Jump to navigation Jump to search

General

Display information for equation id:math.222671.0 on revision:222671

* Page found: Nash embedding theorem (eq math.222671.0)

(force rerendering)

Occurrences on the following pages:

Hash: fe035ead1fe244462ff673d90fcdb08e

TeX (original user input):

g(v,w)=\langle df_\epsilon(v),df_\epsilon(w)\rangle

TeX (checked):

g(v,w)=\langle df_{\epsilon }(v),df_{\epsilon }(w)\rangle

LaTeXML (experimental; uses MathML) rendering

MathML (5.138 KB / 950 B) :

g ( v , w ) = d f ϵ ( v ) , d f ϵ ( w ) 𝑔 𝑣 𝑤 𝑑 subscript 𝑓 italic-ϵ 𝑣 𝑑 subscript 𝑓 italic-ϵ 𝑤 {\displaystyle g(v,w)=\langle df_{\epsilon}(v),df_{\epsilon}(w)\rangle}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle g(v,w)=\langle df_{\epsilon}(v),df_{\epsilon}(w)\rangle}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
      <mrow id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">g</mi>
        <mo id="p1.1.m1.1.23.1.1" xref="p1.1.m1.1.23.1.1.cmml"></mo>
        <mrow id="p1.1.m1.1.23.1.2" xref="p1.1.m1.1.23.1.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.23.1.2.1.cmml">(</mo>
          <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">v</mi>
          <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.23.1.2.1.cmml">,</mo>
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">w</mi>
          <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.23.1.2.1.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">=</mo>
      <mrow id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.1.cmml">
        <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.23.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.23.2.2" xref="p1.1.m1.1.23.2.2.cmml">
          <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">d</mi>
          <mo id="p1.1.m1.1.23.2.2.1" xref="p1.1.m1.1.23.2.2.1.cmml"></mo>
          <msub id="p1.1.m1.1.23.2.2.2" xref="p1.1.m1.1.23.2.2.2.cmml">
            <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">f</mi>
            <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">ϵ</mi>
          </msub>
          <mo id="p1.1.m1.1.23.2.2.1a" xref="p1.1.m1.1.23.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.23.2.2.3" xref="p1.1.m1.1.23.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.23.2.2.cmml">(</mo>
            <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">v</mi>
            <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.23.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.23.2.1.cmml">,</mo>
        <mrow id="p1.1.m1.1.23.2.3" xref="p1.1.m1.1.23.2.3.cmml">
          <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">d</mi>
          <mo id="p1.1.m1.1.23.2.3.1" xref="p1.1.m1.1.23.2.3.1.cmml"></mo>
          <msub id="p1.1.m1.1.23.2.3.2" xref="p1.1.m1.1.23.2.3.2.cmml">
            <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">f</mi>
            <mi id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">ϵ</mi>
          </msub>
          <mo id="p1.1.m1.1.23.2.3.1a" xref="p1.1.m1.1.23.2.3.1.cmml"></mo>
          <mrow id="p1.1.m1.1.23.2.3.3" xref="p1.1.m1.1.23.2.3.cmml">
            <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.23.2.3.cmml">(</mo>
            <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">w</mi>
            <mo stretchy="false" id="p1.1.m1.1.21" xref="p1.1.m1.1.23.2.3.cmml">)</mo>
          </mrow>
        </mrow>
        <mo stretchy="false" id="p1.1.m1.1.22" xref="p1.1.m1.1.23.2.1.cmml"></mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
        <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
        <apply id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">
          <times id="p1.1.m1.1.23.1.1.cmml" xref="p1.1.m1.1.23.1.1"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑔</ci>
          <interval closure="open" id="p1.1.m1.1.23.1.2.1.cmml" xref="p1.1.m1.1.23.1.2">
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑣</ci>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑤</ci>
          </interval>
        </apply>
        <list id="p1.1.m1.1.23.2.1.cmml" xref="p1.1.m1.1.23.2">
          <apply id="p1.1.m1.1.23.2.2.cmml" xref="p1.1.m1.1.23.2.2">
            <times id="p1.1.m1.1.23.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.1"/>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑑</ci>
            <apply id="p1.1.m1.1.23.2.2.2.cmml" xref="p1.1.m1.1.23.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.2.2.1.cmml" xref="p1.1.m1.1.23.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑓</ci>
              <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">italic-ϵ</ci>
            </apply>
            <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑣</ci>
          </apply>
          <apply id="p1.1.m1.1.23.2.3.cmml" xref="p1.1.m1.1.23.2.3">
            <times id="p1.1.m1.1.23.2.3.1.cmml" xref="p1.1.m1.1.23.2.3.1"/>
            <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑑</ci>
            <apply id="p1.1.m1.1.23.2.3.2.cmml" xref="p1.1.m1.1.23.2.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.23.2.3.2.1.cmml" xref="p1.1.m1.1.23.2.3.2">subscript</csymbol>
              <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">𝑓</ci>
              <ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">italic-ϵ</ci>
            </apply>
            <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">𝑤</ci>
          </apply>
        </list>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle g(v,w)=\langle df_{\epsilon}(v),df_{\epsilon}(w)\rangle}</annotation>
  </semantics>
</math>

SVG (9.451 KB / 3.226 KB) :

g times left-parenthesis v comma w right-parenthesis equals mathematical left-angle d times f Subscript epsilon Baseline times left-parenthesis v right-parenthesis comma d times f Subscript epsilon Baseline times left-parenthesis w right-parenthesis mathematical right-angle

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.252 KB / 403 B) :

g ( v , w ) = d f ϵ ( v ) , d f ϵ ( w ) {\displaystyle g(v,w)=\langle df_{\epsilon }(v),df_{\epsilon }(w)\rangle }
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle g(v,w)=\langle df_{\epsilon }(v),df_{\epsilon }(w)\rangle }">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>g</mi>
        <mo stretchy="false">(</mo>
        <mi>v</mi>
        <mo>,</mo>
        <mi>w</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mo fence="false" stretchy="false">&#x27E8;<!-- ⟨ --></mo>
        <mi>d</mi>
        <msub>
          <mi>f</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>&#x03F5;<!-- ϵ --></mi>
          </mrow>
        </msub>
        <mo stretchy="false">(</mo>
        <mi>v</mi>
        <mo stretchy="false">)</mo>
        <mo>,</mo>
        <mi>d</mi>
        <msub>
          <mi>f</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>&#x03F5;<!-- ϵ --></mi>
          </mrow>
        </msub>
        <mo stretchy="false">(</mo>
        <mi>w</mi>
        <mo stretchy="false">)</mo>
        <mo fence="false" stretchy="false">&#x27E9;<!-- ⟩ --></mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle g(v,w)=\langle df_{\epsilon }(v),df_{\epsilon }(w)\rangle }</annotation>
  </semantics>
</math>

SVG (7.044 KB / 2.939 KB) :

{\displaystyle g(v,w)=\langle df_{\epsilon }(v),df_{\epsilon }(w)\rangle }

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Nash embedding theorem page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results