Jump to navigation Jump to search

General

Display information for equation id:math.231560.3 on revision:231560

* Page found: Canonical transformation (eq math.231560.3)

(force rerendering)

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

Occurrences on the following pages:

Hash: ee98465032e27021c1f60c25e9f2eb24

TeX (original user input):

\mathbf{p} \cdot \mathbf{q} \equiv \sum_{k=1}^{N} p_{k} q_{k}.

TeX (checked):

\mathbf {p} \cdot \mathbf {q} \equiv \sum _{k=1}^{N}p_{k}q_{k}.

LaTeXML (experimental; uses MathML) rendering

MathML (4.672 KB / 958 B) :

𝐩 𝐪 k = 1 N p k q k . 𝐩 𝐪 superscript subscript 𝑘 1 𝑁 subscript 𝑝 𝑘 subscript 𝑞 𝑘 {\displaystyle{\displaystyle\mathbf{p}\cdot\mathbf{q}\equiv\sum_{k=1}^{N}p_{k}% q_{k}.}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\mathbf{p}\cdot\mathbf{q}\equiv\sum_{k=1}^{N}p_{k}%&#10;q_{k}.}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.13" xref="p1.1.m1.1.13.2.cmml">
      <mrow id="p1.1.m1.1.13.2" xref="p1.1.m1.1.13.2.cmml">
        <mrow id="p1.1.m1.1.13.2.1" xref="p1.1.m1.1.13.2.1.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">𝐩</mi>
          <mo 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">𝐪</mi>
        </mrow>
        <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml"></mo>
        <mrow id="p1.1.m1.1.13.2.2" xref="p1.1.m1.1.13.2.2.cmml">
          <mstyle displaystyle="true" id="p1.1.m1.1.13.2.2.1" xref="p1.1.m1.1.13.2.2.1.cmml">
            <munderover id="p1.1.m1.1.13.2.2.1a" xref="p1.1.m1.1.13.2.2.1.cmml">
              <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml"></mo>
              <mrow id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">
                <mi id="p1.1.m1.1.6.1.1" xref="p1.1.m1.1.6.1.1.cmml">k</mi>
                <mo id="p1.1.m1.1.6.1.2" xref="p1.1.m1.1.6.1.2.cmml">=</mo>
                <mn id="p1.1.m1.1.6.1.3" xref="p1.1.m1.1.6.1.3.cmml">1</mn>
              </mrow>
              <mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">N</mi>
            </munderover>
          </mstyle>
          <mrow id="p1.1.m1.1.13.2.2.2" xref="p1.1.m1.1.13.2.2.2.cmml">
            <msub id="p1.1.m1.1.13.2.2.2.2" xref="p1.1.m1.1.13.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">p</mi>
              <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">k</mi>
            </msub>
            <mo id="p1.1.m1.1.13.2.2.2.1" xref="p1.1.m1.1.13.2.2.2.1.cmml"></mo>
            <msub id="p1.1.m1.1.13.2.2.2.3" xref="p1.1.m1.1.13.2.2.2.3.cmml">
              <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">q</mi>
              <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">k</mi>
            </msub>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.13.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.13.2.cmml" xref="p1.1.m1.1.13">
        <equivalent id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
        <apply id="p1.1.m1.1.13.2.1.cmml" xref="p1.1.m1.1.13.2.1">
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"></ci>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐩</ci>
          <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝐪</ci>
        </apply>
        <apply id="p1.1.m1.1.13.2.2.cmml" xref="p1.1.m1.1.13.2.2">
          <apply id="p1.1.m1.1.13.2.2.1.cmml" xref="p1.1.m1.1.13.2.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.1.1.cmml" xref="p1.1.m1.1.13.2.2.1">superscript</csymbol>
            <apply id="p1.1.m1.1.13.2.2.1.2.cmml" xref="p1.1.m1.1.13.2.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.1.2.1.cmml" xref="p1.1.m1.1.13.2.2.1">subscript</csymbol>
              <sum id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
              <apply id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">
                <eq id="p1.1.m1.1.6.1.2.cmml" xref="p1.1.m1.1.6.1.2"/>
                <ci id="p1.1.m1.1.6.1.1.cmml" xref="p1.1.m1.1.6.1.1">𝑘</ci>
                <cn type="integer" id="p1.1.m1.1.6.1.3.cmml" xref="p1.1.m1.1.6.1.3">1</cn>
              </apply>
            </apply>
            <ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">𝑁</ci>
          </apply>
          <apply id="p1.1.m1.1.13.2.2.2.cmml" xref="p1.1.m1.1.13.2.2.2">
            <times id="p1.1.m1.1.13.2.2.2.1.cmml" xref="p1.1.m1.1.13.2.2.2.1"/>
            <apply id="p1.1.m1.1.13.2.2.2.2.cmml" xref="p1.1.m1.1.13.2.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.2.2.1.cmml" xref="p1.1.m1.1.13.2.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝑝</ci>
              <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝑘</ci>
            </apply>
            <apply id="p1.1.m1.1.13.2.2.2.3.cmml" xref="p1.1.m1.1.13.2.2.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.13.2.2.2.3.1.cmml" xref="p1.1.m1.1.13.2.2.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑞</ci>
              <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">𝑘</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\mathbf{p}\cdot\mathbf{q}\equiv\sum_{k=1}^{N}p_{k}%
q_{k}.}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (8.299 KB / 3.217 KB) :

bold p dot bold q identical-to sigma-summation Underscript k equals 1 Overscript upper N Endscripts p Subscript k Baseline times q Subscript k Baseline period

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 Canonical transformation page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results