Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.1071.8 on revision:1071

* Page found: Affinie Abbildung (eq math.1071.8)

(force rerendering)

Occurrences on the following pages:

Hash: 0a51ccd9a3903b1c5ec057ba017cd934

TeX (original user input):

\Leftrightarrow \exists {{p}_{0}}\in X:\quad \left( \exists g:{{T}_{M}}\to {{V}_{M}}:\overrightarrow{{{p}_{0}}q}\to \overrightarrow{f({{p}_{0}})f(q)} \right)

TeX (checked):

\Leftrightarrow \exists {{p}_{0}}\in X:\quad \left(\exists g:{{T}_{M}}\to {{V}_{M}}:{\overrightarrow {{{p}_{0}}q}}\to {\overrightarrow {f({{p}_{0}})f(q)}}\right)

LaTeXML (experimentell; verwendet MathML) rendering

MathML (8.176 KB / 1.43 KB) :

p 0 X : ( g : T M V M : p 0 q f ( p 0 ) f ( q ) ) fragments subscript 𝑝 0 X : italic-  fragments ( g : subscript 𝑇 𝑀 subscript 𝑉 𝑀 : subscript 𝑝 0 𝑞 𝑓 subscript 𝑝 0 𝑓 𝑞 ) {\displaystyle{\displaystyle\Leftrightarrow\exists{{p}_{0}}\in X:\quad\left(% \exists g:{{T}_{M}}\to{{V}_{M}}:\overrightarrow{{{p}_{0}}q}\to\overrightarrow{% f({{p}_{0}})f(q)}\right)}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\Leftrightarrow\exists{{p}_{0}}\in X:\quad\left(%&#10;\exists g:{{T}_{M}}\to{{V}_{M}}:\overrightarrow{{{p}_{0}}q}\to\overrightarrow{%&#10;f({{p}_{0}})f(q)}\right)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml"></mo>
      <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml"></mo>
      <msub id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">p</mi>
        <mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">0</mn>
      </msub>
      <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml"></mo>
      <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">X</mi>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">:</mo>
      <mo mathvariant="italic" separator="true" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml"></mo>
      <mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
        <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">(</mo>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml"></mo>
        <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">g</mi>
        <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">:</mo>
        <msub id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
          <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">T</mi>
          <mi id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">M</mi>
        </msub>
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml"></mo>
        <msub id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
          <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">V</mi>
          <mi id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">M</mi>
        </msub>
        <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">:</mo>
        <mover accent="true" id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">
          <mrow id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.cmml">
            <msub id="p1.1.m1.1.19.2.5" xref="p1.1.m1.1.19.2.5.cmml">
              <mi id="p1.1.m1.1.19.2.1" xref="p1.1.m1.1.19.2.1.cmml">p</mi>
              <mn id="p1.1.m1.1.19.2.2.1" xref="p1.1.m1.1.19.2.2.1.cmml">0</mn>
            </msub>
            <mo id="p1.1.m1.1.19.2.4" xref="p1.1.m1.1.19.2.4.cmml"></mo>
            <mi id="p1.1.m1.1.19.2.3" xref="p1.1.m1.1.19.2.3.cmml">q</mi>
          </mrow>
          <mo id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml"></mo>
        </mover>
        <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml"></mo>
        <mover accent="true" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
          <mrow id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.cmml">
            <mi id="p1.1.m1.1.21.2.1" xref="p1.1.m1.1.21.2.1.cmml">f</mi>
            <mo id="p1.1.m1.1.21.2.10" xref="p1.1.m1.1.21.2.10.cmml"></mo>
            <mrow id="p1.1.m1.1.21.2.11" xref="p1.1.m1.1.21.2.11.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.21.2.2" xref="p1.1.m1.1.21.2.11.2.cmml">(</mo>
              <msub id="p1.1.m1.1.21.2.11.2" xref="p1.1.m1.1.21.2.11.2.cmml">
                <mi id="p1.1.m1.1.21.2.3" xref="p1.1.m1.1.21.2.3.cmml">p</mi>
                <mn id="p1.1.m1.1.21.2.4.1" xref="p1.1.m1.1.21.2.4.1.cmml">0</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.21.2.5" xref="p1.1.m1.1.21.2.11.2.cmml">)</mo>
            </mrow>
            <mo id="p1.1.m1.1.21.2.10a" xref="p1.1.m1.1.21.2.10.cmml"></mo>
            <mi id="p1.1.m1.1.21.2.6" xref="p1.1.m1.1.21.2.6.cmml">f</mi>
            <mo id="p1.1.m1.1.21.2.10b" xref="p1.1.m1.1.21.2.10.cmml"></mo>
            <mrow id="p1.1.m1.1.21.2.12" xref="p1.1.m1.1.21.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.21.2.7" xref="p1.1.m1.1.21.2.cmml">(</mo>
              <mi id="p1.1.m1.1.21.2.8" xref="p1.1.m1.1.21.2.8.cmml">q</mi>
              <mo stretchy="false" id="p1.1.m1.1.21.2.9" xref="p1.1.m1.1.21.2.cmml">)</mo>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml"></mo>
        </mover>
        <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">)</mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"></ci>
        <exists id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
