Jump to navigation Jump to search

General

Display information for equation id:math.3884.24 on revision:3884

* Page found: Quotient algebra (eq math.3884.24)

(force rerendering)

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

Occurrences on the following pages:

Hash: ebfa09305d9523c8e8f007c1eb162aef

TeX (original user input):

f^{\mathcal{A}/E}_i ([a_1]_E, \ldots, [a_{n_i}]_E) = [f^{\mathcal{A}}_i(a_1,\ldots, a_{n_i})]_E

TeX (checked):

f_{i}^{{\mathcal {A}}/E}([a_{1}]_{E},\ldots ,[a_{n_{i}}]_{E})=[f_{i}^{\mathcal {A}}(a_{1},\ldots ,a_{n_{i}})]_{E}

LaTeXML (experimental; uses MathML) rendering

MathML (11.388 KB / 1.604 KB) :

f i 𝒜 / E ( [ a 1 ] E , , [ a n i ] E ) = [ f i 𝒜 ( a 1 , , a n i ) ] E superscript subscript 𝑓 𝑖 𝒜 𝐸 subscript delimited-[] subscript 𝑎 1 𝐸 subscript delimited-[] subscript 𝑎 subscript 𝑛 𝑖 𝐸 subscript delimited-[] superscript subscript 𝑓 𝑖 𝒜 subscript 𝑎 1 subscript 𝑎 subscript 𝑛 𝑖 𝐸 {\displaystyle f_{i}^{{{\mathcal{A}}/E}}([a_{1}]_{E},\ldots,[a_{{n_{i}}}]_{E})% =[f_{i}^{{{\mathcal{A}}}}(a_{1},\ldots,a_{{n_{i}}})]_{E}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle f_{i}^{{{\mathcal{A}}/E}}([a_{1}]_{E},\ldots,[a_{{n_{i}}}]_{E})%&#10;=[f_{i}^{{{\mathcal{A}}}}(a_{1},\ldots,a_{{n_{i}}})]_{E}}" 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.m1.1.35.1" xref="p1.1.m1.1.35.1.cmml">
        <msubsup id="p1.1.m1.1.35.1.2" xref="p1.1.m1.1.35.1.2.cmml">
          <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">f</mi>
          <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">i</mi>
          <mrow id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">
            <mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.3.1.1" xref="p1.1.m1.1.3.1.1.cmml">𝒜</mi>
            <mo id="p1.1.m1.1.3.1.2" xref="p1.1.m1.1.3.1.2.cmml">/</mo>
            <mi id="p1.1.m1.1.3.1.3" xref="p1.1.m1.1.3.1.3.cmml">E</mi>
          </mrow>
        </msubsup>
        <mo id="p1.1.m1.1.35.1.1" xref="p1.1.m1.1.35.1.1.cmml"></mo>
        <mrow id="p1.1.m1.1.35.1.3" xref="p1.1.m1.1.35.1.3.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.35.1.3.1.cmml">(</mo>
          <msub id="p1.1.m1.1.35.1.3.2" xref="p1.1.m1.1.35.1.3.2.cmml">
            <mrow id="p1.1.m1.1.35.1.3.2.2" xref="p1.1.m1.1.35.1.3.2.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.35.1.3.2.2.1.1.cmml">[</mo>
              <msub id="p1.1.m1.1.35.1.3.2.2.2" xref="p1.1.m1.1.35.1.3.2.2.2.cmml">
                <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">a</mi>
                <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">1</mn>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.35.1.3.2.2.1.1.cmml">]</mo>
            </mrow>
            <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">E</mi>
          </msub>
          <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.35.1.3.1.cmml">,</mo>
          <mi mathvariant="normal" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml"></mi>
          <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.35.1.3.1.cmml">,</mo>
          <msub id="p1.1.m1.1.35.1.3.3" xref="p1.1.m1.1.35.1.3.3.cmml">
            <mrow id="p1.1.m1.1.35.1.3.3.2" xref="p1.1.m1.1.35.1.3.3.2.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.35.1.3.3.2.1.1.cmml">[</mo>
              <msub id="p1.1.m1.1.35.1.3.3.2.2" xref="p1.1.m1.1.35.1.3.3.2.2.cmml">
                <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">a</mi>
                <msub id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">
                  <mi id="p1.1.m1.1.15.1.1" xref="p1.1.m1.1.15.1.1.cmml">n</mi>
                  <mi id="p1.1.m1.1.15.1.2.1" xref="p1.1.m1.1.15.1.2.1.cmml">i</mi>
                </msub>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.35.1.3.3.2.1.1.cmml">]</mo>
            </mrow>
            <mi id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">E</mi>
          </msub>
          <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.35.1.3.1.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">=</mo>
      <msub id="p1.1.m1.1.35.2" xref="p1.1.m1.1.35.2.cmml">
        <mrow id="p1.1.m1.1.35.2.2" xref="p1.1.m1.1.35.2.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.35.2.2.1.1.cmml">[</mo>
          <mrow id="p1.1.m1.1.35.2.2.2" xref="p1.1.m1.1.35.2.2.2.cmml">
            <msubsup id="p1.1.m1.1.35.2.2.2.2" xref="p1.1.m1.1.35.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">f</mi>
              <mi id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">i</mi>
              <mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">𝒜</mi>
            </msubsup>
            <mo id="p1.1.m1.1.35.2.2.2.1" xref="p1.1.m1.1.35.2.2.2.1.cmml"></mo>
            <mrow id="p1.1.m1.1.35.2.2.2.3" xref="p1.1.m1.1.35.2.2.2.3.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.24" xref="p1.1.m1.1.35.2.2.2.3.1.cmml">(</mo>
              <msub id="p1.1.m1.1.35.2.2.2.3.2" xref="p1.1.m1.1.35.2.2.2.3.2.cmml">
                <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">a</mi>
                <mn id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">1</mn>
              </msub>
              <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.35.2.2.2.3.1.cmml">,</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml"></mi>
              <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.35.2.2.2.3.1.cmml">,</mo>
              <msub id="p1.1.m1.1.35.2.2.2.3.3" xref="p1.1.m1.1.35.2.2.2.3.3.cmml">
                <mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">a</mi>
                <msub id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">
                  <mi id="p1.1.m1.1.31.1.1" xref="p1.1.m1.1.31.1.1.cmml">n</mi>
                  <mi id="p1.1.m1.1.31.1.2.1" xref="p1.1.m1.1.31.1.2.1.cmml">i</mi>
                </msub>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.32" xref="p1.1.m1.1.35.2.2.2.3.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo stretchy="false" id="p1.1.m1.1.33" xref="p1.1.m1.1.35.2.2.1.1.cmml">]</mo>
