Jump to navigation Jump to search

General

Display information for equation id:math.231224.3 on revision:231224

* Page found: Weyl algebra (eq math.231224.3)

(force rerendering)

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

Occurrences on the following pages:

Hash: 0a155fc145e3d52afd5016ec51491704

TeX (original user input): 

W(V) := T(V) / (\!( v \otimes u - u \otimes v - \omega(v,u), \text{ for } v,u \in V )\!),

TeX (checked): 

W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega (v,u),{\text{ for }}v,u\in V)\!),

LaTeXML (experimental; uses MathML) rendering

MathML (7.075 KB / 1.22 KB) :

W ( V ) := T ( V ) / ( ( v ⊗ u - u ⊗ v - ω ( v , u ) ,  for  v , u ∈ V ) ) , fragments W fragments ( V ) assign T fragments ( V ) fragments ( fragments ( v tensor-product u u tensor-product v ω fragments ( v , u ) ,  for  v , u V ) ) , {\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega(v,u),{\text{ for }}% v,u\in V)\!),} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega(v,u),{\text{ for }}%&#10;v,u\in V)\!),}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">W</mi>
      <mrow id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
        <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">(</mo>
        <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">V</mi>
        <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">:=</mo>
      <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">T</mi>
      <mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">
        <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">(</mo>
        <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">V</mi>
        <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">/</mo>
      <mrow id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">
        <mo rspace="0.8pt" stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">(</mo>
        <mrow id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">
          <mo stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">(</mo>
          <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">v</mi>
          <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">⊗</mo>
          <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">u</mi>
          <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">-</mo>
          <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">u</mi>
          <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">⊗</mo>
          <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">v</mi>
          <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">-</mo>
          <mi id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">ω</mi>
          <mrow id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">
            <mo stretchy="false" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">(</mo>
            <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">v</mi>
            <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">,</mo>
            <mi id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">u</mi>
            <mo stretchy="false" id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">,</mo>
          <mtext id="p1.1.m1.1.30" xref="p1.1.m1.1.30a.cmml"> for </mtext>
          <mi id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">v</mi>
          <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">,</mo>
          <mi id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">u</mi>
          <mo id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">∈</mo>
          <mi id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">V</mi>
          <mo rspace="0.8pt" stretchy="false" id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">)</mo>
        </mrow>
        <mo stretchy="false" id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">,</mo>
    </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>
        <csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">W</csymbol>
        <cerror id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
          <csymbol cd="ambiguous" id="p1.1.m1.1.5a.cmml" xref="p1.1.m1.1.5">fragments</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">V</csymbol>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">)</ci>
        </cerror>
        <csymbol cd="latexml" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">assign</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">T</csymbol>
        <cerror id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">
          <csymbol cd="ambiguous" id="p1.1.m1.1.13a.cmml" xref="p1.1.m1.1.13">fragments</csymbol>
          <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">V</csymbol>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">)</ci>
        </cerror>
        <divide id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
        <cerror id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">
          <csymbol cd="ambiguous" id="p1.1.m1.1.41a.cmml" xref="p1.1.m1.1.41">fragments</csymbol>
          <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">(</ci>
          <cerror id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">
            <csymbol cd="ambiguous" id="p1.1.m1.1.40a.cmml" xref="p1.1.m1.1.40">fragments</csymbol>
            <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">(</ci>
            <csymbol cd="unknown" id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">v</csymbol>
            <csymbol cd="latexml" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">tensor-product</csymbol>
            <csymbol cd="unknown" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">u</csymbol>
            <minus id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"/>
            <csymbol cd="unknown" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">u</csymbol>
            <csymbol cd="latexml" id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">tensor-product</csymbol>
            <csymbol cd="unknown" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">v</csymbol>
            <minus id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22"/>
            <csymbol cd="unknown" id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">ω</csymbol>
            <cerror id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">
              <csymbol cd="ambiguous" id="p1.1.m1.1.37a.cmml" xref="p1.1.m1.1.37">fragments</csymbol>
              <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">(</ci>
              <csymbol cd="unknown" id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">v</csymbol>
              <ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">,</ci>
              <csymbol cd="unknown" id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">u</csymbol>
              <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">)</ci>
            </cerror>
            <ci id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">,</ci>
            <ci id="p1.1.m1.1.30a.cmml" xref="p1.1.m1.1.30">
              <mtext id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30"> for </mtext>
            </ci>
            <csymbol cd="unknown" id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31">v</csymbol>
            <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">,</ci>
            <csymbol cd="unknown" id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">u</csymbol>
            <in id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34"/>
            <csymbol cd="unknown" id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">V</csymbol>
            <ci id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36">)</ci>
          </cerror>
          <ci id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38">)</ci>
        </cerror>
        <ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">,</ci>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega(v,u),{\text{ for }}%
v,u\in V)\!),}</annotation>
  </semantics>
</math>

SVG (13.108 KB / 4.524 KB) :

upper W left-parenthesis upper V right-parenthesis colon equals upper T left-parenthesis upper V right-parenthesis slash left-parenthesis left-parenthesis v circled-times u minus u circled-times v minus omega left-parenthesis v comma u right-parenthesis comma for v comma u element-of upper V right-parenthesis right-parenthesis comma

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.633 KB / 479 B) :

W ( V ) := T ( V ) / ( ( v ⊗ u − u ⊗ v − ω ( v , u ) ,  for  v , u ∈ V ) ) , {\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega (v,u),{\text{ for }}v,u\in V)\!),} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega (v,u),{\text{ for }}v,u\in V)\!),}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>W</mi>
        <mo stretchy="false">(</mo>
        <mi>V</mi>
        <mo stretchy="false">)</mo>
        <mo>:=</mo>
        <mi>T</mi>
        <mo stretchy="false">(</mo>
        <mi>V</mi>
        <mo stretchy="false">)</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mo>/</mo>
        </mrow>
        <mo stretchy="false">(</mo>
        <mspace width="negativethinmathspace" />
        <mo stretchy="false">(</mo>
        <mi>v</mi>
        <mo>&#x2297;<!-- ⊗ --></mo>
        <mi>u</mi>
        <mo>&#x2212;<!-- − --></mo>
        <mi>u</mi>
        <mo>&#x2297;<!-- ⊗ --></mo>
        <mi>v</mi>
        <mo>&#x2212;<!-- − --></mo>
        <mi>&#x03C9;<!-- ω --></mi>
        <mo stretchy="false">(</mo>
        <mi>v</mi>
        <mo>,</mo>
        <mi>u</mi>
        <mo stretchy="false">)</mo>
        <mo>,</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mtext>&#xA0;for&#xA0;</mtext>
        </mrow>
        <mi>v</mi>
        <mo>,</mo>
        <mi>u</mi>
        <mo>&#x2208;<!-- ∈ --></mo>
        <mi>V</mi>
        <mo stretchy="false">)</mo>
        <mspace width="negativethinmathspace" />
        <mo stretchy="false">)</mo>
        <mo>,</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega (v,u),{\text{ for }}v,u\in V)\!),}</annotation>
  </semantics>
</math>

SVG (10.436 KB / 4.201 KB) :

{\displaystyle W(V):=T(V)/(\!(v\otimes u-u\otimes v-\omega (v,u),{\text{ for }}v,u\in V)\!),}

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 Weyl algebra page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "https://en.formulasearchengine.com/wiki/Special:FormulaInfo"