Beispiel: Kombination aus Schlüsselwörtern und Modifizierern

Symbolische Mathematik > Arbeiten mit symbolischer Mathematik > Beispiel: Kombination aus Schlüsselwörtern und Modifizierern

Schlüsselwort assume mit Modifizierern real und complex

1. Schreiben Sie Ausdrücke unter Verwendung von rectangular unter der Annahme, dass x reell und komplex ist und werten Sie diese aus.

<region id="ID0EZHCLB" actualWidth="285.72000000000008" actualHeight="39.2" top="172.8" left="96.000000000000014" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="14">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">exp</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">rectangular</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">real</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <pow />
          <id labels="CONSTANT" xml:space="preserve">e</id>
          <id labels="*" xml:space="preserve">x</id>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0ELICLB" actualWidth="434.27666666666676" actualHeight="39.2" top="230.40000000000003" left="96.000000000000014" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="15">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">exp</id>
        <id xml:space="preserve">x</id>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">rectangular</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">complex</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <id labels="FUNCTION" xml:space="preserve">Re</id>
            <apply>
              <pow />
              <id labels="CONSTANT" xml:space="preserve">e</id>
              <id labels="*" xml:space="preserve">x</id>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <id labels="FUNCTION" xml:space="preserve">Im</id>
              <apply>
                <pow />
                <id labels="CONSTANT" xml:space="preserve">e</id>
                <id labels="*" xml:space="preserve">x</id>
              </apply>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Die Ergebnisse unterscheiden sich basierend auf der Annahme.

x ist standardmäßig reell.

Schlüsselwort simplify für Werte größer als 0

1. Schreiben und vereinfachen Sie den Ausdruck unter der Annahme, dass Werte kleiner als oder gleich 0 und größer als 0 sind.

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  <math resultRef="18">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <minus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">3</imag>
          </apply>
        </apply>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">simplify</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <lessOrEqual />
            <id xml:space="preserve">a</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <minus />
              <id labels="*" xml:space="preserve">a</id>
              <imag symbol="i">3</imag>
            </apply>
          </apply>
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <plus />
              <id labels="*" xml:space="preserve">a</id>
              <imag symbol="i">1</imag>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EFMCLB" actualWidth="388.81133427222568" actualHeight="39.2" top="518.40000000000009" left="57.600000000000009" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="19">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <minus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">3</imag>
          </apply>
        </apply>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <id xml:space="preserve">a</id>
            <imag symbol="i">1</imag>
          </apply>
        </apply>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">simplify</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <greaterThan />
            <id xml:space="preserve">a</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <nthRoot />
          <placeholder />
          <apply>
            <plus />
            <apply>
              <minus />
              <apply>
                <pow />
                <id labels="*" xml:space="preserve">a</id>
                <real>2</real>
              </apply>
              <apply>
                <mult />
                <imag symbol="i">2</imag>
                <id labels="*" xml:space="preserve">a</id>
              </apply>
            </apply>
            <real>3</real>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
    <formattingOverride BackgroundColor="#FFC3D9A5" />
  </math>
</region>

Die Ergebnisse unterscheiden sich basierend auf der Annahme.

Schlüsselwort solve und Modifizierer real

1. Schreiben Sie eine Gleichung, und lösen Sie sie.

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  <math resultRef="20">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>5</real>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>1</real>
      </apply>
      <command>
        <id xml:space="preserve">solve</id>
      </command>
      <symResult>
        <matrix rows="5" cols="1">
          <real>-0.80873060047939201374</real>
          <apply>
            <plus />
            <real>-0.46491220160289785433</real>
            <imag symbol="i">1.0714738402702694092</imag>
          </apply>
          <apply>
            <minus />
            <real>-0.46491220160289785433</real>
            <imag symbol="i">1.0714738402702694092</imag>
          </apply>
          <apply>
            <minus />
            <real>0.8692775018425938612</real>
            <imag symbol="i">0.38826940659974035536</imag>
          </apply>
          <apply>
            <plus />
            <real>0.8692775018425938612</real>
            <imag symbol="i">0.38826940659974035536</imag>
          </apply>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

2. Lösen Sie die Gleichung erneut unter der Annahme, dass x reell ist.

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  <math resultRef="21">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>5</real>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>1</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">real</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <real>-0.80873060047939201374</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Das Ergebnis wird gefiltert und es werden nur reelle Werte der Lösung angezeigt.

Schlüsselwort assume und Modifizierer even und odd

1. Schreiben Sie einen Ausdruck, und lösen Sie ihn unter Verwendung von solve.

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  <math resultRef="22">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <minus />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <id xml:space="preserve">solve</id>
      </command>
      <symResult>
        <matrix rows="5" cols="1">
          <real>2</real>
          <real>1</real>
          <real>-2</real>
          <apply>
            <div />
            <apply>
              <minus />
              <apply>
                <mult />
                <apply>
                  <nthRoot />
                  <placeholder />
                  <real>3</real>
                </apply>
                <imag symbol="i">1</imag>
              </apply>
              <real>1</real>
            </apply>
            <real>2</real>
          </apply>
          <apply>
            <div />
            <apply>
              <minus />
              <apply>
                <neg />
                <parens>
                  <apply>
                    <mult />
                    <apply>
                      <nthRoot />
                      <placeholder />
                      <real>3</real>
                    </apply>
                    <imag symbol="i">1</imag>
                  </apply>
                </parens>
              </apply>
              <real>1</real>
            </apply>
            <real>2</real>
          </apply>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

2. Werten Sie die Gleichung aus unter der Annahme, dass x eine Ganzzahl ist.

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  <math resultRef="23">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <minus />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">integer</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="3" cols="1">
          <real>2</real>
          <real>1</real>
          <real>-2</real>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

3. Werten Sie die Gleichung aus unter der Annahme, dass x gerade ist.

<region id="ID0E3WCLB" actualWidth="335.08" actualHeight="49.49" top="1209.6000000000001" left="76.800000000000011" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="24">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <minus />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">even</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <matrix rows="2" cols="1">
          <real>2</real>
          <real>-2</real>
        </matrix>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

4. Werten Sie die Gleichung aus unter der Annahme, dass x ungerade ist.

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  <math resultRef="25">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <minus />
            <apply>
              <pow />
              <id xml:space="preserve">x</id>
              <real>5</real>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>3</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">x</id>
            <real>2</real>
          </apply>
        </apply>
        <real>4</real>
      </apply>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">solve</id>
            <id xml:space="preserve">assume</id>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">odd</id>
          </apply>
        </sequence>
      </command>
      <symResult>
        <real>1</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

Die Ergebnisse unterscheiden sich basierend auf der Annahme. Das Ergebnis für even und odd ist im Ergebnis für integer kombiniert.

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