        <apply id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">
          <csymbol cd="ambiguous" id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25">subscript</csymbol>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑝</ci>
          <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">0</cn>
        </apply>
        <in id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
        <csymbol cd="unknown" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">X</csymbol>
        <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">:</ci>
        <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">italic-</ci>
        <cerror id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
          <csymbol cd="ambiguous" id="p1.1.m1.1.4a.cmml" xref="p1.1.m1.1.4">fragments</csymbol>
          <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">(</ci>
          <exists id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10"/>
          <csymbol cd="unknown" id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">g</csymbol>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">:</ci>
          <apply id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
            <csymbol cd="ambiguous" id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26">subscript</csymbol>
            <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑇</ci>
            <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">𝑀</ci>
          </apply>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15"></ci>
          <apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
            <csymbol cd="ambiguous" id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27">subscript</csymbol>
            <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑉</ci>
            <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">𝑀</ci>
          </apply>
          <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">:</ci>
          <apply id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">
            <ci id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1"></ci>
            <apply id="p1.1.m1.1.19.2.cmml" xref="p1.1.m1.1.19.2">
              <times id="p1.1.m1.1.19.2.4.cmml" xref="p1.1.m1.1.19.2.4"/>
              <apply id="p1.1.m1.1.19.2.5.cmml" xref="p1.1.m1.1.19.2.5">
                <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.5.1.cmml" xref="p1.1.m1.1.19.2.5">subscript</csymbol>
                <ci id="p1.1.m1.1.19.2.1.cmml" xref="p1.1.m1.1.19.2.1">𝑝</ci>
                <cn type="integer" id="p1.1.m1.1.19.2.2.1.cmml" xref="p1.1.m1.1.19.2.2.1">0</cn>
              </apply>
              <ci id="p1.1.m1.1.19.2.3.cmml" xref="p1.1.m1.1.19.2.3">𝑞</ci>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"></ci>
          <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
            <ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1"></ci>
            <apply id="p1.1.m1.1.21.2.cmml" xref="p1.1.m1.1.21.2">
              <times id="p1.1.m1.1.21.2.10.cmml" xref="p1.1.m1.1.21.2.10"/>
              <ci id="p1.1.m1.1.21.2.1.cmml" xref="p1.1.m1.1.21.2.1">𝑓</ci>
              <apply id="p1.1.m1.1.21.2.11.2.cmml" xref="p1.1.m1.1.21.2.11">
                <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.11.2.1.cmml" xref="p1.1.m1.1.21.2.11">subscript</csymbol>
                <ci id="p1.1.m1.1.21.2.3.cmml" xref="p1.1.m1.1.21.2.3">𝑝</ci>
                <cn type="integer" id="p1.1.m1.1.21.2.4.1.cmml" xref="p1.1.m1.1.21.2.4.1">0</cn>
              </apply>
              <ci id="p1.1.m1.1.21.2.6.cmml" xref="p1.1.m1.1.21.2.6">𝑓</ci>
              <ci id="p1.1.m1.1.21.2.8.cmml" xref="p1.1.m1.1.21.2.8">𝑞</ci>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">)</ci>
        </cerror>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\Leftrightarrow\exists{{p}_{0}}\in X:\quad\left(%
\exists g:{{T}_{M}}\to{{V}_{M}}:\overrightarrow{{{p}_{0}}q}\to\overrightarrow{%
f({{p}_{0}})f(q)}\right)}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (1.215 KB / 370 B) :

p0X:(g:TMVM:p0qf(p0)f(q))
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo>&#x21D4;</mo><mi mathvariant="normal">&#x2203;</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>&#x2208;</mo><mi>X</mi><mi>:</mi><mspace width="1em"></mspace><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">&#x2203;</mi><mi>g</mi><mi>:</mi><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></msub><mo accent="false">&#x2192;</mo><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></msub><mi>:</mi><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mi>q</mi></mrow><mo>&#x2192;</mo></mover></mrow><mo accent="false">&#x2192;</mo><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi>f</mi><mo stretchy="false">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mi>f</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo></mrow><mo>&#x2192;</mo></mover></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>

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 Affinie Abbildung page

Identifiers

  • p0
  • X
  • g
  • TM
  • VM
  • p0q
  • f
  • p0
  • f
  • q

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results