Beispiel: Ausdrücke vereinfachen und umschreiben

Symbolische Mathematik > Arbeiten mit symbolischer Mathematik > Ausdrücke vereinfachen und umschreiben > Beispiel: Ausdrücke vereinfachen und umschreiben

Verwenden Sie die Schlüsselwörter combine und rewrite zum Kombinieren und Umschreiben von Ausdrücken.

Schlüsselwort: simplify

• Vereinfachen Sie die folgenden Ausdrücke:

• Fügen Sie den symbolischen Auswertungsoperator ein.

• Fügen Sie das Schlüsselwort simplify in den Platzhalter ein.

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  <math resultRef="24">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>7</real>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">simplify</id>
      </command>
      <symResult>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT">e</id>
          <apply>
            <plus />
            <apply>
              <mult />
              <real>7</real>
              <id xml:space="preserve" labels="*">y</id>
            </apply>
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Schlüsselwort: combine

• Verwenden Sie das Schlüsselwort combine, um den folgenden Ausdruck zu kombinieren:

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  <math resultRef="26">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
          <id xml:space="preserve">x</id>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">combine</id>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cos</id>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">sin</id>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Das Schlüsselwort combine wirkt sich nicht auf das Ergebnis aus.

• Fügen Sie den Modifizierer sincos hinzu, um das Umschreiben des Ergebnisses in Bezug auf Sinus und Kosinus bestimmen.

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  <math resultRef="27">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
            <id xml:space="preserve">x</id>
          </apply>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
          <id xml:space="preserve">x</id>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve">sincos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">sin</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• Verwenden Sie das Schlüsselwort combine mit anderen Modifizierern, um weitere Ausdrücke zu kombinieren.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <id xml:space="preserve">x</id>
        </apply>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <pow />
          <id xml:space="preserve" labels="CONSTANT">e</id>
          <apply>
            <plus />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="*">y</id>
            </apply>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <minus />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
            <real>3</real>
          </apply>
        </apply>
        <apply>
          <mult />
          <real>3</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
            <real>2</real>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">ln</id>
          <apply>
            <div />
            <real>9</real>
            <real>8</real>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <minus />
        <apply>
          <mult />
          <real>2</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
            <sequence>
              <real>3</real>
              <id xml:space="preserve">b</id>
            </sequence>
          </apply>
        </apply>
        <apply>
          <mult />
          <real>3</real>
          <apply>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
            <sequence>
              <real>2</real>
              <id xml:space="preserve">b</id>
            </sequence>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <apply>
              <div />
              <real>9</real>
              <real>8</real>
            </apply>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <id xml:space="preserve" labels="*">b</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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  <math resultRef="31">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
          <id xml:space="preserve">x</id>
        </apply>
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">combine</id>
          <id xml:space="preserve">sinhcosh</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <minus />
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cosh</id>
              <apply>
                <plus />
                <id xml:space="preserve" labels="*">y</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
            </apply>
            <apply>
              <id xml:space="preserve" labels="FUNCTION">cosh</id>
              <apply>
                <minus />
                <id xml:space="preserve" labels="*">y</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
            </apply>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

Schlüsselwort: rewrite

• Verwenden Sie das Schlüsselwort rewrite, um den folgenden Ausdruck mit bestimmten Identitäten umzuschreiben:

PTC Mathcad gibt einen Fehler zurück, da rewrite einen Modifizierer erfordert.

• Fügen Sie den Modifizierer exp hinzu.

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  <math resultRef="33">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <neg />
            <parens>
              <apply>
                <mult />
                <imag symbol="i">1</imag>
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="CONSTANT">e</id>
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="*">x</id>
                        <imag symbol="i">1</imag>
                      </apply>
                    </apply>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="CONSTANT">e</id>
                      <apply>
                        <neg />
                        <parens>
                          <apply>
                            <mult />
                            <id xml:space="preserve" labels="*">x</id>
                            <imag symbol="i">1</imag>
                          </apply>
                        </parens>
                      </apply>
                    </apply>
                  </apply>
                </parens>
              </apply>
            </parens>
          </apply>
          <real>2</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

PTC Mathcad schreibt sin in Bezug auf Exponentialfunktionen um.

• Verwenden Sie das Schlüsselwort rewrite mit anderen Modifizierern, um den gewünschten Ergebnistyp zu erhalten.