        </mrow>
        <mi id="p1.1.m1.1.34.1" xref="p1.1.m1.1.34.1.cmml">E</mi>
      </msub>
    </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">
        <eq id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
        <apply id="p1.1.m1.1.35.1.cmml" xref="p1.1.m1.1.35.1">
          <times id="p1.1.m1.1.35.1.1.cmml" xref="p1.1.m1.1.35.1.1"/>
          <apply id="p1.1.m1.1.35.1.2.cmml" xref="p1.1.m1.1.35.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.2.1.cmml" xref="p1.1.m1.1.35.1.2">superscript</csymbol>
            <apply id="p1.1.m1.1.35.1.2.2.cmml" xref="p1.1.m1.1.35.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.2.2.1.cmml" xref="p1.1.m1.1.35.1.2">subscript</csymbol>
              <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑓</ci>
              <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑖</ci>
            </apply>
            <apply id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">
              <divide id="p1.1.m1.1.3.1.2.cmml" xref="p1.1.m1.1.3.1.2"/>
              <ci id="p1.1.m1.1.3.1.1.cmml" xref="p1.1.m1.1.3.1.1">𝒜</ci>
              <ci id="p1.1.m1.1.3.1.3.cmml" xref="p1.1.m1.1.3.1.3">𝐸</ci>
            </apply>
          </apply>
          <vector id="p1.1.m1.1.35.1.3.1.cmml" xref="p1.1.m1.1.35.1.3">
            <apply id="p1.1.m1.1.35.1.3.2.cmml" xref="p1.1.m1.1.35.1.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.3.2.1.cmml" xref="p1.1.m1.1.35.1.3.2">subscript</csymbol>
              <apply id="p1.1.m1.1.35.1.3.2.2.1.cmml" xref="p1.1.m1.1.35.1.3.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.35.1.3.2.2.1.1.cmml" xref="p1.1.m1.1.5">delimited-[]</csymbol>
                <apply id="p1.1.m1.1.35.1.3.2.2.2.cmml" xref="p1.1.m1.1.35.1.3.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.3.2.2.2.1.cmml" xref="p1.1.m1.1.35.1.3.2.2.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑎</ci>
                  <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">1</cn>
                </apply>
              </apply>
              <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">𝐸</ci>
            </apply>
            <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"></ci>
            <apply id="p1.1.m1.1.35.1.3.3.cmml" xref="p1.1.m1.1.35.1.3.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.3.3.1.cmml" xref="p1.1.m1.1.35.1.3.3">subscript</csymbol>
              <apply id="p1.1.m1.1.35.1.3.3.2.1.cmml" xref="p1.1.m1.1.35.1.3.3.2">
                <csymbol cd="latexml" id="p1.1.m1.1.35.1.3.3.2.1.1.cmml" xref="p1.1.m1.1.13">delimited-[]</csymbol>
                <apply id="p1.1.m1.1.35.1.3.3.2.2.cmml" xref="p1.1.m1.1.35.1.3.3.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.35.1.3.3.2.2.1.cmml" xref="p1.1.m1.1.35.1.3.3.2.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑎</ci>
                  <apply id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.15.1.3.cmml" xref="p1.1.m1.1.15.1">subscript</csymbol>
                    <ci id="p1.1.m1.1.15.1.1.cmml" xref="p1.1.m1.1.15.1.1">𝑛</ci>
                    <ci id="p1.1.m1.1.15.1.2.1.cmml" xref="p1.1.m1.1.15.1.2.1">𝑖</ci>
                  </apply>
                </apply>
              </apply>
              <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">𝐸</ci>
            </apply>
          </vector>
        </apply>
        <apply id="p1.1.m1.1.35.2.cmml" xref="p1.1.m1.1.35.2">
          <csymbol cd="ambiguous" id="p1.1.m1.1.35.2.1.cmml" xref="p1.1.m1.1.35.2">subscript</csymbol>
          <apply id="p1.1.m1.1.35.2.2.1.cmml" xref="p1.1.m1.1.35.2.2">
            <csymbol cd="latexml" id="p1.1.m1.1.35.2.2.1.1.cmml" xref="p1.1.m1.1.20">delimited-[]</csymbol>
            <apply id="p1.1.m1.1.35.2.2.2.cmml" xref="p1.1.m1.1.35.2.2.2">
              <times id="p1.1.m1.1.35.2.2.2.1.cmml" xref="p1.1.m1.1.35.2.2.2.1"/>
              <apply id="p1.1.m1.1.35.2.2.2.2.cmml" xref="p1.1.m1.1.35.2.2.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.35.2.2.2.2.1.cmml" xref="p1.1.m1.1.35.2.2.2.2">superscript</csymbol>
                <apply id="p1.1.m1.1.35.2.2.2.2.2.cmml" xref="p1.1.m1.1.35.2.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.35.2.2.2.2.2.1.cmml" xref="p1.1.m1.1.35.2.2.2.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝑓</ci>
                  <ci id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">𝑖</ci>
                </apply>
                <ci id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">𝒜</ci>
              </apply>
              <vector id="p1.1.m1.1.35.2.2.2.3.1.cmml" xref="p1.1.m1.1.35.2.2.2.3">
                <apply id="p1.1.m1.1.35.2.2.2.3.2.cmml" xref="p1.1.m1.1.35.2.2.2.3.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.35.2.2.2.3.2.1.cmml" xref="p1.1.m1.1.35.2.2.2.3.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">𝑎</ci>
                  <cn type="integer" id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">1</cn>
                </apply>
                <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28"></ci>
                <apply id="p1.1.m1.1.35.2.2.2.3.3.cmml" xref="p1.1.m1.1.35.2.2.2.3.3">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.35.2.2.2.3.3.1.cmml" xref="p1.1.m1.1.35.2.2.2.3.3">subscript</csymbol>
                  <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">𝑎</ci>
                  <apply id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.31.1.3.cmml" xref="p1.1.m1.1.31.1">subscript</csymbol>
                    <ci id="p1.1.m1.1.31.1.1.cmml" xref="p1.1.m1.1.31.1.1">𝑛</ci>
                    <ci id="p1.1.m1.1.31.1.2.1.cmml" xref="p1.1.m1.1.31.1.2.1">𝑖</ci>
                  </apply>
                </apply>
              </vector>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34.1">𝐸</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle f_{i}^{{{\mathcal{A}}/E}}([a_{1}]_{E},\ldots,[a_{{n_{i}}}]_{E})%
=[f_{i}^{{{\mathcal{A}}}}(a_{1},\ldots,a_{{n_{i}}})]_{E}}</annotation>
  </semantics>
</math>

