Jump to navigation Jump to search

General

Display information for equation id:math.223950.0 on revision:223950

* Page found: Snake lemma (eq math.223950.0)

(force rerendering)

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

Occurrences on the following pages:

Hash: 47c30d0f7e9f906d135de21739297cfa

TeX (original user input):

\ker a \; {\color{Gray}\longrightarrow} \ker b \; {\color{Gray}\longrightarrow} \ker c \; \overset{d}{\longrightarrow} \operatorname{coker}a \; {\color{Gray}\longrightarrow} \operatorname{coker}b \; {\color{Gray}\longrightarrow} \operatorname{coker}c

TeX (checked):

\ker a\;{\color {Gray}\longrightarrow }\ker b\;{\color {Gray}\longrightarrow }\ker c\;{\overset {d}{\longrightarrow }}\operatorname {coker} a\;{\color {Gray}\longrightarrow }\operatorname {coker} b\;{\color {Gray}\longrightarrow }\operatorname {coker} c

LaTeXML (experimental; uses MathML) rendering

MathML (6.589 KB / 1.073 KB) :

ker a ker b ker c 𝑑 coker a coker b coker c kernel 𝑎 kernel 𝑏 kernel 𝑐 𝑑 coker 𝑎 coker 𝑏 coker 𝑐 {\displaystyle{\displaystyle\ker a\;{\color[rgb]{0,0,0}\longrightarrow}\ker b% \;{\color[rgb]{0,0,0}\longrightarrow}\ker c\;\overset{d}{\longrightarrow}% \operatorname{coker}a\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}% b\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}c}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\ker a\;{\color[rgb]{0,0,0}\longrightarrow}\ker b%&#10;\;{\color[rgb]{0,0,0}\longrightarrow}\ker c\;\overset{d}{\longrightarrow}%&#10;\operatorname{coker}a\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}%&#10;b\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}c}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">
      <mrow id="p1.1.m1.1.35.2" xref="p1.1.m1.1.35.2.cmml">
        <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">ker</mi>
        <mo id="p1.1.m1.1.35.2a" xref="p1.1.m1.1.35.2.cmml"></mo>
        <mpadded width="+2.8pt" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
          <mi id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">a</mi>
        </mpadded>
      </mrow>
      <mo mathcolor="#000000" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml"></mo>
      <mrow id="p1.1.m1.1.35.3" xref="p1.1.m1.1.35.3.cmml">
        <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">ker</mi>
        <mo id="p1.1.m1.1.35.3a" xref="p1.1.m1.1.35.3.cmml"></mo>
        <mpadded width="+2.8pt" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
          <mi id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">b</mi>
        </mpadded>
      </mrow>
      <mo mathcolor="#000000" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml"></mo>
      <mrow id="p1.1.m1.1.35.4" xref="p1.1.m1.1.35.4.cmml">
        <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">ker</mi>
        <mo id="p1.1.m1.1.35.4a" xref="p1.1.m1.1.35.4.cmml"></mo>
        <mrow id="p1.1.m1.1.35.4.1" xref="p1.1.m1.1.35.4.1.cmml">
          <mpadded width="+2.8pt" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
            <mi id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">c</mi>
          </mpadded>
          <mo id="p1.1.m1.1.35.4.1.1" xref="p1.1.m1.1.35.4.1.1.cmml"></mo>
          <mover accent="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
            <mo id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml"></mo>
            <mo id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">𝑑</mo>
          </mover>
          <mo id="p1.1.m1.1.35.4.1.1a" xref="p1.1.m1.1.35.4.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.35.4.1.2" xref="p1.1.m1.1.35.4.1.2.cmml">
            <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">coker</mi>
            <mo id="p1.1.m1.1.35.4.1.2a" xref="p1.1.m1.1.35.4.1.2.cmml"></mo>
            <mpadded width="+2.8pt" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
              <mi id="p1.1.m1.1.18a" xref="p1.1.m1.1.18.cmml">a</mi>
            </mpadded>
          </mrow>
        </mrow>
      </mrow>
      <mo mathcolor="#000000" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml"></mo>
      <mrow id="p1.1.m1.1.35.5" xref="p1.1.m1.1.35.5.cmml">
