript</csymbol>
              <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">g</ci>
              <ci id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">j</ci>
            </apply>
            <ci id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">i</ci>
          </apply>
          <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">G</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\phi^{*}\gamma^{i}(y)=g_{j}^{i}(x)\theta^{j}(x),\ (g_{j}^{i})\in
G}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (13.12 KB / 4.593 KB) :

phi Superscript asterisk Baseline times gamma Superscript i Baseline times left-parenthesis y right-parenthesis equals g Subscript j Superscript i Baseline times left-parenthesis x right-parenthesis times theta Superscript j Baseline times left-parenthesis x right-parenthesis comma left-parenthesis g Subscript j Superscript i Baseline right-parenthesis element-of upper G

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Translation to Mathematica

In Mathematica:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Similar pages

Calculated based on the variables occurring on the entire Cartan's equivalence method page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results