SVG (13.758 KB / 4.192 KB) :

f Subscript i Superscript script upper A slash upper E Baseline times left-parenthesis left-bracket a 1 right-bracket Subscript upper E Baseline comma ellipsis comma left-bracket a Subscript n Sub Subscript i Subscript Baseline right-bracket Subscript upper E Baseline right-parenthesis equals left-bracket f Subscript i Superscript script upper A Baseline times left-parenthesis a 1 comma ellipsis comma a Subscript n Sub Subscript i Subscript Baseline right-parenthesis right-bracket Subscript upper E

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: (f[i])^(A/ E)*([a[1]][E], .. ,[a[n[i]]][E])[f(f[i])^(A)*(a[1], .. , a[n[i]])][E]

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Maple uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


i: the imaginary unit == the principal square root of -1 was translated to: i


Translation to Mathematica

In Mathematica: (Subscript[f, i])^(A/ E)*(Subscript[[Subscript[a, 1]], E], ... ,Subscript[[Subscript[a, Subscript[n, i]]], E])Subscript[[f(Subscript[f, i])^(A)*(Subscript[a, 1], ... , Subscript[a, Subscript[n, i]])], E]

Information about the conversion process:

I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Mathematica uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


i: the imaginary unit == the principal square root of -1 was translated to: i


Similar pages

Calculated based on the variables occurring on the entire Quotient algebra page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results