        <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">coker</mi>
        <mo id="p1.1.m1.1.35.5a" xref="p1.1.m1.1.35.5.cmml"></mo>
        <mpadded width="+2.8pt" id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
          <mi id="p1.1.m1.1.26a" xref="p1.1.m1.1.26.cmml">b</mi>
        </mpadded>
      </mrow>
      <mo mathcolor="#000000" id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml"></mo>
      <mrow id="p1.1.m1.1.35.6" xref="p1.1.m1.1.35.6.cmml">
        <mi id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">coker</mi>
        <mo id="p1.1.m1.1.35.6a" xref="p1.1.m1.1.35.6.cmml"></mo>
        <mi id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">c</mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">
        <and id="p1.1.m1.1.35a.cmml" xref="p1.1.m1.1.35"/>
        <apply id="p1.1.m1.1.35b.cmml" xref="p1.1.m1.1.35">
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"></ci>
          <apply id="p1.1.m1.1.35.2.cmml" xref="p1.1.m1.1.35.2">
            <csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">kernel</csymbol>
            <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑎</ci>
          </apply>
          <apply id="p1.1.m1.1.35.3.cmml" xref="p1.1.m1.1.35.3">
            <csymbol cd="latexml" id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">kernel</csymbol>
            <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑏</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.35c.cmml" xref="p1.1.m1.1.35">
          <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"></ci>
          <share href="#p1.1.m1.1.35.3.cmml" id="p1.1.m1.1.35d.cmml" xref="p1.1.m1.1.35"/>
          <apply id="p1.1.m1.1.35.4.cmml" xref="p1.1.m1.1.35.4">
            <csymbol cd="latexml" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">kernel</csymbol>
            <apply id="p1.1.m1.1.35.4.1.cmml" xref="p1.1.m1.1.35.4.1">
              <times id="p1.1.m1.1.35.4.1.1.cmml" xref="p1.1.m1.1.35.4.1.1"/>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑐</ci>
              <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
                <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">𝑑</ci>
                <ci id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2"></ci>
              </apply>
              <apply id="p1.1.m1.1.35.4.1.2.cmml" xref="p1.1.m1.1.35.4.1.2">
                <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">coker</ci>
                <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">𝑎</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.35e.cmml" xref="p1.1.m1.1.35">
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"></ci>
          <share href="#p1.1.m1.1.35.4.cmml" id="p1.1.m1.1.35f.cmml" xref="p1.1.m1.1.35"/>
          <apply id="p1.1.m1.1.35.5.cmml" xref="p1.1.m1.1.35.5">
            <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">coker</ci>
            <ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">𝑏</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.35g.cmml" xref="p1.1.m1.1.35">
          <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28"></ci>
          <share href="#p1.1.m1.1.35.5.cmml" id="p1.1.m1.1.35h.cmml" xref="p1.1.m1.1.35"/>
          <apply id="p1.1.m1.1.35.6.cmml" xref="p1.1.m1.1.35.6">
            <ci id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">coker</ci>
            <ci id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">𝑐</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\ker a\;{\color[rgb]{0,0,0}\longrightarrow}\ker b%
\;{\color[rgb]{0,0,0}\longrightarrow}\ker c\;\overset{d}{\longrightarrow}%
\operatorname{coker}a\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}%
b\;{\color[rgb]{0,0,0}\longrightarrow}\operatorname{coker}c}}</annotation>
  </semantics>
</math>

SVG (10.578 KB / 3.281 KB) :

kernel a long right-arrow kernel b long right-arrow kernel c times long right-arrow Overscript italic d Endscripts times c o k e r a long right-arrow c o k e r b long right-arrow c o k e r c

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:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Snake lemma page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results