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <pow />
        <apply>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sin</id>
          <id xml:space="preserve">x</id>
        </apply>
        <real>2</real>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">cos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <neg />
            <apply>
              <pow />
              <apply>
                <id xml:space="preserve" labels="FUNCTION">cos</id>
                <id xml:space="preserve" labels="*">x</id>
              </apply>
              <real>2</real>
            </apply>
          </apply>
          <real>1</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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  <math resultRef="35">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">asinh</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">ln</id>
          <apply>
            <plus />
            <apply>
              <nthRoot />
              <placeholder />
              <apply>
                <plus />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="*">x</id>
                  <real>2</real>
                </apply>
                <real>1</real>
              </apply>
            </apply>
            <id xml:space="preserve" labels="*">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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  <math resultRef="36">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">ln</id>
        <real>7</real>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">log</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <real>7</real>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">log</id>
            <id xml:space="preserve" labels="CONSTANT">e</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <neg />
          <apply>
            <div />
            <apply>
              <mult />
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
                <apply>
                  <mult />
                  <id xml:space="preserve">x</id>
                  <imag symbol="i">1</imag>
                </apply>
              </apply>
              <imag symbol="i">1</imag>
            </apply>
            <real>2</real>
          </apply>
        </apply>
        <apply>
          <div />
          <apply>
            <mult />
            <apply>
              <pow />
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
              <apply>
                <neg />
                <parens>
                  <apply>
                    <mult />
                    <id xml:space="preserve">x</id>
                    <imag symbol="i">1</imag>
                  </apply>
                </parens>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
          <real>2</real>
        </apply>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve">sincos</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">sin</id>
          <id xml:space="preserve" labels="*">x</id>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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      <apply>
        <pow />
        <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">sinh</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <plus />
            <apply>
              <id xml:space="preserve" labels="FUNCTION">sinh</id>
              <id xml:space="preserve" labels="*">x</id>
            </apply>
            <apply>
              <mult />
              <real>2</real>
              <apply>
                <pow />
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">sinh</id>
                  <apply>
                    <div />
                    <id xml:space="preserve" labels="*">x</id>
                    <real>2</real>
                  </apply>
                </apply>
                <real>2</real>
              </apply>
            </apply>
          </apply>
          <real>1</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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        <id xml:space="preserve">x</id>
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          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">e</id>
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      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <neg />
            <apply>
              <div />
              <real>2</real>
              <apply>
                <plus />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="CONSTANT">e</id>
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="*">x</id>
                  </apply>
                </apply>
                <real>1</real>
              </apply>
            </apply>
          </apply>
          <real>1</real>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">tanh</id>
          <id xml:space="preserve">x</id>
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        <command>
          <sequence>
            <id xml:space="preserve">rewrite</id>
            <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
          </sequence>
        </command>
        <symResult>
          <apply>
            <plus />
            <apply>
              <neg />
              <apply>
                <div />
                <real>2</real>
                <apply>
                  <plus />
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="CONSTANT">e</id>
                    <apply>
                      <mult />
                      <real>2</real>
                      <id xml:space="preserve" labels="*">x</id>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
            <real>1</real>
          </apply>
        </symResult>
      </symEval>
      <command>
        <sequence>
          <id xml:space="preserve">rewrite</id>
          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">tanh</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">tanh</id>
          <id xml:space="preserve" labels="*">x</id>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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          <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">tanh</id>
          <id xml:space="preserve">x</id>
        </apply>
        <command>
          <sequence>
            <sequence>
              <id xml:space="preserve">rewrite</id>
              <id xml:space="preserve" labels="FUNCTION" label-is-contextual="true">exp</id>
            </sequence>
            <id xml:space="preserve">raw</id>
          </sequence>
        </command>
        <symResult>
          <apply>
            <div />
            <apply>
              <minus />
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="*">x</id>
                </apply>
              </apply>
              <real>1</real>
            </apply>
            <apply>
              <plus />
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="*">x</id>
                </apply>
              </apply>
              <real>1</real>
            </apply>
          </apply>
        </symResult>
      </symEval>
      <command>
        <sequence>
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          <id xml:space="preserve">raw</id>
        </sequence>
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            <parens>
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          <apply>
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            <parens>
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                <plus />
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">tanh</id>
                  <id xml:space="preserve" labels="*">x</id>
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                <real>1</real>
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          </apply>
        </apply>
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            <apply>
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                <plus />
                <id xml:space="preserve" labels="*">q</id>
                <real>1</real>
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          <apply>
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